The document provides information on measures of central tendency. It discusses five main measures - arithmetic mean, geometric mean, harmonic mean, mode, and median. For arithmetic mean, it provides formulas and examples for calculating the mean from ungrouped and grouped data using both the direct and assumed mean methods. It also discusses the merits and demerits of each measure.
Mean- Mean is an essential concept in mathematics and statistics. The mean is the average or the most common value in a collection of numbers
Types of Mean
A. Arithmetic Mean
a. Simple Arithmetic Mean
b. Weighted Arithmetic Mean
B. Geometric Mean
C. Harmonic Mean
1.Calculation of Simple Arithmetic Mean
a) Direct Method
b) Shortcut Method
c) Step Deviation Method
2. Calculation of Weighted Arithmetic Mean
a) Direct Method
b) Shortcut Method
Merits and Demerits of Different types of Mean.
Measures of central tendency are used to describe the center or typical value of a dataset. The three most common measures are:
1. The mean (average) is calculated by adding all values and dividing by the number of values. It is impacted by outliers.
2. The median is the middle value when data is arranged from lowest to highest. Half the values are above it and half below.
3. The mode is the value that occurs most frequently. Datasets can have multiple modes or no clear mode.
Other measures include weighted mean, quartiles, deciles and percentiles which divide the data into progressively more segments. The choice of measure depends on the characteristics of the data and purpose of
1. The document discusses different types of means or averages, including arithmetic mean, geometric mean, and harmonic mean.
2. It provides definitions and formulas for calculating simple arithmetic mean, combined arithmetic mean, and arithmetic mean of grouped data using both direct and shortcut methods.
3. Examples are given to demonstrate calculating the arithmetic mean from both ungrouped and grouped data using the frequency distribution method and the assumed mean method.
The document discusses various measures of central tendency and methods to calculate the arithmetic mean. It defines central tendency as a single value that describes a typical or average value in a data set. The three most common measures of central tendency are the mean, median, and mode. The document outlines different methods to calculate the arithmetic mean, including the direct method, short method, and step deviation method. It provides examples and step-by-step calculations for each method.
Measure of central tendency provides a very convenient way of describing a set of scores with a single number that describes the PERFORMANCE of the group.
It is also defined as a single value that is used to describe the “center” of the data.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
This document discusses the calculation of arithmetic mean from data in various formats. It defines arithmetic mean as the sum of all values divided by the number of observations. It then provides examples of calculating the arithmetic mean using direct and shortcut methods for individual series, discrete series with frequencies, continuous series with class intervals, and series with open-ended classes. The different methods are demonstrated using example data sets. References on biostatistics are also included.
This document discusses various measures of central tendency including arithmetic mean, geometric mean, and harmonic mean. It provides formulas to calculate each measure and examples worked out step-by-step. For arithmetic mean, the sum of all values is divided by the total number of values. Geometric mean is calculated by taking the nth root of the product of all values. Harmonic mean is calculated as the reciprocal of the arithmetic mean of the reciprocals. In all examples shown, the relationship between the measures holds such that the arithmetic mean is greater than the geometric mean, which is greater than the harmonic mean.
Mean- Mean is an essential concept in mathematics and statistics. The mean is the average or the most common value in a collection of numbers
Types of Mean
A. Arithmetic Mean
a. Simple Arithmetic Mean
b. Weighted Arithmetic Mean
B. Geometric Mean
C. Harmonic Mean
1.Calculation of Simple Arithmetic Mean
a) Direct Method
b) Shortcut Method
c) Step Deviation Method
2. Calculation of Weighted Arithmetic Mean
a) Direct Method
b) Shortcut Method
Merits and Demerits of Different types of Mean.
Measures of central tendency are used to describe the center or typical value of a dataset. The three most common measures are:
1. The mean (average) is calculated by adding all values and dividing by the number of values. It is impacted by outliers.
2. The median is the middle value when data is arranged from lowest to highest. Half the values are above it and half below.
3. The mode is the value that occurs most frequently. Datasets can have multiple modes or no clear mode.
Other measures include weighted mean, quartiles, deciles and percentiles which divide the data into progressively more segments. The choice of measure depends on the characteristics of the data and purpose of
1. The document discusses different types of means or averages, including arithmetic mean, geometric mean, and harmonic mean.
2. It provides definitions and formulas for calculating simple arithmetic mean, combined arithmetic mean, and arithmetic mean of grouped data using both direct and shortcut methods.
3. Examples are given to demonstrate calculating the arithmetic mean from both ungrouped and grouped data using the frequency distribution method and the assumed mean method.
The document discusses various measures of central tendency and methods to calculate the arithmetic mean. It defines central tendency as a single value that describes a typical or average value in a data set. The three most common measures of central tendency are the mean, median, and mode. The document outlines different methods to calculate the arithmetic mean, including the direct method, short method, and step deviation method. It provides examples and step-by-step calculations for each method.
Measure of central tendency provides a very convenient way of describing a set of scores with a single number that describes the PERFORMANCE of the group.
It is also defined as a single value that is used to describe the “center” of the data.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
This document discusses the calculation of arithmetic mean from data in various formats. It defines arithmetic mean as the sum of all values divided by the number of observations. It then provides examples of calculating the arithmetic mean using direct and shortcut methods for individual series, discrete series with frequencies, continuous series with class intervals, and series with open-ended classes. The different methods are demonstrated using example data sets. References on biostatistics are also included.
This document discusses various measures of central tendency including arithmetic mean, geometric mean, and harmonic mean. It provides formulas to calculate each measure and examples worked out step-by-step. For arithmetic mean, the sum of all values is divided by the total number of values. Geometric mean is calculated by taking the nth root of the product of all values. Harmonic mean is calculated as the reciprocal of the arithmetic mean of the reciprocals. In all examples shown, the relationship between the measures holds such that the arithmetic mean is greater than the geometric mean, which is greater than the harmonic mean.
MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN.pptxyogi7397041626
A short description on the arithmetic mean of the measures of central tendency and how to find the arithmetic mean of the ungrouped data , Grouped data and in the step deviation method
This document discusses measures of central tendency and variation for numerical data. It defines and provides formulas for the mean, median, mode, range, variance, standard deviation, and coefficient of variation. Quartiles and interquartile range are introduced as measures of spread less influenced by outliers. The relationship between these measures and the shape of a distribution are also covered at a high level.
The document discusses different measures of central tendency including the mean, median and mode. It provides definitions and formulas for calculating different types of means:
- The arithmetic mean is calculated by summing all values and dividing by the total number of values. It can be calculated using direct or short-cut methods for both individual observations and grouped data.
- Other means include the geometric mean and harmonic mean, which are called special averages.
- The median is the middle value when values are arranged in order. The mode is the value that occurs most frequently.
- Data can be in the form of individual observations, discrete series or continuous series. Formulas are provided for calculating the mean of grouped or ungrouped data
This document discusses measures of central tendency, specifically the arithmetic mean. It provides formulas and examples for calculating the arithmetic mean using direct, short-cut, and step-deviation methods for both ungrouped and grouped data. It also discusses calculating the weighted mean and combined mean of two or more related groups. Key characteristics of the arithmetic mean are that the sum of deviations from the mean is zero and the sum of squared deviations is minimum.
This document provides information about statistics and probability. It defines statistics as the collection, analysis, and interpretation of data. There are two main categories of statistics: descriptive statistics, which summarizes and describes data, and inferential statistics, which is used to estimate, predict, and generalize results. The document also discusses population and sample, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), qualitative vs. quantitative data, ways of representing quantitative data (numerically and graphically), and examples of organizing data using a stem-and-leaf plot.
Measures of dispersion describe how spread out or varied the values in a data set are. There are absolute measures like range and interquartile range, and relative measures like coefficient of variation. Range is the difference between the highest and lowest values, while interquartile range describes the middle 50% of values. Mean deviation, variance, and standard deviation are also measures of dispersion that take into account how far values are from the mean or average. Standard error describes the precision of the sample mean as an estimate of the population mean. These measures help determine how representative the central value or mean is of the overall data set.
This document discusses measures of central tendency, specifically mean, median, and mode. It begins by defining measures of central tendency as averages that represent central or typical values within a data set. The document then outlines different methods for calculating the mean, or arithmetic average, of both raw (ungrouped) and grouped data sets. It provides examples of calculating the mean of raw data sets directly using the formula for mean, and through the assumed mean method which uses deviations from an assumed mean to simplify calculations for large data sets. The document emphasizes that the mean is the sum of all values divided by the number of values. It also discusses how mean is calculated for grouped data by assigning values to class intervals based on their midpoints.
This document provides an introduction to measures of central tendency in statistics. It defines measures of central tendency as statistical measures that describe the center of a data distribution. The three most commonly used measures are the mean, median, and mode. The document focuses on explaining the arithmetic mean in detail, including how to calculate the mean from individual data series, discrete data series, and continuous data series using different methods. It also discusses weighted means, combined means, and the relationship between the mean, median and mode. The objectives and advantages and disadvantages of the mean are provided.
Class 3 Measures central tendency 2024.pptxassaasdf351
The document discusses measures of central tendency, which are statistics that represent the center of a data distribution. It describes three common measures: the arithmetic mean, median, and mode. The arithmetic mean is the most widely used measure of central tendency and is calculated by adding all values and dividing by the total number of values. The document provides examples of calculating the arithmetic mean for raw data, grouped data, and class-interval data.
Unit 1 - Measures of Dispersion - 18MAB303T - PPT - Part 2.pdfAravindS199
The document discusses various measures of dispersion, which describe how data values are spread around the mean. It describes absolute measures like range, interquartile range, mean deviation, and standard deviation. Range is the difference between highest and lowest values. Standard deviation calculates the average distance of all values from the mean. It is the most robust measure as it considers all data points. The document also provides examples of calculating different dispersion measures and their merits and limitations.
1. Measures of central tendency include the mean, median, and mode.
2. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged in order. The mode is the value that appears most frequently.
3. For grouped data, the mean is calculated using the sum of the frequency multiplied by the class midpoint divided by the total frequency. The median class is identified which has a cumulative frequency above and below half the total. The mode is the class with the highest frequency.
The document discusses analysis of economic data and calculation of arithmetic mean. It provides definitions and formulas for calculating the arithmetic mean for different types of data series, including individual series, discrete series, and continuous series. The key points are:
1) Economic data is usually analyzed using statistical methods to extract meaningful information from numerical data. The arithmetic mean is commonly used as a measure of central tendency.
2) The arithmetic mean is calculated by dividing the sum of all values by the total number of values. It provides a single representative value for a data set.
3) Arithmetic mean can be calculated for different types of data series using direct or shortcut methods, with appropriate modifications to the basic formula for calculating the mean.
Lesson 23 planning data analyses using statisticsmjlobetos
This document discusses strategies for analyzing collected data, including descriptive and inferential statistics. Descriptive statistics like measures of central tendency (mean, median, mode) and dispersion (range, standard deviation) are used to summarize and describe data. Inferential statistics like t-tests, ANOVA, and tests of correlation can analyze relationships, differences between groups, and make generalizations from samples to populations. The document provides formulas and examples of how to calculate and interpret various statistical measures.
CAVENDISH COLLEGE LESSON NOTE FOR FIRST TERM ECONOMICS SSS2 UPDATED..docxDORISAHMADU
The document provides information about measures of central tendency and dispersion from economics lessons at Cavendish College. It defines terms like mean, median, mode, range, variance, and standard deviation. For measures of central tendency, it gives the formulas to calculate each measure and provides an example using exam marks. For measures of dispersion, it similarly defines terms like range, mean deviation, variance, and standard deviation and gives the relevant formulas. It also includes an example using student weights to demonstrate calculating these measures.
Analysis and interpretation of Assessment.pptxAeonneFlux
The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.
Dispersion- It is a statistical term that describes the size of the distribution of values expected for a particular variable and can be measured by several different statistics, such as Range, Variance and standard deviation.
Method of Dispersion-A measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of their distribution.
Methods of Dispersion.
1.Relative Dispersion
a. Coefficient of Mean Deviation
b. Coefficient of Quartile Deviation
c. Coefficient of Range
d. Coefficient of Variation
2. Absolute Dispersion
a. Range
b. Quartile range
c. Standard deviation
d. Mean Deviation
Range- It is the difference between smallest & largest values in the dataset. Also the relative measure of range is known as Coefficient of Range.
Advantages and disadvantages of Range.
Calculation of Range by different Methods.
b. Quartile Range- The interquartile range of a group of observations is the interval between the values of upper quartile and the lower quartile for that group.
Advantages and Disadvantages of Quartile Range.
Calculation of Quartile Range by different Methods.
c. Standard Deviation- It measures the absolute dispersion (or) variability of a distribution. A small standard deviation means a high degree of uniformity of the observations as well as homogeneity in the series.
Advantages and Disadvantages of Quartile Range.
Calculation of Standard Deviation using.
i) Direct Method
ii) Short-cut Method
iii) Step Deviation Method.
This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.
Chronic illnesses last over 6 months and include conditions like cancer, heart disease, and arthritis. They are caused by genetics, lifestyle, and environment. People with chronic illnesses have significant needs related to employment, finances, health, housing, and self-esteem. Meeting these needs can be challenging, especially if the illness limits one physically or psychologically or impacts their ability to work. Access to resources may also be affected by one's socioeconomic status, age, or disabilities.
MEASURES OF CENTRAL TENDENCY ARITHMETIC MEAN.pptxyogi7397041626
A short description on the arithmetic mean of the measures of central tendency and how to find the arithmetic mean of the ungrouped data , Grouped data and in the step deviation method
This document discusses measures of central tendency and variation for numerical data. It defines and provides formulas for the mean, median, mode, range, variance, standard deviation, and coefficient of variation. Quartiles and interquartile range are introduced as measures of spread less influenced by outliers. The relationship between these measures and the shape of a distribution are also covered at a high level.
The document discusses different measures of central tendency including the mean, median and mode. It provides definitions and formulas for calculating different types of means:
- The arithmetic mean is calculated by summing all values and dividing by the total number of values. It can be calculated using direct or short-cut methods for both individual observations and grouped data.
- Other means include the geometric mean and harmonic mean, which are called special averages.
- The median is the middle value when values are arranged in order. The mode is the value that occurs most frequently.
- Data can be in the form of individual observations, discrete series or continuous series. Formulas are provided for calculating the mean of grouped or ungrouped data
This document discusses measures of central tendency, specifically the arithmetic mean. It provides formulas and examples for calculating the arithmetic mean using direct, short-cut, and step-deviation methods for both ungrouped and grouped data. It also discusses calculating the weighted mean and combined mean of two or more related groups. Key characteristics of the arithmetic mean are that the sum of deviations from the mean is zero and the sum of squared deviations is minimum.
This document provides information about statistics and probability. It defines statistics as the collection, analysis, and interpretation of data. There are two main categories of statistics: descriptive statistics, which summarizes and describes data, and inferential statistics, which is used to estimate, predict, and generalize results. The document also discusses population and sample, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), qualitative vs. quantitative data, ways of representing quantitative data (numerically and graphically), and examples of organizing data using a stem-and-leaf plot.
Measures of dispersion describe how spread out or varied the values in a data set are. There are absolute measures like range and interquartile range, and relative measures like coefficient of variation. Range is the difference between the highest and lowest values, while interquartile range describes the middle 50% of values. Mean deviation, variance, and standard deviation are also measures of dispersion that take into account how far values are from the mean or average. Standard error describes the precision of the sample mean as an estimate of the population mean. These measures help determine how representative the central value or mean is of the overall data set.
This document discusses measures of central tendency, specifically mean, median, and mode. It begins by defining measures of central tendency as averages that represent central or typical values within a data set. The document then outlines different methods for calculating the mean, or arithmetic average, of both raw (ungrouped) and grouped data sets. It provides examples of calculating the mean of raw data sets directly using the formula for mean, and through the assumed mean method which uses deviations from an assumed mean to simplify calculations for large data sets. The document emphasizes that the mean is the sum of all values divided by the number of values. It also discusses how mean is calculated for grouped data by assigning values to class intervals based on their midpoints.
This document provides an introduction to measures of central tendency in statistics. It defines measures of central tendency as statistical measures that describe the center of a data distribution. The three most commonly used measures are the mean, median, and mode. The document focuses on explaining the arithmetic mean in detail, including how to calculate the mean from individual data series, discrete data series, and continuous data series using different methods. It also discusses weighted means, combined means, and the relationship between the mean, median and mode. The objectives and advantages and disadvantages of the mean are provided.
Class 3 Measures central tendency 2024.pptxassaasdf351
The document discusses measures of central tendency, which are statistics that represent the center of a data distribution. It describes three common measures: the arithmetic mean, median, and mode. The arithmetic mean is the most widely used measure of central tendency and is calculated by adding all values and dividing by the total number of values. The document provides examples of calculating the arithmetic mean for raw data, grouped data, and class-interval data.
Unit 1 - Measures of Dispersion - 18MAB303T - PPT - Part 2.pdfAravindS199
The document discusses various measures of dispersion, which describe how data values are spread around the mean. It describes absolute measures like range, interquartile range, mean deviation, and standard deviation. Range is the difference between highest and lowest values. Standard deviation calculates the average distance of all values from the mean. It is the most robust measure as it considers all data points. The document also provides examples of calculating different dispersion measures and their merits and limitations.
1. Measures of central tendency include the mean, median, and mode.
2. The mean is the average value found by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged in order. The mode is the value that appears most frequently.
3. For grouped data, the mean is calculated using the sum of the frequency multiplied by the class midpoint divided by the total frequency. The median class is identified which has a cumulative frequency above and below half the total. The mode is the class with the highest frequency.
The document discusses analysis of economic data and calculation of arithmetic mean. It provides definitions and formulas for calculating the arithmetic mean for different types of data series, including individual series, discrete series, and continuous series. The key points are:
1) Economic data is usually analyzed using statistical methods to extract meaningful information from numerical data. The arithmetic mean is commonly used as a measure of central tendency.
2) The arithmetic mean is calculated by dividing the sum of all values by the total number of values. It provides a single representative value for a data set.
3) Arithmetic mean can be calculated for different types of data series using direct or shortcut methods, with appropriate modifications to the basic formula for calculating the mean.
Lesson 23 planning data analyses using statisticsmjlobetos
This document discusses strategies for analyzing collected data, including descriptive and inferential statistics. Descriptive statistics like measures of central tendency (mean, median, mode) and dispersion (range, standard deviation) are used to summarize and describe data. Inferential statistics like t-tests, ANOVA, and tests of correlation can analyze relationships, differences between groups, and make generalizations from samples to populations. The document provides formulas and examples of how to calculate and interpret various statistical measures.
CAVENDISH COLLEGE LESSON NOTE FOR FIRST TERM ECONOMICS SSS2 UPDATED..docxDORISAHMADU
The document provides information about measures of central tendency and dispersion from economics lessons at Cavendish College. It defines terms like mean, median, mode, range, variance, and standard deviation. For measures of central tendency, it gives the formulas to calculate each measure and provides an example using exam marks. For measures of dispersion, it similarly defines terms like range, mean deviation, variance, and standard deviation and gives the relevant formulas. It also includes an example using student weights to demonstrate calculating these measures.
Analysis and interpretation of Assessment.pptxAeonneFlux
The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.
Dispersion- It is a statistical term that describes the size of the distribution of values expected for a particular variable and can be measured by several different statistics, such as Range, Variance and standard deviation.
Method of Dispersion-A measure of dispersion indicates the scattering of data. It explains the disparity of data from one another, delivering a precise view of their distribution.
Methods of Dispersion.
1.Relative Dispersion
a. Coefficient of Mean Deviation
b. Coefficient of Quartile Deviation
c. Coefficient of Range
d. Coefficient of Variation
2. Absolute Dispersion
a. Range
b. Quartile range
c. Standard deviation
d. Mean Deviation
Range- It is the difference between smallest & largest values in the dataset. Also the relative measure of range is known as Coefficient of Range.
Advantages and disadvantages of Range.
Calculation of Range by different Methods.
b. Quartile Range- The interquartile range of a group of observations is the interval between the values of upper quartile and the lower quartile for that group.
Advantages and Disadvantages of Quartile Range.
Calculation of Quartile Range by different Methods.
c. Standard Deviation- It measures the absolute dispersion (or) variability of a distribution. A small standard deviation means a high degree of uniformity of the observations as well as homogeneity in the series.
Advantages and Disadvantages of Quartile Range.
Calculation of Standard Deviation using.
i) Direct Method
ii) Short-cut Method
iii) Step Deviation Method.
This document discusses analyzing and interpreting test data using measures of central tendency, variability, position, and co-variability. It defines these statistical measures and how to calculate and apply them. Key points covered include calculating the mean, median, and mode of a data set; measures of variability like standard deviation; and how these measures can be used to analyze test scores and interpret results to improve teaching. Formulas and examples are provided to demonstrate calculating and applying these statistical concepts to educational test data.
Chronic illnesses last over 6 months and include conditions like cancer, heart disease, and arthritis. They are caused by genetics, lifestyle, and environment. People with chronic illnesses have significant needs related to employment, finances, health, housing, and self-esteem. Meeting these needs can be challenging, especially if the illness limits one physically or psychologically or impacts their ability to work. Access to resources may also be affected by one's socioeconomic status, age, or disabilities.
Health surveillance systems monitor communicable diseases, injuries, birth defects and other health conditions to help public health agencies set priorities and plan programs. Surveillance can take many forms, from mandatory disease reporting to monitoring of health behaviors. In Bangladesh, the Institute of Epidemiology, Disease Control and Research conducts various surveillance activities including monitoring priority communicable diseases, outbreak investigations, and influenza and Nipah virus surveillance.
Peritonitis is an inflammation of the peritoneum caused by bacterial or fungal infection. Left untreated, it can lead to sepsis, multiple organ failure and death. There are three main types: primary occurs spontaneously with liver failure; secondary follows a perforation of abdominal organs; tertiary occurs in immuno-compromised people like with AIDS and tuberculosis. Symptoms include severe abdominal pain, fever, nausea and vomiting. Diagnosis involves medical history, exams, blood tests and imaging scans. Treatment requires intravenous fluids, antibiotics, pain relief, and may require surgery to repair damaged organs and drain infections. With proper treatment outcomes are good, but risks include sepsis, adhesions and organ failure if not addressed promptly.
This document provides information about gastritis, including its definition, types, causes, symptoms, diagnosis, and treatment. It begins by defining gastritis as an inflammation of the stomach lining. It then describes the two main types as acute or chronic gastritis, and subtypes based on appearance and cause. Common causes include H. pylori infection, NSAID use, alcohol, and stress. Symptoms vary from pain and nausea to bleeding and anemia. Diagnosis involves history, endoscopy, and tests for H. pylori. Treatment focuses on relieving pain, antibiotics for H. pylori, proton pump inhibitors, bland diets, and managing complications.
This document discusses dysphagia, or difficulty swallowing. It begins by defining dysphagia and describing the normal physiology of swallowing in three stages. It then discusses the various types, causes, signs and symptoms, diagnostic tests, complications and management approaches for dysphagia. Management may include dietary changes, swallowing exercises and techniques, botulinum toxin injections, dilation procedures, or surgeries like myotomy. Nurses play an important role in educating patients and monitoring for signs of aspiration during meals.
1. Bowel obstruction occurs when the bowel becomes blocked, preventing food and liquids from passing through the intestines. This can affect either the small or large intestine.
2. There are different types of bowel obstruction including small or large intestine obstruction, partial or complete obstruction, and mechanical or functional obstruction.
3. Symptoms of bowel obstruction include abdominal pain, bloating, vomiting, constipation, and loss of appetite. Diagnosis involves imaging tests and physical examination to locate the blockage.
4. Treatment depends on the severity and includes managing symptoms, surgery to remove or bypass the blockage, and nursing care during recovery. Complications can include infection, sepsis, and short bowel syndrome.
This document provides information about appendicitis including:
1) The appendix is a small finger-shaped pouch located where the small and large intestines meet that is prone to obstruction and infection.
2) Appendicitis is an inflammation of the appendix that most commonly affects adolescents and young adults. It can be acute, chronic, simple, or complex depending on symptoms and complications.
3) Risk factors include age, sex, family history, infection, and obstruction. Symptoms are evaluated and diagnostic tests like blood tests, imaging, and urine tests are used to confirm appendicitis.
The document discusses Virginia Henderson's nursing needs theory and Abraham Maslow's hierarchy of needs theory.
1. Henderson developed a nursing needs theory that identifies 14 basic human needs that nurses help patients meet, such as breathing normally, eating and drinking adequately, eliminating body wastes, dressing and undressing appropriately, and expressing emotions.
2. Maslow's hierarchy of needs theory proposes that people are motivated to fulfill basic physiological needs before moving on to more advanced needs like safety, love, esteem and self-actualization.
3. Henderson's 14 needs are aligned with Maslow's hierarchy, with needs like breathing, food/water, sleep, and eliminating wastes mapping to Maslow's basic physiological needs
The document discusses comprehensive nursing and pathophysiology. It begins by introducing the author and defining comprehensive nursing as an approach that encompasses the total care of patients, including their physical, mental, social and spiritual needs. It then discusses the importance of comprehensive nursing in developing nurse competence and empowering them to provide holistic care.
The document provides anticipatory guidance for families with toddlers to promote health and safety. It discusses recommendations in 3 key areas:
1) Promoting healthy and safe habits such as frequent handwashing, cleaning toys, limiting TV time, and maintaining regular sleep schedules.
2) Injury prevention including using forward-facing car seats, maintaining a safe home environment, and proper supervision around water, smoke, and hazards.
3) Nutrition with recommendations to provide 3 meals and 2-3 snacks per day and make mealtimes family-oriented.
The guidance aims to educate caregivers on child development and injury risks to help prevent problems and ensure toddler well-being.
This document provides guidance on making effective presentations using engaging backgrounds to capture audience attention. It recommends focusing presentations on key points to efficiently convey essential information while holding audience interest through visually appealing backgrounds and engaging delivery.
TEST BANK For Community Health Nursing A Canadian Perspective, 5th Edition by...Donc Test
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Osteoporosis - Definition , Evaluation and Management .pdfJim Jacob Roy
Osteoporosis is an increasing cause of morbidity among the elderly.
In this document , a brief outline of osteoporosis is given , including the risk factors of osteoporosis fractures , the indications for testing bone mineral density and the management of osteoporosis
share - Lions, tigers, AI and health misinformation, oh my!.pptxTina Purnat
• Pitfalls and pivots needed to use AI effectively in public health
• Evidence-based strategies to address health misinformation effectively
• Building trust with communities online and offline
• Equipping health professionals to address questions, concerns and health misinformation
• Assessing risk and mitigating harm from adverse health narratives in communities, health workforce and health system
Integrating Ayurveda into Parkinson’s Management: A Holistic ApproachAyurveda ForAll
Explore the benefits of combining Ayurveda with conventional Parkinson's treatments. Learn how a holistic approach can manage symptoms, enhance well-being, and balance body energies. Discover the steps to safely integrate Ayurvedic practices into your Parkinson’s care plan, including expert guidance on diet, herbal remedies, and lifestyle modifications.
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Dive into an in-depth exploration of the histological structure of female reproductive system with this comprehensive lecture. Presented by Dr. Ayesha Irfan, Assistant Professor of Anatomy, this presentation covers the Gross anatomy and functional histology of the female reproductive organs. Ideal for students, educators, and anyone interested in medical science, this lecture provides clear explanations, detailed diagrams, and valuable insights into female reproductive system. Enhance your knowledge and understanding of this essential aspect of human biology.
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- Video recording of this lecture in English language: https://youtu.be/kqbnxVAZs-0
- Video recording of this lecture in Arabic language: https://youtu.be/SINlygW1Mpc
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3. INTRODUCTION
Summarization of Data set in a single value is necessary. Such a value usually
somewhere in the center and represent the entire data set and hence it is called
measure of central tendency or averages.
Since a measure of central tendency (i.e. an average) indicates the location or
the general position of the distribution on the X-axis therefore it is also
known as a measure of location or position.
There are several statistical measures of central tendency or “averages”. They
are 1. Arithmetic Mean, 2. Geometric Mean, 3. Harmonic Mean,
4. Mode, 5. Median
3
5. ARITHMETIC MEAN
• Arithmetic mean is the most commonly used
measure of central tendency. “A value obtained by
dividing the sum of all the observations by the
number of observation is called arithmetic Mean”
and is usually denoted by
In general, if there are N observations as X1 + X2 +
X3 + X4+.........+ XN
5
6. ARITHMETIC MEAN
• In general, if there are N observations as X1 + X2 +
X3 + X4+.........+ XN then the Arithmetic Mean is
given by
Thus where X = sum of all observations
And n = total number of observations.
The calculation of arithmetic mean can be studied
under two broad categories:
1. Arithmetic Mean for Ungrouped Data.
2. Arithmetic Mean for Grouped Data. 6
7. ARITHMETIC MEAN
Arithmetic Mean for Ungrouped Data
Calculate Arithmetic Mean from discrete data
:(Direct Method)
• Example 1: Calculate Arithmetic Mean from the data
showing marks of students in a class in an economics test:
40, 50, 55,78, 58.
The average mark of students in the economics test is 56.2.
7
8. ARITHMETIC MEAN
• Example 2: The haemoglobin levels of the 10
women are given here, i.e. 12.5,
13,10,11,5,11,14, 9,7.5, 10, 12
• Example 3: The marks scored by the 10
students are given here, i.e. 75,58,
62,84,63,76,75,69,60,64 calculate the mean
8
9. Assumed Mean Method to Calculate Arithmetic Mean from
discrete data (Short cut Method) :
• In order to save time in calculating mean from a data set containing a large
number of observations as well as large numerical figures, you can use assumed
mean method.
Let, A = assumed mean , X = individual observations, N = total numbers of
observations d = deviation of assumed mean from individual observation, i.e. d
= X – A Then sum of all deviations is taken as Σd= Σ (X-A)
ARITHMETIC MEAN
9
10. ARITHMETIC MEAN
Exercise : The following data shows the weekly income of 10
families.
Family A B C D E F G H I J
Weekly income in taka 850 700 100 750 5000 80 420 2500 400 360
10
11. X d = X – A ( A = 700)
80 - 620
100 - 600
360 - 340
400 - 300
420 - 280
700 0
750 50
850 150
2500 1800
5000 4300
Total 4160
= 700 + 4160/10
= 700 + 416
= 1116
11
12. ARITHMETIC MEAN
Arithmetic Mean for Grouped Data
Calculate Arithmetic Mean from discrete data
with frequency :(Direct Method)
In discrete frequency table the mean is calculated
using the following formula
Where x = corresponding value variable, f = frequency
12
13. ARITHMETIC MEAN
Arithmetic Mean for Grouped Data
Calculate Arithmetic Mean from discrete data with
frequency :(Direct Method)
For an example the following data gives the age of 100
adolescent girls . Find the mean age
Age in
years (x)
No. of
students (f)
16 30
17 25
18 14
19 12
20 19 13
14. Age in
years
(x)
No. of
students
(f )
fx
16 30 480
17 25 425
18 14 252
19 12 228
20 19 380
Total Σf =
100
Σfx =
1765
= 1765
100
= 17.65
The mean age of 100
students is 17.65
14
15. ARITHMETIC MEAN
Sum No : 1 Calculate the mean protein level of 100 patients
Protein
level (x)
No of
patients(f)
7.5 7
12.5 13
15 20
17.5 10
20 35
22.5 15
15
16. ARITHMETIC MEAN
Arithmetic Mean for Grouped Data
Calculate Arithmetic Mean from Class interval with frequency :(Direct
Method)
Example, Find Mean from the table
Marks
Scored
0 - 5 5 - 15 15 - 30 30 - 40 40 - 60
No. of
Students
6 9 11 14 10
16
17. Marks
scored (x)
No. of
students
(f )
Mid x fx
0 - 5 6 2.5 15
5 - 15 9 10 90
15 - 30 11 22.5 247.5
30 - 40 14 35 490
40 - 60 10 50 500
Total Σf = 50 Σfx =
1342.5
= 1342.5
50
= 26.9
The average
marks scored
by the students
is 26.9
17
18. ARITHMETIC MEAN
Sum No : 1 Calculate the Mean from the following data
Class
interval (x)
Frequency(f)
0 - 10 3
10 - 20 14
20 - 30 6
30 - 40 7
40 - 50 5
50 - 60 10
18
19. Assumed Mean Method to Calculate Arithmetic Mean from
class interval with Frequency (Short cut Method) :
• In order to save time in calculating mean from a data set containing a large
number of observations as well as large numerical figures, you can use assumed
mean method.
Let, A = assumed mean , X = individual observations, Σf = total numbers of
observations d = deviation of assumed mean from individual observation, i.e. d
= X – A Then sum of all deviations is taken as Σfd= Σ (X-A)
ARITHMETIC MEAN
19
20. ARITHMETIC MEAN
Arithmetic Mean for Grouped Data
Calculate Arithmetic Mean from Class interval with frequency :(short cut
Method)
Example, Find Mean from the table
Marks
Scored
0 - 5 5 - 15 15 - 30 30 - 40 40 - 60
No. of
Students
6 9 11 14 10
20
21. Marks
scored
(x)
No. of
studen
ts (f )
Mid
x
d = (X – A)
A = 22.5
fd
0 - 5 6 2.5 -20 -120
5 - 15 9 10 - 12.5 -112.5
15 - 30 11 22.5 0 0
30 - 40 14 35 12.5 175
40 - 60 10 50 27.5 275
Total Σf = 50 Σfd =
217.5
217.5
= 22.5 + 50
= 22.5 + 4.35
The average
marks scored
by the
students is
26.9
21
22. ARITHMETIC MEAN
Arithmetic Mean for Grouped Data
Calculate Arithmetic Mean from Class interval with frequency :(step
deviation method)
Formula using to calculate step deviation method is
A = Assumed mean , h = class width
Example, Find Mean for the following frequency distribution
Age in years 50 - 55 45- 50 40 - 45 35 - 40 30 - 35 25 - 30
No . Of
Labors
28 29 31 47 51 70
22
23. Age of
the years
(x)
No. of
labors
(f )
Mid
x
d = (X– A)
h
A = 42.5
h = 5
fd
50 - 55 28 52.5 2 56
45 - 50 29 47.5 1 29
40 - 45 31 42.5 0 0
35 - 40 47 37.5 -1 - 47
30 - 35 51 32.5 -2 - 102
25 - 30 70 27.5 -3 - 210
Total Σf =
256
Σfd =
- 274
= 42.5 + 5 X -274
256
= 42.5 + 5 X (-1.07)
= 42.5 + (- 5.35)
= 37.15
The average of the
labor is 37.15
23
24. ARITHMETIC MEAN
Merits of Mean :
1) Arithmetic mean rigidly defined by Algebraic
Formula therefore the result will be same.
2) It is easy to calculate and simple to
understand.
3) It is based on all observations of the given
data.
4) It is capable of being treated mathematically
hence it is widely used in statistical analysis.
6) It is least affected by the fluctuation of
sampling.
7) For every kind of data mean can be
calculated.
Demerits of Arithmetic mean :
1) Arithmetic mean can not be computed for
qualitative data like data on intelligence honesty and
smoking habit etc.
2) It is too much affected by extreme observations
and hence it is not adequately represent data
consisting of some extreme point.
3) Arithmetic mean can not be computed when class
intervals have open ends.
4) If any one of the data is missing then mean can not
be calculated.
5) It cannot be located graphically.
24
25. GEOMETRIC MEAN
• The Geometric Mean (GM) is the average of a set of products, It is
technically defined as the nth root of the product of observation.
• In the arithmetic mean, data values are added and then divided by the
total number of values. But in geometric mean, the given data values are
multiplied, and then you take the root with the radical index for the final
product of data values.
• For example, if you have two data values, take the square root, or if you
have three data values, then take the cube root, or else if you have four
data values, then take the 4th root, and so on.
• GM = (X1 x X2 x X3 x X4 x.........x Xn )1/n
25
26. GEOMETRIC MEAN
Geometric Mean for Ungrouped Data
Calculate Geometric Mean from discrete data :
Example 1: Calculate Geometric Mean from the data
10, 5, 25,100,7,50
x Log x
10 1.0000
5 0.6989
25 1.3979
100 2.0000
7 0.8450
50 1.6989
Total 7.6407
GM = Antilog (7.6407/ 6)
= Antilog 1.2734
GM = 18.767
26
27. GEOMETRIC MEAN
Geometric Mean for Ungrouped Data
Calculate Geometric Mean from discrete data :
• Example 2: Calculate Geometric Mean from the data showing marks
of students in a class in an economics test: 40, 50, 55,78, 58.
27
28. GEOMETRIC MEAN
Geometric Mean for grouped Data
Calculate Geometric Mean from discrete data with
frequency :
Example 1: Calculate Geometric Mean from the data
x f
7 3
10 2
13 6
15 7
6 9
5 5
28
29. GEOMETRIC MEAN
x f Log x f log x
7 3 0.8450 2.5350
10 2 1.0000 2.0000
13 6 1.1139 6.6834
15 7 1.1760 8.232
6 9 0.7781 7.0029
5 5 0.6989 3.4945
Total Σf = 32 Σf log x =
29.9478
GM = Antilog (29.9478/ 32)
= Antilog (0.9358)
GM = 8.6258
29
30. GEOMETRIC MEAN
Calculate Geometric Mean from discrete data with
frequency :
Example 2: Calculate Geometric Mean from the data
Age in
years (x)
No. of
students (f)
16 30
17 25
18 14
19 12
20 19 30
31. GEOMETRIC MEAN
Geometric Mean for grouped Data
Calculate Geometric Mean from class interval with
frequency :
Example 1: Calculate Geometric Mean from the data
CI f
0 - 4 3
4 - 8 13
8 - 12 7
12 - 16 27
16 - 20 10
31
32. GEOMETRIC MEAN
CI Mid x f Log x f log x
0 - 4 2 3 0.3010 0.9030
4 - 8 6 13 0.7781 10.1153
8 - 12 10 7 1.0000 7.0000
12 - 16 14 27 1.1461 30.9447
16 - 20 18 10 1.2552 12.552
Total Σf = 60 Σf log x =
61.515
GM = Antilog (61.515/
60)
= Antilog (1.02525)
GM = 10.5986
32
33. GEOMETRIC MEAN
Calculate Geometric Mean from class interval with
frequency :
Example 2: Calculate Geometric Mean from the data
Marks
Scored
0 - 5 5 - 15 15 - 30 30 - 40 40 - 60
No. of
Students
6 9 11 14 10
33
34. GEOMETRIC MEAN
Merits of Geometric Mean :
Geometric Mean is calculated based on all observations
in the series.
Geometric Mean is clearly defined.
Geometric Mean is not affected by extreme values in
the series.
Geometric Mean is amenable to further algebraic
treatment.
Geometric Mean is useful in averaging ratios and
percentages.
Logarithm of GM for a set of observation, is the
Arithmetic mean of the logarithm of the observation.
Demerits of Geometric mean :
Geometric Mean is difficult to
understand.
We cannot compute geometric
mean if there are both positive
and negative values occur in the
series.
We cannot compute geometric
mean if one or more of the values
in the series is zero.
34
35. HARMONIC MEAN
• Harmonic Mean (HM) is defined as the reciprocal of Arithmetic mean of
the reciprocal of the observation. The harmonic mean is often used to
calculate the average of the ratios or rates of the given values. It is the most
appropriate measure for ratios and rates because it equalizes the weights of
each data point.
Note the following:
• Arithmetic mean is used when the data values have the same units.
• The geometric mean is used when the data set values have differing units.
• When the values are expressed in rates we use harmonic mean.
35
36. HARMONIC MEAN
Harmonic Mean for Ungrouped Data
Calculate Harmonic Mean from discrete data :
Example 1: Calculate Harmonic Mean from the data 2,5, 9,7,6
HM = 5
1 + 1 + 1 + 1 + 1
2 5 9 7 6
HM = 5
0.5 + 0.2+0.111 + 0.142 + 0.166
HM = 5 = 4.46
1.119 36
37. HARMONIC MEAN
Harmonic Mean for grouped Data
Calculate Harmonic Mean from discrete data with
frequency :
Example 1: Calculate Harmonic Mean from the data
x f
7 3
10 2
13 6
15 7
6 9
5 5
HM = 32
3 + 2 + 6 + 7 + 9 + 5
7 10 13 15 6 5
HM = 32
0.4285 + 0.2+0.4615 + 0.4666 + 1.5 + 1
HM = 32 = 7.88
4.0566 37
38. HARMONIC MEAN
Harmonic Mean for grouped Data
Calculate Harmonic Mean from class interval with frequency :
Example 1: Calculate Harmonic Mean from the data
CI f
0 - 4 3
4 - 8 13
8 - 12 7
12 - 16 27
16 - 20 10
HM = 60
3 + 13 + 7 + 27 + 10
2 6 10 14 18
HM = 60
1.5 + 2.166 +0.7 + 1.9285 + 0.5555
HM = 60
6.8506
HM = 8.75
38
39. HARMONIC MEAN
Merits of Harmonic Mean :
It will always be the lowest as compared to the
geometric and arithmetic mean. HM will have the lowest
value, geometric mean will have the middle value and
arithmetic mean will have the highest value.
The products of the harmonic mean (HM) and the
arithmetic mean (AM) will always be equal to the square
of the geometric mean (GM) of the given data set so
GM2 = HM × AM. Thus, HM = GM2 / AM
Demerits of Harmonic mean :
It cannot be used on a data set
consisting of negative or zero
rates.
The method to calculate the
harmonic mean can be lengthy and
complicated.
The extreme values in a series
greatly affect the harmonic mean.
39
40. COMBINED MEAN
A combined mean is a mean of two or more separate groups.The formula
for calculating combined mean is
40
41. Example: 1, Calculate the combined
mean for M.sc first year and
second year students There are 13
M.Sc 2nd year and 12 M.sc 1st
year students and their mean are
17 and 24 respectively.
= 13 x 17 + 12 x 24
13 + 12
= 221 + 288
25
= 509
25
CM = 20.36
41
42. Example: 2, Calculate the combined mean for
two classes
.
CM = 5 x 22 + 7 x 4.85
5 + 7
= 110 + 33.95
12
= 143.95
12
CM = 11.99
Class
A
13 26 15 25 30
Class
B
7 6 4 4 3 9 1
.
= 13 + 26+ 15+ 25+ 30 = 22
5
= 7+6+4+4+3+9+1
7
= 34
7
= 4.85
42
43. MEDIAN
Median, in statistics, is the middle value of the given list
of data when arranged in an order.
To Calculate the Median: Arrange the n measurements in
ascending (or descending) order.
We denote the median of the data by M.
1. If n is odd, M is the middle number.
2. If n is even, M is the average of the two middle numbers.
• The calculation of median can be studied under two
broad categories:
• 1. Median for Ungrouped Data.
• 2. Median for Grouped Data.
43
44. MEDIAN
• 1. Median for Ungrouped Data.
• In this case, the data is arranged in either ascending or
descending order of magnitude.
I. If the number of observations n is an odd number, then the
median is represented by the numerical value of x, corresponds
to the positioning point of n+1 / 2 in ordered observations. That
is,
II. If the number of observations n is an even number, then the
median is defined as the arithmetic mean of the middle values
in the array That is,
44
45. 1. Median for Ungrouped Data.
Example : 1
The number of rooms in the seven girls hotel in Dhaka city is 71,
30, 61, 59, 31, 40 and 29. Find the median number of rooms
Solution:
Arrange the data in ascending order 29, 30, 31, 40, 59, 61, 71
n = 7 (odd)
Median = 7+1 / 2 = 4th positional value
Median = 40 rooms
MEDIAN
45
46. 1. Median for Ungrouped Data.
Example : 2
The export of agricultural product in million dollars from a
country during eight quarters in 1974 and 1975 was recorded as
29.7, 16.6, 2.3, 14.1, 36.6, 18.7, 3.5, 21.3
Find the median of the given set of values
Solution:
We arrange the data in descending order
36.6, 29.7, 21.3, 18.7, 16.6, 14.1, 3.5, 2.3
MEDIAN
46
48. 1. Median for grouped Data with frequency.
In case of Discrete grouped data, first we find the
cumulative frequency and then use the following
formula for median.
MEDIAN
48
49. 1. Median for grouped Data with frequency.
Example : 3 Calculate the median for the following frequency
with values
MEDIAN
x 10 20 30 40 50 60 70
f 3 6 5 9 7 10 20
X f Lcf
10 3 3
20 6 9
30 5 14
40 9 23
50 7 30
60 10 40
70 20 60
N = 60
M = 60 + 1 th term
2
= 30.5 th term
M = 60
49
50. 1. Median for grouped Data with frequency.
Example : 5 Calculate the median for the following frequency with values
MEDIAN
x 10 20 30 40 50 60 70 80
f 3 6 5 9 7 10 20 24
X f Lcf
10 3 3
20 6 9
30 5 14
40 9 23
50 7 30
60 10 40
70 20 60
80 24 84
N = 84
M = 84 + 1 th
2 term
= (85/2)th term
= (42.5) th term
M = 70 50
51. 1. Median for grouped Data with frequency.
Example : 4 Calculate the median for the following frequency
with values
MEDIAN
x f
7 3
10 2
13 6
15 7
6 9
5 5
51
52. MEDIAN
1. Median for grouped Data class interval
with frequency.
The formula for computing median is
Where
l = Lower class interval of
the median class
N = sum of frequency
m = cumulative frequency
of the class preceding
the median class
c = width of the median
class
52
53. 1. Median for grouped Data with frequency.
Example : 6 Calculate the median for the following frequency
with values
MEDIAN
x f
0 - 10 3
10 - 20 5
20 - 30 4
30 - 40 8
40 - 50 2
Where
N/2 = 22/2 = 11
l = 20
m = 8
c = 10
M = 20 + (11 – 8)/4 x 10
M = 20 + (3/4) x 10
M = 20 + 30/4
M = 20+ 7.5 = 27.5
x f Lcf
0 - 10 3 3
10 - 20 5 8
20 - 30 4 12
30 - 40 8 20
40 - 50 2 22
N = 22
53
54. 1. Median for grouped Data with frequency.
Example : 7 Calculate the median for the following frequency
with values
MEDIAN
x f
0 - 100 5
100 - 200 17
200 - 250 33
250 - 300 40
300 - 400 5
54
55. MEDIAN
Merits of Median :
Median can be calculated in all distributions.
Median can be understood even by common
people.
Median can be ascertained even with the extreme
items.
It can be located graphically
It is most useful dealing with qualitative data
Demerits of Median:
It is not based on all the values.
It is not capable of further
mathematical treatment.
It is affected fluctuation of
sampling.
In case of even no. of values it
may not the value from the
data.
55
56. MODE
Mode is the most frequent value or score in the distribution. Or A
mode is defined as the value that has a higher frequency in a given
set of values. It is the value that appears the most number of times.
It is denoted by the capital letter Z.
• When there are two modes in a data set, then the set is
called bimodal
• For example, The mode of Set A = {2,2,2,3,4,4,5,5,5} is 2 and 5,
because both 2 and 5 is repeated three times in the given set.
• When there are three modes in a data set, then the set is
called trimodal
• For example, the mode of set A = {2,2,2,3,4,4,5,5,5,7,8,8,8} is 2, 5
and 8
• When there are four or more modes in a data set, then the set is
called multimodal
56
57. 1. Mode for Ungrouped Data.
Example: {19, 8, 29, 35, 19, 28, 15}
• Arrange them in order: {8, 15, 19, 19, 28, 29,
35}
19 appears twice, all the rest appear only once,
so 19 is the mode.
MODE
57
58. 2. Mode for grouped Data ( Discreate value with Frequency).
Example : 1 Example : 2
MODE
x f
2 3
7 8
10 3
19 9
25 2
32 5
Mode = 19
x f
5 4
10 8
15 5
20 8
25 4
30 2
Mode = 10 and 20 58
59. 3.Mode for grouped Data ( class interval with Frequency).
Formula to calculate mode for grouped data is
MODE
• Where,
• l = lower limit of the modal class
• h = size of the class interval
• f1 = frequency of the modal class
• f0 = frequency of the class preceding the modal class
• f2 = frequency of the class succeeding the modal class
59
60. 3.Mode for grouped Data ( class interval with Frequency).
Example : 1
MODE
x f
20 -25 7
25 - 30 3
30 - 35 11
35 - 40 5
40 - 45 2
45 - 50 9
l = 30
f1 = 11
f2 = 5
f0 = 3, h = 5
Mode = 30 + (11 – 3) x 5
(2 x 11 – 3 – 5)
Mode = 30 + 8 x 5 = 30 + 40
22 -8 14
Mode = 30 + 2.857 = 32.857 60
61. 3.Mode for grouped Data ( class interval with Frequency).
Example : 2
MODE
x f
20 - 39 6
40 - 59 4
60 - 79 3
80 - 99 7
100 - 119 10
120 - 139 5
l = 99.5
f1 = 10
f2 = 5
f0 = 7, h = 20
Mode = 99.5 + (10 – 7) x 20
(2 x 10 – 7 – 5)
Mode = 99.5 + 3 x 20 = 99.5 + 60
20 -12 8
Mode = 99.5 + 7.5 = 107
x f
19.5 – 39.5 6
39.5 – 59.5 4
59.5 – 79.5 3
79.5 – 99.5 7
99.5 – 119.5 10
119.5 – 139.5 5
61
62. MODE
Merits of Mode :
Mode is readily comprehensible and easily
calculated
It is the best representative of data
It is not at all affected by extreme value.
The value of mode can also be determined
graphically.
It is usually an actual value of an important
part of the series.
Demerits of Mode :
It is not based on all
observations.
It is not capable of further
mathematical manipulation.
Mode is affected to a great
extent by sampling fluctuations.
Choice of grouping has great
influence on the value of mode.
62
63. FORMULA TO CALCULATE CENTRAL TENDENCY
Methods Ungrouped Data Grouped Data ( Discrete
data with Frequency)
Grouped Data (class
interval with frequency)
Short cut method
Arithmetic
Mean
Geometric
Mean
Harmonic
Mean
Median
Mode
63