A measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.
Measures of Central Tendency Final.pptAdamManlunas
Here is the summary of the data set:
Mean = 30
Median = 27
Mode = No mode (each value occurs only once)
The outlier is 118. Removing the outlier, the mean would decrease to 28 and the median would remain 27. The median best describes the data set as it is not greatly affected by outliers and most of the data is clustered around 27.
A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution. The are some limitations to using the mode. In some distributions, the mode may not reflect the centre of the distribution very well. When the distribution of retirement age is ordered from lowest to highest value, it is easy to see that the centre of the distribution is 57 years, but the mode is lower, at 54 years.
This document contains a lesson on calculating and interpreting measures of central tendency (mean, median, mode) and spread (range) from data sets. It includes definitions of these statistical terms, examples of calculating them for various data sets, and discussions of how outliers impact the mean, median and mode. The key lesson is on identifying which measure of central tendency (mean, median or mode) best describes a particular data set and why.
This document contains a lesson on calculating and interpreting measures of central tendency (mean, median, mode) and range from data sets. It includes definitions of these terms, examples of finding the mean, median, mode and range of various data sets, and discussions of how outliers impact the measures of central tendency. The lesson emphasizes that different measures may be best suited for different data distribution shapes and the presence of outliers.
This document contains a lesson on mean, median, mode, and range. It includes definitions of these statistical terms, examples of calculating them for different data sets, and discussions of how outliers can affect the values. The lesson emphasizes that the mean, median, and mode should be selected based on which measure best describes the distribution of the actual data.
This document contains a lesson plan on measures of central tendency of ungrouped data for 7th grade mathematics. The lesson plan defines mean, median, and mode, and provides examples of calculating each. It includes an activity that challenges students to solve problems involving finding the mean, median, and mode of various data sets. The activity is meant to assess students' understanding of applying these measures of central tendency to real-world scenarios. The lesson concludes by having students practice defining and calculating measures of central tendency, and applying them to sample data sets and a real-life example.
This document provides a lesson on measures of central tendency and dispersion. It defines mean, median, mode, range, quartiles, interquartile range, and outliers. Examples are provided to demonstrate how to calculate and interpret these measures for data sets. The document also explains how to construct box-and-whisker plots and choose the best measure of central tendency depending on the presence of outliers. Students are then quizzed on applying these concepts to analyze sample data sets.
This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.
Measures of Central Tendency Final.pptAdamManlunas
Here is the summary of the data set:
Mean = 30
Median = 27
Mode = No mode (each value occurs only once)
The outlier is 118. Removing the outlier, the mean would decrease to 28 and the median would remain 27. The median best describes the data set as it is not greatly affected by outliers and most of the data is clustered around 27.
A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution. The are some limitations to using the mode. In some distributions, the mode may not reflect the centre of the distribution very well. When the distribution of retirement age is ordered from lowest to highest value, it is easy to see that the centre of the distribution is 57 years, but the mode is lower, at 54 years.
This document contains a lesson on calculating and interpreting measures of central tendency (mean, median, mode) and spread (range) from data sets. It includes definitions of these statistical terms, examples of calculating them for various data sets, and discussions of how outliers impact the mean, median and mode. The key lesson is on identifying which measure of central tendency (mean, median or mode) best describes a particular data set and why.
This document contains a lesson on calculating and interpreting measures of central tendency (mean, median, mode) and range from data sets. It includes definitions of these terms, examples of finding the mean, median, mode and range of various data sets, and discussions of how outliers impact the measures of central tendency. The lesson emphasizes that different measures may be best suited for different data distribution shapes and the presence of outliers.
This document contains a lesson on mean, median, mode, and range. It includes definitions of these statistical terms, examples of calculating them for different data sets, and discussions of how outliers can affect the values. The lesson emphasizes that the mean, median, and mode should be selected based on which measure best describes the distribution of the actual data.
This document contains a lesson plan on measures of central tendency of ungrouped data for 7th grade mathematics. The lesson plan defines mean, median, and mode, and provides examples of calculating each. It includes an activity that challenges students to solve problems involving finding the mean, median, and mode of various data sets. The activity is meant to assess students' understanding of applying these measures of central tendency to real-world scenarios. The lesson concludes by having students practice defining and calculating measures of central tendency, and applying them to sample data sets and a real-life example.
This document provides a lesson on measures of central tendency and dispersion. It defines mean, median, mode, range, quartiles, interquartile range, and outliers. Examples are provided to demonstrate how to calculate and interpret these measures for data sets. The document also explains how to construct box-and-whisker plots and choose the best measure of central tendency depending on the presence of outliers. Students are then quizzed on applying these concepts to analyze sample data sets.
This document provides an introduction to statistics. It discusses what statistics is, the two main branches of statistics (descriptive and inferential), and the different types of data. It then describes several key measures used in statistics, including measures of central tendency (mean, median, mode) and measures of dispersion (range, mean deviation, standard deviation). The mean is the average value, the median is the middle value, and the mode is the most frequent value. The range is the difference between highest and lowest values, the mean deviation is the average distance from the mean, and the standard deviation measures how spread out values are from the mean. Examples are provided to demonstrate how to calculate each measure.
This document discusses various statistical measures used to summarize and describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It provides definitions and examples of calculating each measure. Standardized scores like z-scores and t-scores are also introduced as ways to compare performance across different tests or distributions. Exercises are included for readers to practice calculating and interpreting these common descriptive statistics.
The document defines and provides examples of various statistical measures used to summarize data, including measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation, coefficient of variation), and shape of data distribution. It explains how to calculate and interpret these measures and when each is most appropriate to use. Examples are provided to demonstrate calculating various measures for different datasets.
This document discusses measures of central tendency including the mean, median, and mode. It provides formulas to calculate each and examples showing how to find the mean, median, and mode of data sets. It also discusses what measure is most appropriate depending on the type of data, noting that the mode should be used for nominal data, the median for ordinal data, and the mean can be used for numeric data that is sufficiently symmetric according to the Hildebrand Rule.
Lecture 3 & 4 Measure of Central Tendency.pdfkelashraisal
This document provides an overview of measures of central tendency including average, mean, median, mode, and midrange. It defines each measure and provides examples of calculating them for both individual values and grouped data. The mean is the sum of all values divided by the total number of values. The median is the middle value of data in ascending order. The mode is the most frequent value. The midrange is the average of the minimum and maximum values. Formulas are given for calculating each measure for both individual data and grouped frequency distributions.
UNIT III - Arrays - Measures of Center and Variation (2).pptAjithGhoyal
This document provides information on measures of central tendency and dispersion in data sets. It defines and provides examples of calculating the mean, median, mode, and midrange as common measures of central tendency. It also discusses weighted averages and trimmed means. The document then covers measures of dispersion such as range, variance and standard deviation. It provides formulas and examples of calculating these measures to quantify the spread of data around the central tendency.
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and examples of how to calculate each measure. It also discusses how transformations of data and outliers can affect measures of central tendency, with the mean being most impacted by outliers and the mode least impacted. The median and mode are considered more resistant measures of central tendency than the mean.
This document discusses different measures of central tendency including mode, median, and mean. It provides examples and explanations of how to calculate each measure for a set of data. For mode, it explains that the mode is the most frequent value. For median, it describes that the median is the middle value when values are arranged in order. And for mean, it defines the mean as the sum of all values divided by the number of values.
The document discusses different types of averages including mode, mean, and median. It provides definitions and examples of how to calculate each. The mode is the most common value, the mean is the average found by adding all values and dividing by the total count, and the median is the middle value when data is arranged in order. The document shows how to identify the mode, mean, and median in various data sets and discusses when each measure is most appropriate.
2Power point Lesson 10-3 (measures of central tendency and box and whisker pl...ArinezDante
This document discusses measures of central tendency (mean, median, mode) and range used to describe data distributions. It provides examples of calculating these values for different data sets, including finding the mean, median, mode, and range. The steps shown are writing the data in numerical order, calculating the mean by adding all values and dividing by the number of values, determining the median value for odd and even data sets, identifying any modes where values occur most often, and calculating the range as the difference between highest and lowest values.
Mean, Median, Mode and Range Central Tendency.pptxYanieSilao
This document provides definitions and examples for calculating measures of central tendency (mean, median, mode) and dispersion (range) from numeric data. It defines each concept - mean as the average, median as the middle value, mode as the most frequent value, and range as the difference between highest and lowest values. Formulas for calculating each are presented. Worked examples demonstrate calculating the mean, median, mode, and range for sample data sets. The purpose is to help students understand and apply these statistical concepts to analyze and interpret data in daily life.
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.
For this project, students in Mrs. Beile's learning center math class were tasked with creating a Powerpoint presentation that explained how to solve a math problem. The students were expected to select a math concept they were struggling with themselves and pretend they were explaining the concept to a friend. By going through the process, the students were able to develop mastery and reinforce the concept for themselves. Everyone did a fantastic job!
This document provides an overview of basic statistics concepts including descriptive statistics, measures of central tendency, variability, sampling, and distributions. It defines key terms like mean, median, mode, range, standard deviation, variance, and quantiles. Examples are provided to demonstrate how to calculate and interpret these common statistical measures.
This document provides demonstrations of calculating the mean, median, mode, and range for various data sets. It explains how to find each average value and compares the strengths and weaknesses of each. The mean averages all values, the median ignores outliers, and the mode represents non-numerical or categorical data. Examples are worked through step-by-step and the key is to order the data before analyzing it using these different averaging methods.
This document provides demonstrations of calculating the mean, median, mode, and range for various data sets. It explains how to find each average value and compares the strengths and weaknesses of each. The mean averages all values, the median ignores outliers, and the mode represents non-numerical or categorical data. Examples are worked through step-by-step and the key is to order the data before analyzing it using these different averaging methods.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
Central tendency refers to measures that describe the center or typical value of a dataset. The three main measures of central tendency are the mean, median, and mode.
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 data is arranged in order. For even datasets, the median is the average of the two middle values. The mode is the value that occurs most frequently in the dataset.
Central tendency refers to a single value that describes the center of a dataset and is one of the most fundamental concepts in statistics. The three main measures of central tendency are the mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the total number of values. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value. Central tendency provides a summary of a dataset without conveying information about individual values.
This document discusses various statistical measures used to summarize and describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It provides definitions and examples of calculating each measure. Standardized scores like z-scores and t-scores are also introduced as ways to compare performance across different tests or distributions. Exercises are included for readers to practice calculating and interpreting these common descriptive statistics.
The document defines and provides examples of various statistical measures used to summarize data, including measures of central tendency (mean, median, mode), measures of variation (variance, standard deviation, coefficient of variation), and shape of data distribution. It explains how to calculate and interpret these measures and when each is most appropriate to use. Examples are provided to demonstrate calculating various measures for different datasets.
This document discusses measures of central tendency including the mean, median, and mode. It provides formulas to calculate each and examples showing how to find the mean, median, and mode of data sets. It also discusses what measure is most appropriate depending on the type of data, noting that the mode should be used for nominal data, the median for ordinal data, and the mean can be used for numeric data that is sufficiently symmetric according to the Hildebrand Rule.
Lecture 3 & 4 Measure of Central Tendency.pdfkelashraisal
This document provides an overview of measures of central tendency including average, mean, median, mode, and midrange. It defines each measure and provides examples of calculating them for both individual values and grouped data. The mean is the sum of all values divided by the total number of values. The median is the middle value of data in ascending order. The mode is the most frequent value. The midrange is the average of the minimum and maximum values. Formulas are given for calculating each measure for both individual data and grouped frequency distributions.
UNIT III - Arrays - Measures of Center and Variation (2).pptAjithGhoyal
This document provides information on measures of central tendency and dispersion in data sets. It defines and provides examples of calculating the mean, median, mode, and midrange as common measures of central tendency. It also discusses weighted averages and trimmed means. The document then covers measures of dispersion such as range, variance and standard deviation. It provides formulas and examples of calculating these measures to quantify the spread of data around the central tendency.
The document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and examples of how to calculate each measure. It also discusses how transformations of data and outliers can affect measures of central tendency, with the mean being most impacted by outliers and the mode least impacted. The median and mode are considered more resistant measures of central tendency than the mean.
This document discusses different measures of central tendency including mode, median, and mean. It provides examples and explanations of how to calculate each measure for a set of data. For mode, it explains that the mode is the most frequent value. For median, it describes that the median is the middle value when values are arranged in order. And for mean, it defines the mean as the sum of all values divided by the number of values.
The document discusses different types of averages including mode, mean, and median. It provides definitions and examples of how to calculate each. The mode is the most common value, the mean is the average found by adding all values and dividing by the total count, and the median is the middle value when data is arranged in order. The document shows how to identify the mode, mean, and median in various data sets and discusses when each measure is most appropriate.
2Power point Lesson 10-3 (measures of central tendency and box and whisker pl...ArinezDante
This document discusses measures of central tendency (mean, median, mode) and range used to describe data distributions. It provides examples of calculating these values for different data sets, including finding the mean, median, mode, and range. The steps shown are writing the data in numerical order, calculating the mean by adding all values and dividing by the number of values, determining the median value for odd and even data sets, identifying any modes where values occur most often, and calculating the range as the difference between highest and lowest values.
Mean, Median, Mode and Range Central Tendency.pptxYanieSilao
This document provides definitions and examples for calculating measures of central tendency (mean, median, mode) and dispersion (range) from numeric data. It defines each concept - mean as the average, median as the middle value, mode as the most frequent value, and range as the difference between highest and lowest values. Formulas for calculating each are presented. Worked examples demonstrate calculating the mean, median, mode, and range for sample data sets. The purpose is to help students understand and apply these statistical concepts to analyze and interpret data in daily life.
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.
For this project, students in Mrs. Beile's learning center math class were tasked with creating a Powerpoint presentation that explained how to solve a math problem. The students were expected to select a math concept they were struggling with themselves and pretend they were explaining the concept to a friend. By going through the process, the students were able to develop mastery and reinforce the concept for themselves. Everyone did a fantastic job!
This document provides an overview of basic statistics concepts including descriptive statistics, measures of central tendency, variability, sampling, and distributions. It defines key terms like mean, median, mode, range, standard deviation, variance, and quantiles. Examples are provided to demonstrate how to calculate and interpret these common statistical measures.
This document provides demonstrations of calculating the mean, median, mode, and range for various data sets. It explains how to find each average value and compares the strengths and weaknesses of each. The mean averages all values, the median ignores outliers, and the mode represents non-numerical or categorical data. Examples are worked through step-by-step and the key is to order the data before analyzing it using these different averaging methods.
This document provides demonstrations of calculating the mean, median, mode, and range for various data sets. It explains how to find each average value and compares the strengths and weaknesses of each. The mean averages all values, the median ignores outliers, and the mode represents non-numerical or categorical data. Examples are worked through step-by-step and the key is to order the data before analyzing it using these different averaging methods.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
Central tendency refers to measures that describe the center or typical value of a dataset. The three main measures of central tendency are the mean, median, and mode.
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 data is arranged in order. For even datasets, the median is the average of the two middle values. The mode is the value that occurs most frequently in the dataset.
Central tendency refers to a single value that describes the center of a dataset and is one of the most fundamental concepts in statistics. The three main measures of central tendency are the mean, median, and mode. The mean is the average value calculated by summing all values and dividing by the total number of values. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value. Central tendency provides a summary of a dataset without conveying information about individual values.
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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
8. The mean is the sum of the data
values divided by the number of
data items.
The median is the middle value of
an odd number of data items arranged in order.
For an even number of data items, the median is
the average of the two middle values.
The mode is the value or values that occur most
often. When all the data values occur the same
number of times, there is no mode.
The range of a set of data is the difference
between the greatest and least values. It is used
to show the spread of the data in a data set.
Mean, Median, Mode, and Range
The mean is
sometimes called
the average.
Helpful Hint
9. Symmetric data is observed when the values of
variables appear at regular frequencies or intervals
around the mean.
Example:
45, 43, 42, 40, 41, 46, 47, 48, 45, 43, 43
Data are appeared at regular or close interval.
Asymmetric data, on the other hand, may have
skewness or noise such that the data appears at
irregular or haphazard intervals.
Mean, Median, Mode, and Range
Example:
45, 43, 80, 40, 41, 46, 47, 15, 45, 43, 43
Data are appeared at irregular interval. Take note
numbers 15 and 80.
10. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1: Finding the Mean, Median,
Mode, and Range of Data
Mean, Median, Mode, and Range
mean:
Add the values.
4 + 7 + 8 + 2 + 1 + 2 + 4 + 2 =
Divide the sum by the number of
items.
Mean = Sum of the terms / Number
of terms
30
30 3.75
8 items
The mean is 3.75.
sum
8
=
11. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
median:
Arrange the values in order.
1, 2, 2, 2, 4, 4, 7, 8
There are two middle values, so
find the mean of these two values.
The median is 3.
2 + 4 = 6
6 2 = 3
12. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
mode:
The value 2 occurs three times.
1, 2, 2, 2, 4, 4, 7, 8
The mode is 2.
13. Find the mean, median, mode, and range of the data set.
4, 7, 8, 2, 1, 2, 4, 2
Additional Example 1 Continued
Mean, Median, Mode, and Range
range:
Subtract the least value
1, 2, 2, 2, 4, 4, 7, 8
The range is 7.
from the greatest value.
– 1 =
8 7
14. Find the mean, median, mode, and range of the data set.
6, 4, 3, 5, 2, 5, 1, 8
Check It Out: Example 1
Mean, Median, Mode, and Range
mean:
Add the values.
6 + 4 + 3 + 5 + 2 + 5 + 1 + 8 =
Divide the sum
34
34 4.25
8 items
The mean is 4.25.
sum
by the number of items.
8
=
15. Find the mean, median, mode, and range of the data set.
6, 4, 3, 5, 2, 5, 1, 8
Check It Out: Example 1 Continued
Mean, Median, Mode, and Range
median:
Arrange the values in order.
1, 2, 3, 4, 5, 5, 6, 8
There are two middle values, so find
the mean of these two values.
The median is 4.5.
4 + 5 = 9
9 2 = 4.5
16. Find the mean, median, mode, and range of the data set.
6, 4, 3, 5, 2, 5, 1, 8
Check It Out: Example 1 Continued
7-2 Mean, Median, Mode, and Range
mode:
The value 5 occurs two times.
1, 2, 3, 4, 5, 5, 6, 8
The mode is 5.
17. Find the mean, median, mode, and range of the data set.
6, 4, 3, 5, 2, 5, 1, 8
Check It Out: Example 1 Continued
Mean, Median, Mode, and Range
range:
Subtract the least value
1, 2, 3, 4, 5, 5, 6, 8
The range is 7.
from the greatest value.
– 1 =
8 7
18. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Additional Example 2: Choosing the Best Measure to
Describe a Set of Data
Mean, Median, Mode, and Range
4 6 8 10 12 14 16
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
19. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Additional Example 3 Continued
Mean, Median, Mode, and Range
mean:
4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 14 + 15 + 15 + 15 + 15 + 16 + 16
17
= 153
17
The mean is 9. The mean best describes the data
set because the data is clustered fairly evenly
about two areas.
= 9
20. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Additional Example 3 Continued
Mean, Median, Mode, and Range
median:
The median is 6. The median does not best
describe the data set because many values are
not clustered around the data value 6.
4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 14, 15, 15, 15, 15,
16, 16
21. The line plot shows the number of miles each
of the 17 members of the cross-country team
ran in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Additional Example 3 Continued
Mean, Median, Mode, and Range
mode:
The greatest number of X’s occur above the
number 4 on the line plot.
The mode is 4.
The mode focuses on one data value and does
not describe the data set.
22. The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
Check It Out: Example 4
Mean, Median, Mode, and Range
10 20 30 40 50 60 70
X
X
X
X
X
X X
X
X X
23. Check It Out: Example 4 Continued
Mean, Median, Mode, and Range
mean:
15 + 15 + 15 + 15 + 20 + 20 + 40 + 60 + 60 + 70
10
= 330
10
The mean is 33. Most of the cheerleaders raised
less than $33, so the mean does not describe the
data set best.
= 33
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
24. Check It Out: Example 4 Continued
Mean, Median, Mode, and Range
median:
The median is 20. The median best describes the
data set because it is closest to the amount most
cheerleaders raised.
15, 15, 15, 15, 20, 20, 40, 60, 60, 70
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
25. Check It Out: Example 4 Continued
Mean, Median, Mode, and Range
mode:
The greatest number of X’s occur above the
number 15 on the line plot.
The mode is 15.
The mode focuses on one data value and does
not describe the data set.
The line plot shows the number of dollars each
of the 10 members of the cheerleading team
raised in a week. Which measure of central
tendency best describes this data? Justify
your answer.
26. Mean, Median, Mode, and Range
Measure Most Useful When
mean
median
mode
The data are spread fairly evenly
The data set has an outlier
The data involve a subject in which
many data points of one value are
important, such as election results.
27. In the data set below, the value 12 is much less than
the other values in the set. An extreme value such as
this is called an outlier.
Mean, Median, Mode, and Range
35, 38, 27, 12, 30, 41, 31, 35
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
x x
x x xx x
x
28. The data shows Sara’s scores for the last 5
math tests: 88, 90, 55, 94, and 89. Identify
the outlier in the data set. Then determine
how the outlier affects the mean, median, and
mode of the data. Then tell which measure of
central tendency best describes the data with
the outlier.
Additional Example 5: Exploring the Effects of
Outliers on Measures of Central Tendency
Mean, Median, Mode, and Range
outlier 55
55, 88, 89, 90, 94
29. Additional Example 5 Continued
Mean, Median, Mode, and Range
outlier 55
55, 88, 89, 90, 94
With the Outlier
55+88+89+90+94 = 416
416 5 = 83.2
The mean is 83.2.
55, 88, 89, 90, 94
The median is 89. There is no mode.
mean: median: mode:
30. Additional Example 5 Continued
Mean, Median, Mode, and Range
55, 88, 89, 90, 94
Without the Outlier
88+89+90+94 = 361
361 4 = 90.25
The mean is 90.25.
88, 89, 90, 94
The median is 89.5. There is no mode.
mean: median: mode:
+
2
= 89.5
31. Mean, Median, Mode, and Range
Since all the data values occur the same
number of times, the set has no mode.
Caution!
32. Course 2
Mean, Median, Mode, and Range
Adding the outlier decreased the mean by 7.05
and the median by 0.5.
Without the Outlier With the Outlier
mean
median
mode
90.25 83.2
89.5 89
no mode no mode
The mode did not change.
Additional Example 5 Continued
The median best describes the data with the
outlier.
33. Identify the outlier in the data set. Then
determine how the outlier affects the mean,
median, and mode of the data. The tell
which measure of central tendency best
describes the data with the outlier.
63, 58, 57, 61, 42
Check It Out: Example 6
Mean, Median, Mode, and Range
outlier 42
42, 57, 58, 61, 63
34. Check It Out: Example 6 Continued
Course 2
Mean, Median, Mode, and Range
outlier 42
42, 57, 58, 61, 63
With the Outlier
42+57+58+61+63 = 281
281 5 = 56.2
The mean is 56.2.
42, 57, 58, 61, 63
The median is 58. There is no mode.
mean: median: mode:
35. Check It Out: Example 6 Continued
Course 2
Mean, Median, Mode, and Range
42, 57, 58, 61, 63
Without the Outlier
57+58+61+63 = 239
239 4 = 59.75
The mean is 59.75.
57, 58, 61, 63
The median is 59.5. There is no mode.
mean: median: mode:
+
2
= 59.5
36. Course 2
Mean, Median, Mode, and Range
Adding the outlier decreased the mean by 3.55
and decreased the median by 1.5.
Without the Outlier With the Outlier
mean
median
mode
59.75 56.2
59.5 58
no mode no mode
The mode did not change.
Check It Out: Example 6 Continued
The median best describes the data with the
outlier.
38. Lesson Quiz: Part I
1. Find the mean, median, mode, and range of
the data set. 8, 10, 46, 37, 20, 8, and 11
mean: 20; median: 11; mode: 8; range: 38
Mean, Median, Mode, and Range
39. Lesson Quiz: Part II
2. Identify the outlier in the data set, and determine how the
outlier affects the mean, median, and mode of the data.
Then tell which measure of central tendency best describes
the data with and without the outlier. Justify your answer.
85, 91, 83, 78, 79, 64, 81, 97
The outlier is 64. Without the outlier the mean is 85, the
median is 83, and there is no mode. With the outlier the
mean is 82, the median is 82, and there is no mode.
Including the outlier decreases the mean by 3 and the
median by 1, there is no mode.
Mean, Median, Mode, and Range