This tutorial gives the detailed explanation of "Measure of Dispersion" (Range, Quartile Deviation, Interquartile Range, Mean Deviation) with suitable illustrative example with MS Excel Commands of calculation in excel.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
A basic task in numerous statistical analyses is to characterize the position and variability of a data set. Another characterization of the data includes skewness and kurtosis.
Skewness is a measure of balance, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the centre point.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation
Lecture on Introduction to Descriptive Statistics - Part 1 and Part 2. These slides were presented during a lecture at the Colombo Institute of Research and Psychology.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
A basic task in numerous statistical analyses is to characterize the position and variability of a data set. Another characterization of the data includes skewness and kurtosis.
Skewness is a measure of balance, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the centre point.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation
Lecture on Introduction to Descriptive Statistics - Part 1 and Part 2. These slides were presented during a lecture at the Colombo Institute of Research and Psychology.
A few month ago I'm participate a workshop "How to prepare thesis writing or project book" in my university. Workshop is conduct by M. NURUL ISLAM. He is the Asst.Professor on DEPARTMENT OF STATISTICS,
UNIVERSITY OF DHAKA
Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...Shakehand with Life
This tutorial gives the detailed explanation measure of dispersion part II (standard deviation, properties of standard deviation, variance, and coefficient of variation). It also explains why std. deviation is used widely in place of variance. This tutorial also teaches the MS excel commands of calculation in excel.
Levels of Measurement: Nominal = Data one collects when doing a wide-open descriptive or exploratory study, however, it is not limited to these kinds of studies. We can count this data, but we can’t order it. We need to be able to put this data into categories that are mutually exclusive, i.e. it can’t be in more than one category at a time. An example would be looking at age, race, sex, or some other type of data that you either are or aren’t. The categories need to be exhaustive – there need to be enough categories to cover the data you collect. Ordinal = this category has mutually exclusive categories, but with ordinal data you can order the data within each category. The ratings of poor, fair, good are an example of ordinal information. Note that you can order the ratings, but you can’t really tell how far apart each of these descriptors are from each other. You could also look at who finishes a task first, second, third, and so on. Again, you can rank this data, but you don’t know how much faster the first person was in relation to the second person or subsequent people. Interval-ratio data = this type of data allows you to measure the difference between each of your rankings. Data is ordered (as with ordinal data) and you can tell how much difference there is between each observation because there is a scale that is divided into equal units. You can measure a race with a stopwatch in terms of seconds or tenths of seconds. A thermometer gives you data with measurements in degrees. Ratio data is like interval data (and is often lumped together with it because they are usually handled the same way statistically). Its primary difference is that there is a zero point on the scale so that you can do multiplication and division. Money is an example of a ratio scale – two dollars are exactly twice one dollar. Volume, area, and distance measures are also ratio scales (2 times 1 liter equals 2 liters). This is different from a strict interval scale like a thermometer – we can’t say that 10 degrees Fahrenheit is twice as warm as 5 degrees Fahrenheit. Statistical Distributions: According to Shi, “a distribution organizes the values of a variable into categories. Frequency Distribution (aka Marginal Distribution): Displays the number of cases that falls into each category. Percentage Distribution: Found by dividing the number of frequency of cases in the category by the total N. Measures of Central Tendency: Mean: The most common measure of central tendency. It simply the sum of the numbers divided by the number of numbers. Median: It is defined as the middle position or midpoint of a distribution. Mode: Is defined as the most frequently occurring value. What is variability? Amount of spread or dispersion within a distribution of scores within a set of data. Measures of Variability: Range: The difference between the highest and lowest values in a distribution. Interquartile Range: Known as the ‘midspread’ or ‘middle fifty.” It contains the middle 50% of
Levels of Measurement: Nominal = Data one collects when doing a wide-open descriptive or exploratory study, however, it is not limited to these kinds of studies. We can count this data, but we can’t order it. We need to be able to put this data into categories that are mutually exclusive, i.e. it can’t be in more than one category at a time. An example would be looking at age, race, sex, or some other type of data that you either are or aren’t. The categories need to be exhaustive – there need to be enough categories to cover the data you collect. Ordinal = this category has mutually exclusive categories, but with ordinal data you can order the data within each category. The ratings of poor, fair, good are an example of ordinal information. Note that you can order the ratings, but you can’t really tell how far apart each of these descriptors are from each other. You could also look at who finishes a task first, second, third, and so on. Again, you can rank this data, but you don’t know how much faster the first person was in relation to the second person or subsequent people. Interval-ratio data = this type of data allows you to measure the difference between each of your rankings. Data is ordered (as with ordinal data) and you can tell how much difference there is between each observation because there is a scale that is divided into equal units. You can measure a race with a stopwatch in terms of seconds or tenths of seconds. A thermometer gives you data with measurements in degrees. Ratio data is like interval data (and is often lumped together with it because they are usually handled the same way statistically). Its primary difference is that there is a zero point on the scale so that you can do multiplication and division. Money is an example of a ratio scale – two dollars are exactly twice one dollar. Volume, area, and distance measures are also ratio scales (2 times 1 liter equals 2 liters). This is different from a strict interval scale like a thermometer – we can’t say that 10 degrees Fahrenheit is twice as warm as 5 degrees Fahrenheit. Statistical Distributions: According to Shi, “a distribution organizes the values of a variable into categories. Frequency Distribution (aka Marginal Distribution): Displays the number of cases that falls into each category. Percentage Distribution: Found by dividing the number of frequency of cases in the category by the total N. Measures of Central Tendency: Mean: The most common measure of central tendency. It simply the sum of the numbers divided by the number of numbers. Median: It is defined as the middle position or midpoint of a distribution. Mode: Is defined as the most frequently occurring value. What is variability? Amount of spread or dispersion within a distribution of scores within a set of data. Measures of Variability: Range: The difference between the highest and lowest values in a distribution. Interquartile Range: Known as the ‘midspread’ or ‘middle fifty.” It contains the middle 50% of
Similar to Measure of dispersion part I (Range, Quartile Deviation, Interquartile deviation, Mean deviation) (20)
7 QC Tools PDF | An eBook with A Detailed Description and Practical ExamplesShakehand with Life
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Train yourself and be the master of 7 QC Tools with this eBook of 7 QC Tools in PDF with a detailed description and illustrative examples of all 7 Quality Control Tools. Learn to construct the Histogram, Pareto Chart, Scatter Chart, Control Charts in Excel and analyze the data in Excel.
Activity network diagram helps to schedule a project efficiently. It gives an idea of the minimum and maximum time to complete a project. The 7th tool among the New 7 management development tool.
Process Decision and Program is designed to achieve a particular objective. Used especially in new process development. The tool avoids surprises and identifies the possible countermeasures.
Prioritization matrix prioritizes issues, based on weighted criteria using a combination of Tree and Matrix diagram. It is a very important tool for the management to prioritize the issue to work on.
Interrelationship digraph is another important tool out of New 7 Quality Tools. It helps to clarify the interrelationship of many factors of a complex situation. It identifies key drivers and the key outcomes.
New 7 QC Tools; Affinity diagram, Interrelationship digraph, Tree diagram, Matrix diagram, Prioritization matrices, Process Decision and Program Chart (PDPC), and Activity Network Diagram. The New 7 QC Tools also known as 7 Management Development Tools. These tools unlike the 7 fundamentals quality control tools, process the subjective data and help the management to make the better decision, regarding project management and quality improvement.
The affinity diagram is one among the New 7 Quality Contol tools, helps to categorize the same type of ideas or issues. Affintiy diagram process the same type of subjective data in a particular category.
Course Catalog 2016-17, is the overview of various corporate trainings courses for our deemed clientele, so that they can lock the dates for in-house training facilitation at company site in the year of 2016-17.
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Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
People are often like a train, some are like its engine, leading the train forward. Some are like the bogies, chugging along, following the leader. While a few others are like the brakes, putting a stop to its motion. A leader is like the engine of this train. A man who will lead with trust and honesty, with speed and also ensure there are no accidents.”…………………………Narender Sharma
Times of India, LEAD INDIA, MAIL BOX, Page 2, dated; Aug. 24, 2007
Go through the seven quality tools training quiz and compare, how much you have learnt from this online training of 7QC tools? The quiz has 15 multiple choice questions based on seven quality tools. Choose one answer out of the given choices for every question write these choices on a paper. After completing the quiz compare yourself with answer key in the end of quiz. Find yourself where you are in learning of 7 QC Tools. If you find your performance is not up to the mark then go again for the training of seven QC tools. You may do it as many times as you want. Improve your performance every time you go through the training.
Seven QC Tools Training; Control Charts (Mean Chart and Range Chart)Shakehand with Life
Seven quality tools training is incomplete without learning of control charts. Control charts help to control the process with in the set control limits. Control charts are mainly two types; Mean Chart and Range Chart. Mean chart showcase the process data complied by the designated person and signal when the data go beyond the control limits. Every process has variation and due to this variation data get fluctuated. This fluctuation shown on the mean and range chart by data points. The causes of fluctuation in the data are assignable and common causes. Due to common causes data fluctuated around the average of the data but due to assignable cause data go beyond the control limits. When data go beyond the control limits control charts warn the operator that something is going wrong in the process and need to special attention. Mean chart is the spread of the mean values of the samples around the mean line. Range chart is spread of the range of samples around the mean line of range.
Scatter diagram is the graphical presentation of relationship between two variables. Scatter diagram is an important tool out of 7 fundamental tools of quality control. Scatter diagram helps to confirm the degree of relationship between cause and effect. Here cause is an independent variable and effect is dependent variable. Scatter diagram is an important statistical tool to analyze the relationship of two variables. To create the scatter diagram take the values of independent variable on X-Axis where as the dependent variable is taken on Y-Axis. Plot the intersection points of X and Y on the graph. Draw a straight line passing through all the points. Analyze the pattern of the points. For different degree of relationship different pattern of scatter diagram is formed. If Y increases as X increases and data points are on the straight line then there is perfect positive correlation. If Y decreases with increase of X and data points are on the straight line then there is perfect negative correlation. But when data is scattered all over the graph then there is zero correlation.
Process flow chart or Flow process chart among the seven quality control tools considered as the first and base of application of every quality tool. Process flow chart is the pictorial representations of all activities of process using different shape of boxes. Process flow chart is the guiding map of the whole process. With a single view, process flow chart gives almost every information about the whole process. Process flow diagram inform the starting and end point of the process along with the operations, decision, storage, delay, direction etc. through which the product or service passing. Different shapes like circle, rectangular circle, diamond, rectangle, arrows, D shapes, inverted rectangles etc. are used to construct process flow diagram. Process flow diagram clearly explains which operation is followed by which operation. Process flow chart helps to find out the potential trouble spots in the process so that corrective action can be taken to remove the hurdles at an early stage. To audit the whole process, process flow chart plays a vital role. Even for the new comers in the organization, process flow chart is an opportunity to understand their process easily.
Visit www.shakehandwithlife.in to buy this Book. This E-Book on 7QC tools is complete training workshop for Junior, Middle and Senior quality quality professionals. The USP of this workshop is the text and graphics in the book for understanding the tools while applying to solve the practial problems. Illustrative worked examples , Construction of tools in Excel like Histogram, Pareto Chart, Scatter Diagram, Control charts are beautifully explained in step step manner. A newcomer in the area of quality can easily understand how the tools be used and applied.
This tutorial explain the measure of central tendency (Mean, Median and Mode in detail with suitable working examples pictures. The tutorial also teach the excel commands for calculation of Mean, Median and Mode.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Biological screening of herbal drugs: Introduction and Need for
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
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• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Topic covered in this tutorial
S.No. Topic Page No.
1
Measure of Variability or Dispersion
Introduction
Objective of Measuring Dispersion
Absolute or Relative Measure
Types of Measure of Dispersion
3-6
2
Range
Introduction
Coefficient of Range
Method of calculation
7-8
3
Interquartile Deviation and Quartile Deviation
Introduction
Interquartile Range,
Quartile Deviation,
Coefficient of Quartile Deviation
Method of calculation
9-12
4
Mean Deviation
Introduction
Mean Deviation from Mean
Mean Deviation from Median
Coefficient of Mean Deviation from Mean
Coefficient of Mean Deviation from Median
13-17
5
Excel Commands
Minimum Value
Maximum Value
Range
1st Quartile
2nd Quartile
3rd Quartile
Interquartile Range
Quartile Deviation
Mean Deviation
18
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Measures of Variability or Dispersion
What is measure of variability or dispersion?
Consider the following two data sets.
Set I : 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11
Set II : 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8
Compute the mean, median and mode for each of the two data sets. We find that the two data sets have the
same mean , the same median, and the same mode, all equal to 6.
The two data set also have the same number of observations, i.e. n=12. But the two data sets are
different. What is the main difference between them?
The two data sets have the same central tendency (as measured by any of the three measures of
centrality) but they have different variability or the dispersion or spread.
In particular, we see that data set I is more variable than data set II. The values in set I are more spread out:
they lie farther away from their mean than do those of set II.
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Objective of measuring dispersion
To determine the reliability of an average
The measures of dispersion help in determining the reliability of an average. It points out as to how far an
average is representative of a statistical series. If the dispersion or variation is small, the average will closely
represent the individual values and it is highly representative. On the other hand if the dispersion or
variation is large, the average will be quite unreliable
To compare the variability of two or more series
The measures of dispersion is useful to determine the consistency or uniformity of the two or more series. It
helps to comparing the variability of the variability of two or more series. A high degree of variability means
the less consistency in the data and if the series shows high consistency that means the data series has less
variability.
For facilitating the use of other statistical measures
Measures of dispersion serve the basis of man other statistical measures such as correlation, regression,
testing of hypothesis etc. These measures are based on measures of variation of one kind or another.
Basic of statistical quality control
The measures of dispersion serve the quality control in the manufacturing or service industries. These help
to trace the process variation. Control chart is one of the measure tool to find variation so control the causes
of variation in the process.
Absolute or relative measure of dispersion
Measures of dispersion may be either absolute or relative.
Absolute measure of dispersion
Absolute measure of dispersion are expressed in the same unit in which data of the series are expressed.
They are expressed in same statistical unit, e.g., rupees, kilogram, tons, years, centimeters etc.
Relative measure of dispersion
Relative measure of dispersion refers to the variability stated in the form of ratio or percentage. Thus,
relative measure of dispersion is independent of unit of measurement. It is also called coefficient of
dispersion. These measure are used to compare two series expressed in different units.
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Types of measures of dispersion
Following are the types of measure of dispersion or variability as shown above in the fig.
1. Range
2. Interquartile Range and Quartile Deviation
3. Mean Deviation
4. Standard Deviation
5. Coefficient of Variation
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Range
It is the simplest measure of dispersion. It is defined as the difference between the largest and smallest
value in the series. Its formula is;
Where R= Range, L= Largest value in the series, S = Smallest value in the series
The relative measure of range, also called coefficient of range, is defined as
The following examples illustrate the calculation of range;
Calculation of Range
Individual series
Example 1 10 pcs of a product in manufacturing industry taken from an hourly lot and weighted, the
weight (gms) of the product was
10.5, 10.7, 10.3, 10.2, 10.9, 11, 11.1, 11.2, 10.3, 10.9
Find the Range and Coefficient of Range
Solution : L=11.2 and S=10.2
Discrete Series
Example 2 Find the range and coefficient of range from the following data;
Marks 10 20 30 40 50 60 70
No. of Students 15 18 25 30 16 10 9
Solution Here L=70 and S=10
Continuous series
Example 3 Find out range and coefficient of range of the following series
Size 5-10 10-15 15-20 20-25 25-30
Frequency 4 9 15 30 40
Solution:
Here, L = Upper limit of the largest class =30
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S = Lower limit of the smallest class =5
Note : Since the maximum and minimum of the observations are not identifiable for a continuous series,
the range is defined as the difference between the upper limit of the largest class and the lower limit of the
smallest class.
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Interquartile Range and Quartile Deviation
We know about the median, which divide the whole data set into two equal parts, one part less than the
median and other half is greater than median.
In the same manner the quartiles ( divide the data into four parts. First part of the data is less
than , second part of the data lies between and the third part of the data is lies between
and fourth or the last part of the data is greater than is called lower quartile and is
called the upper quartile.
Formula for calculation of quartiles
[ ]
[ ]
[ ]
Second Quartile is also called the median because the second quartile or median divides the data into
two equal parts.
The Interquartile range and quartile deviation are another measure of dispersion which can be calculated
with help of quartiles and defined as below.
The difference between the upper quartile ( ) and lower quartile ( ) is called the
interquartile range. Symbolically,
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The interquartile ranges covers dispersion of middle 50% of the items of the series.
Quartile deviation, also called Semi-interquartile Range is half of the difference between
the upper and lower quartile i.e. half of the interquartile range. Symbolically
Coefficient of quartile deviation (The relative measure of quartile deviation)
Calculation of Interquartile Range, Q.D., Coefficient of Q.D.
Individual Series
Example 4 Find interquartile range, quartile deviation and coefficient of quartile deviation from the
following data;
28, 18, 20, 24, 27, 30, 15
Solution: Arrange the data in ascending order;
15, 18, 20, 24, 27, 28, 30
[ ] [ ]
Discrete Series
Example 5 Calculate interquartile range, quartile deviation and the coefficient of quartile deviation from
the following data;
Earnings (₹) 10 20 30 40 50 60
No. of People 2 8 20 35 42 20
Solution : Calculation of Q.D.
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