This document discusses key concepts in statistics including descriptive statistics, inferential statistics, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and measures of relative position (percentiles, quartiles, deciles). It provides examples of calculating these statistical measures from sample data sets. The document also covers methods of data collection and presentation including raw vs grouped data and textual, tabular, and graphical presentation formats.
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.
1. The document defines statistics as the scientific method of collecting, organizing, presenting, analyzing and interpreting numerical information to assist in decision making.
2. It discusses descriptive and inferential statistics, levels of measurement, data types, and provides examples of measures of central tendency and dispersion.
3. The document also covers topics such as hypothesis testing, sampling techniques, methods of data collection, and government and international sources of statistics.
Measures of central tendency and dispersionAbhinav yadav
This document discusses various measures of central tendency and dispersion. It defines the mean, median, and mode as measures of central tendency, and describes how to calculate the arithmetic mean, geometric mean, harmonic mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation, and classifies them as either measures of absolute dispersion or relative dispersion.
This document provides an overview of key concepts in statistics and probability. It discusses descriptive statistics, which includes techniques for summarizing and describing numerical data through tables, graphs and charts. It also covers inferential statistics, which allows generalization from samples to populations through hypothesis testing and determining relationships. Key terms are defined, such as data, population, sample, and variable. Common statistical measures like the mean, median and mode are also introduced.
This document provides definitions and explanations of key statistical concepts including:
1. Statistics is defined as the science of collecting, classifying, presenting, and interpreting data. Central tendency measures like mean, median, and mode are used to summarize data.
2. Measures of dispersion like range, interquartile range, mean deviation, and standard deviation describe how spread out the data is from the central tendency. Standard deviation is the most accurate measure as it considers both the deviation from the mean and the mathematical signs.
3. Examples are provided to demonstrate calculating the mean, median, mode, and standard deviation for both ungrouped and grouped data series. The standard deviation provides the best estimation of the population mean when
Descriptions of data statistics for researchHarve Abella
This document defines and describes various measures of central tendency and variation that are used to summarize and describe sets of data. It discusses the mean, median, mode, midrange, percentiles, quartiles, range, variance, standard deviation, interquartile range, coefficient of variation, measures of skewness and kurtosis. Examples are provided to demonstrate how to compute and interpret these statistical measures.
This document provides an overview of descriptive statistics and statistical concepts. It discusses topics such as data collection, organization, analysis, interpretation and presentation. It also covers frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and hypothesis testing. Hypothesis testing involves forming a null hypothesis and alternative hypothesis, and using statistical tests to either reject or fail to reject the null hypothesis based on sample data. Common statistical tests include ones for comparing means, variances or proportions.
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.
1. The document defines statistics as the scientific method of collecting, organizing, presenting, analyzing and interpreting numerical information to assist in decision making.
2. It discusses descriptive and inferential statistics, levels of measurement, data types, and provides examples of measures of central tendency and dispersion.
3. The document also covers topics such as hypothesis testing, sampling techniques, methods of data collection, and government and international sources of statistics.
Measures of central tendency and dispersionAbhinav yadav
This document discusses various measures of central tendency and dispersion. It defines the mean, median, and mode as measures of central tendency, and describes how to calculate the arithmetic mean, geometric mean, harmonic mean, median, and mode. It also discusses measures of dispersion such as variance and standard deviation, and classifies them as either measures of absolute dispersion or relative dispersion.
This document provides an overview of key concepts in statistics and probability. It discusses descriptive statistics, which includes techniques for summarizing and describing numerical data through tables, graphs and charts. It also covers inferential statistics, which allows generalization from samples to populations through hypothesis testing and determining relationships. Key terms are defined, such as data, population, sample, and variable. Common statistical measures like the mean, median and mode are also introduced.
This document provides definitions and explanations of key statistical concepts including:
1. Statistics is defined as the science of collecting, classifying, presenting, and interpreting data. Central tendency measures like mean, median, and mode are used to summarize data.
2. Measures of dispersion like range, interquartile range, mean deviation, and standard deviation describe how spread out the data is from the central tendency. Standard deviation is the most accurate measure as it considers both the deviation from the mean and the mathematical signs.
3. Examples are provided to demonstrate calculating the mean, median, mode, and standard deviation for both ungrouped and grouped data series. The standard deviation provides the best estimation of the population mean when
Descriptions of data statistics for researchHarve Abella
This document defines and describes various measures of central tendency and variation that are used to summarize and describe sets of data. It discusses the mean, median, mode, midrange, percentiles, quartiles, range, variance, standard deviation, interquartile range, coefficient of variation, measures of skewness and kurtosis. Examples are provided to demonstrate how to compute and interpret these statistical measures.
This document provides an overview of descriptive statistics and statistical concepts. It discusses topics such as data collection, organization, analysis, interpretation and presentation. It also covers frequency distributions, measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), and hypothesis testing. Hypothesis testing involves forming a null hypothesis and alternative hypothesis, and using statistical tests to either reject or fail to reject the null hypothesis based on sample data. Common statistical tests include ones for comparing means, variances or proportions.
Statistics is the study of collecting, analyzing, and presenting quantitative data. It involves planning data collection through surveys and experiments, as well as analyzing the data using measures of central tendency like the mean, median, and mode. The mean is the average value found by summing all values and dividing by the total number of values. The median is the middle value when data is arranged in order. The mode is the most frequent value. Statistics has limitations as it does not study qualitative data or individuals, and statistical laws may not be universally applicable. Frequency distributions organize data values and their frequencies to understand patterns in the data.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to ensure the data is appropriate for the technique. Students should ask what the technique can prove and if the data is in the right format before performing calculations.
3. Common methods for summarizing a large data set are the mean, median, and mode. The mean is the average, the median is the middle value, and the mode is the most frequent value. These give a single value for the data but do not show the variation around that value.
This document discusses analyzing and interpreting test data using various statistical measures. It describes desired learning outcomes around measures of central tendency, variability, position, and covariability. Key measures are defined, including:
- Mean, median, and mode as measures of central tendency
- Standard deviation as a measure of variability
- Measures of position like percentiles and z-scores
- Covariability measures the relationship between two variables
Examples are provided to demonstrate calculating and interpreting these different statistical measures from test data distributions. The appropriate use of measures depends on the level of measurement (nominal, ordinal, interval, ratio). Measures reveal properties like skewness and help evaluate teaching and learning.
1. The document discusses key concepts in biostatistics including measures of central tendency, dispersion, correlation, regression, and sampling.
2. Measures of central tendency described are the mean, median, and mode. Measures of dispersion include range, standard deviation, and quartile deviation.
3. The importance of statistical analysis for living organisms in areas like medicine, biology and public health is highlighted. Examples are provided to demonstrate calculation of statistical measures.
This document provides an overview of chapter 2 from an elementary statistics textbook. It covers exploring and organizing data using frequency distributions, histograms, graphs, scatterplots, and other methods. The objectives are to organize data using frequency distributions and represent data graphically. It defines key terms like population, sample, parameter, and statistic. It also describes procedures for constructing frequency distributions and calculating cumulative frequencies. Examples are provided to demonstrate how to organize various data sets into frequency distributions.
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 provides an introduction to statistics, including definitions, scope, and measures of central tendency. It defines statistics as the science of collecting, organizing, analyzing, interpreting, and presenting data. Statistics has applications in various fields including social sciences, planning, mathematics, economics, and business management. Common measures of central tendency discussed are the arithmetic mean, geometric mean, harmonic mean, median, and mode. Formulas for calculating the arithmetic mean using individual data, frequency distributions, and class intervals are provided.
The document discusses various methods for describing data distributions numerically, including measures of center (mean, median), measures of spread (standard deviation, interquartile range), and graphical representations (boxplots). It explains how to calculate and interpret the mean, median, quartiles, five-number summary, standard deviation, and identifies outliers. Choosing an appropriate measure of center and spread depends on the symmetry of the distribution and presence of outliers. Changing the measurement units affects the calculated values but not the underlying shape of the distribution.
This document discusses various stages and techniques in data analysis, including data processing, distribution, tabulation, analysis, interpretation, and presentation. It describes common statistical analyses like descriptive analysis, inferential analysis, differences analysis, associative analysis, and predictive analysis. Specific techniques covered include measures of central tendency, measures of variability, correlation, regression, hypothesis testing, and types of errors in decision making.
1. The document discusses various measures of central tendency including mode, median, and quartiles.
2. Mode is the most frequent value in a data set. Median divides the data set into two equal halves. Quartiles divide the data set into four equal groups.
3. The document provides formulas and examples for calculating mode, median, and quartiles for both grouped and ungrouped data sets. Advantages and disadvantages of each measure are also discussed.
This document provides an overview of key concepts in descriptive statistics, including measures of center, variation, and relative standing. It discusses the mean, median, mode, range, standard deviation, z-scores, percentiles, quartiles, interquartile range, and boxplots. Formulas and properties of these statistical concepts are presented along with guidelines for interpreting and applying them to describe data distributions.
This document provides an overview of biostatistics and various statistical concepts used in dental sciences. It discusses measures of central tendency including mean, median, and mode. It also covers measures of dispersion such as range, mean deviation, and standard deviation. The normal distribution curve and properties are explained. Various statistical tests are mentioned including t-test, ANOVA, chi-square test, and their applications in dental research. Steps for testing hypotheses and types of errors are summarized.
This document discusses statistical procedures and their applications. It defines key statistical terminology like population, sample, parameter, and variable. It describes the two main types of statistics - descriptive and inferential statistics. Descriptive statistics summarize and describe data through measures of central tendency (mean, median, mode), dispersion, frequency, and position. The mean is the average value, the median is the middle value, and the mode is the most frequent value in a data set. Descriptive statistics help understand the characteristics of a sample or small population.
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfAravindS199
Sir Francis Galton was a prominent English statistician, anthropologist, eugenicist, and psychometrician in the 19th century. He produced over 340 papers and books, and created the statistical concepts of correlation and regression. As a pioneer in meteorology and differential psychology, he devised early weather maps, proposed theories of weather patterns, and developed questionnaires to study human communities and intelligence. The document discusses Galton's background and contributions to statistics, anthropology, meteorology, and psychometrics.
Describing quantitative data with numbersUlster BOCES
1. Quantitative data can be summarized using measures of center (mean, median), spread (range, IQR, standard deviation), and position (quartiles, percentiles, z-scores).
2. The mean is more affected by outliers than the median. The median is more resistant to outliers and a better measure of center for skewed data.
3. Additional summaries like the five-number summary and boxplots provide a graphical view of the distribution and identify potential outliers.
More Related Content
Similar to Lecture_4_-_Data_Management_using_Statistics(3).pptx
Statistics is the study of collecting, analyzing, and presenting quantitative data. It involves planning data collection through surveys and experiments, as well as analyzing the data using measures of central tendency like the mean, median, and mode. The mean is the average value found by summing all values and dividing by the total number of values. The median is the middle value when data is arranged in order. The mode is the most frequent value. Statistics has limitations as it does not study qualitative data or individuals, and statistical laws may not be universally applicable. Frequency distributions organize data values and their frequencies to understand patterns in the data.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to ensure the data is appropriate for the technique. Students should ask what the technique can prove and if the data is in the right format before performing calculations.
3. Common methods for summarizing a large data set are the mean, median, and mode. The mean is the average, the median is the middle value, and the mode is the most frequent value. These give a single value for the data but do not show the variation around that value.
This document discusses analyzing and interpreting test data using various statistical measures. It describes desired learning outcomes around measures of central tendency, variability, position, and covariability. Key measures are defined, including:
- Mean, median, and mode as measures of central tendency
- Standard deviation as a measure of variability
- Measures of position like percentiles and z-scores
- Covariability measures the relationship between two variables
Examples are provided to demonstrate calculating and interpreting these different statistical measures from test data distributions. The appropriate use of measures depends on the level of measurement (nominal, ordinal, interval, ratio). Measures reveal properties like skewness and help evaluate teaching and learning.
1. The document discusses key concepts in biostatistics including measures of central tendency, dispersion, correlation, regression, and sampling.
2. Measures of central tendency described are the mean, median, and mode. Measures of dispersion include range, standard deviation, and quartile deviation.
3. The importance of statistical analysis for living organisms in areas like medicine, biology and public health is highlighted. Examples are provided to demonstrate calculation of statistical measures.
This document provides an overview of chapter 2 from an elementary statistics textbook. It covers exploring and organizing data using frequency distributions, histograms, graphs, scatterplots, and other methods. The objectives are to organize data using frequency distributions and represent data graphically. It defines key terms like population, sample, parameter, and statistic. It also describes procedures for constructing frequency distributions and calculating cumulative frequencies. Examples are provided to demonstrate how to organize various data sets into frequency distributions.
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 provides an introduction to statistics, including definitions, scope, and measures of central tendency. It defines statistics as the science of collecting, organizing, analyzing, interpreting, and presenting data. Statistics has applications in various fields including social sciences, planning, mathematics, economics, and business management. Common measures of central tendency discussed are the arithmetic mean, geometric mean, harmonic mean, median, and mode. Formulas for calculating the arithmetic mean using individual data, frequency distributions, and class intervals are provided.
The document discusses various methods for describing data distributions numerically, including measures of center (mean, median), measures of spread (standard deviation, interquartile range), and graphical representations (boxplots). It explains how to calculate and interpret the mean, median, quartiles, five-number summary, standard deviation, and identifies outliers. Choosing an appropriate measure of center and spread depends on the symmetry of the distribution and presence of outliers. Changing the measurement units affects the calculated values but not the underlying shape of the distribution.
This document discusses various stages and techniques in data analysis, including data processing, distribution, tabulation, analysis, interpretation, and presentation. It describes common statistical analyses like descriptive analysis, inferential analysis, differences analysis, associative analysis, and predictive analysis. Specific techniques covered include measures of central tendency, measures of variability, correlation, regression, hypothesis testing, and types of errors in decision making.
1. The document discusses various measures of central tendency including mode, median, and quartiles.
2. Mode is the most frequent value in a data set. Median divides the data set into two equal halves. Quartiles divide the data set into four equal groups.
3. The document provides formulas and examples for calculating mode, median, and quartiles for both grouped and ungrouped data sets. Advantages and disadvantages of each measure are also discussed.
This document provides an overview of key concepts in descriptive statistics, including measures of center, variation, and relative standing. It discusses the mean, median, mode, range, standard deviation, z-scores, percentiles, quartiles, interquartile range, and boxplots. Formulas and properties of these statistical concepts are presented along with guidelines for interpreting and applying them to describe data distributions.
This document provides an overview of biostatistics and various statistical concepts used in dental sciences. It discusses measures of central tendency including mean, median, and mode. It also covers measures of dispersion such as range, mean deviation, and standard deviation. The normal distribution curve and properties are explained. Various statistical tests are mentioned including t-test, ANOVA, chi-square test, and their applications in dental research. Steps for testing hypotheses and types of errors are summarized.
This document discusses statistical procedures and their applications. It defines key statistical terminology like population, sample, parameter, and variable. It describes the two main types of statistics - descriptive and inferential statistics. Descriptive statistics summarize and describe data through measures of central tendency (mean, median, mode), dispersion, frequency, and position. The mean is the average value, the median is the middle value, and the mode is the most frequent value in a data set. Descriptive statistics help understand the characteristics of a sample or small population.
Unit 1 - Mean Median Mode - 18MAB303T - PPT - Part 1.pdfAravindS199
Sir Francis Galton was a prominent English statistician, anthropologist, eugenicist, and psychometrician in the 19th century. He produced over 340 papers and books, and created the statistical concepts of correlation and regression. As a pioneer in meteorology and differential psychology, he devised early weather maps, proposed theories of weather patterns, and developed questionnaires to study human communities and intelligence. The document discusses Galton's background and contributions to statistics, anthropology, meteorology, and psychometrics.
Describing quantitative data with numbersUlster BOCES
1. Quantitative data can be summarized using measures of center (mean, median), spread (range, IQR, standard deviation), and position (quartiles, percentiles, z-scores).
2. The mean is more affected by outliers than the median. The median is more resistant to outliers and a better measure of center for skewed data.
3. Additional summaries like the five-number summary and boxplots provide a graphical view of the distribution and identify potential outliers.
Similar to Lecture_4_-_Data_Management_using_Statistics(3).pptx (20)
2. “statistics” has been derived from Latin word “status” or the Italian
word “statista”, which is a “Political State” or a Govt.
Statistics - the science of collecting, analyzing, presenting, and
interpreting data.
Division of Statistics
1. Descriptive Statistics – is a statistical procedure concerned
with describing the characteristics and properties of a group of
persons, places or things that was based on easily verifiable
facts.
2. Inferential Statistics – is a statistical procedure used to draw
inferences for the population on the basis of information
obtained from the sample using the techniques of descriptive
statistics.
Statistics
3. Data Collection and Presentation of
Statistical Data
A. Types of Data
1. Raw Data – data in their original form and structure.
2. Grouped Data – place in tabular form characterized by class
intervals with the corresponding frequency.
3. Primary Data – measured and gathered by the researcher
who published it.
4. Secondary Data – republished by another researcher or
agency.
B. Data Presentation
1. Textual Presentation – in sentences or paragraph.
2. Tabular Presentation – makes use of rows and columns.
3. Graphical Presentation – using pictorial representation.
4. C. Data Gathering Techniques
1. Direct or Interview Method – person to person exchange of
data from interviewer to interviewee.
2. Indirect or Questionnaire Method – responses are written
and given more time to answer.
3. Registration Method – respondents provide information in
compliance with certain laws, policies, rules, decrees,
regulations or standard practices.
4. Experimental Method – the researcher wants to control the
factors affecting the variable being studied to find out cause
and effect relationship.
5. Observation Method – utilized to gather data regarding
attitudes, behavior or values and cultural pattern of the
samples under investigation.
Data Collection and Presentation of
Statistical Data
5. - is the numerical descriptive measures which indicate or
locate the center of distribution of a set of data.
1. Mean (Arithmetic) - is equal to the sum of all the values in
the data set divided by the number of values in the data set.
2. Median - is the middle score for a set of data that has been
arranged in order of magnitude.
3. Mode - is the most frequent score in our data set.
4. Weighted Mean – is an average in which each quantity to be
averaged is a assigned a weight.
Measures of Central Tendency
6. Ex. 1. Find the mean, median and mode in the given data.
63, 55, 89, 56, 35,14, 58, 55, 87,45, 92
Solution:
n = 11
a. mean = (63+55+89+56+35+14+58+55+87+45+92)/11
= 59
b. median – arranging the data from lowest to highest data
14 35 45 55 55 56 58 63 87 89 92
Median location is on the sixth position: median = 56
c. mode = 55
Measures of Central Tendency
7. Ex. 2. Find the median in the given data.
65 55 89 56 35 14 56 55 87 45
Solution: arranging the data
14 35 45 55 55 56 56 65 87 89
Median location is on the 5th and 6th position:
median = (55 + 56)/2 = 55.5
Note: If the number of observed values (N) is odd, the median
position is equal to (n+1)/2, and the value in the (n+1)/2 th is taken
as the median. If N is even, the mean of the two middle values is
the median.
Measures of Central Tendency
8. Ex. 3. Given the data below, determine if Roy passed the
subject.
Solution: Grade = (0.25)(75) + (0.15)(92) + (0.20)(88) + (0.10)(68)
+ (0.30(72)
Grade = 78.55 (passed)
Measures of Central Tendency
Grading
Criteria
Weighted
Percentage
Roy’s Score
Quizzes 25% 75
Recitation 15% 92
Assignment 20% 88
Seatwork 10% 68
Term
Examination
30% 72
9. - indicate the extent to which individual items in a series are
scattered about an average. It is used to determine the
extent of the scatter so that steps may be taken to control
the existing variation. It is also used as a measure of
reliability of the average value.
A. Measures of absolute Dispersion
- expressed in the units of the original observations.
1. Range – can be determined by finding the difference
between the largest and smallest values.
Range (R) = maximum value - minimum value
Ex. 4. The test results of five students are 90, 98, 76, 85
and 92. Find the range.
Solution: R = 98 – 76 = 22
Measures of Dispersion
10. 2. Variance – describes how the data is spread out. It is the average
of the squared deviations about the mean for a set of numbers
Measures of Dispersion
11. 3. Standard Deviation – is the most reliable measure of
dispersion. Standard Deviation is a measure of how much
the data is dispersed from its mean. A high standard deviation
implies that the data values are more spread out from the
mean. The population standard deviation is denoted by σ.
Measures of Dispersion
12. Measures of Dispersion
Ex. 5. A sample of five households showed the following
number of household members: 3, 8, 5, 4 and 4. Find the
variance (σ2) and the standard deviation(σ).
Solution:
13. B. Measures of Relative Dispersion
- are unit less and are used when one wishes to compare
the scatterings of one distribution with another distribution.
The coefficient of variation (CV) is the ratio of the
standard deviation to the mean and is usually expressed
in percentage.
Measures of Dispersion
14. Ex. 6. A company analyst studied recent measurements made
with two different instruments. The first measure obtained a
mean of 4.96 mm with a standard deviation of 0.022 mm. The
second measure obtained a mean of 6.48 mm with a standard
deviation of 0.032. Which of the two instruments was relatively
more precise?
Solution:
instrument #1: CV = (0.022/4.96) (100%) = 0.44%
instrument #2: CV = (0.032/6.48) (100%) = 0.49%
instrument #1 was relatively more precise than
instrument#2
Measures of Relative Dispersion
15. C. Measures of Relative Position or Fractiles
Fractiles – is the division of an array into equivalent
subgroups. It identifies the position of a value in an array.
An array divided into hundred equal parts is Percentile.
In Quartile, array is divided into four equal parts and Decile
dividers an array into 10 equal parts.
Measures of Dispersion
16. Fractiles
Ex. 7. The following were the scores of 12 students in 20-item
quiz, find the : a) 80th percentile b) 6th decile c) 1st quartile.
4 3 6 12 11 6 18 5 6 6 17 13
Solution: arranging the data from lowest to highest,
a) P80th: i = 80, n = 12 and F = 100 (percentile)
P80 = i(n+1)/F = (80)(12+1)/100 = 10.4th or 11th position
P80 = 17 – which means that 80% of the scores are below 17.
b) D6th: I = 6, n = 12 and F = 10 (decile)
D6 = i(n+1)/F = (6)(12+1)/10 = 7.8th or 8th position
D6 = 11 – which means that 60% of the scores are below 11.
Number 3 4 5 6 6 6 6 11 12 13 17 18
Position 1 2 3 4 5 6 7 8 9 10 11 12
17. Fractiles
c) Q1st: I = 1, n = 12 and F = 4 (quartile)
Q1 = i(n+1)/F = (1)(12+1)/4 = 3.25 or 4th position
Q1 = 6 – which means that 25% of the scores are below 6.
Number 3 4 5 6 6 6 6 11 12 13 17 18
Position 1 2 3 4 5 6 7 8 9 10 11 12
18. Exercises A:
Find the mean, median and mode(s)
1. 4, 3, 12, 5, 13, 3
2. -3, 0, 5, -2, 5, -3, 0
3. 120, 123, 123, 120, 112, 134, 128, 126, 162
Exercises B:
The scores of 10 students in a Math Test are given as: 9, 10, 16,
15, 18, 25, 20, 32, 30, 35. Find: a) P70 b) D8 c) Q3