# Characteristics of a good measure of dispersion. Measures of dispersion Characteristics of good measures of dispersion range QD 2022-10-31

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A good measure of dispersion, also known as a measure of variability or scatter, is a statistical tool that describes the spread or variation of a dataset. It helps to understand how much the data points in a sample or population differ from one another, as well as how far they are from the mean or median. Dispersion is an important concept in statistical analysis because it gives us a sense of how diverse or uniform a dataset is, which can inform decisions and predictions based on the data.

There are several characteristics that a good measure of dispersion should possess:

1. Sensitivity: A good measure of dispersion should be able to detect even small changes in the data. For example, if a dataset has a small dispersion, a measure that is not sensitive enough may not be able to detect any differences in the data points. On the other hand, a sensitive measure will be able to pick up on even slight variations in the data.

2. Range: A good measure of dispersion should have a wide range, meaning it should be able to handle a variety of data types and distributions. For example, a measure that is only suitable for data that follows a normal distribution will not be effective for data that is skewed or has outliers.

3. Reliability: A good measure of dispersion should be reliable, meaning it should give consistent results when applied to the same data multiple times. This ensures that the measure is not affected by random fluctuations or errors, and that the results can be trusted.

4. Simplicity: A good measure of dispersion should be easy to understand and calculate, even for those who are not experts in statistics. This makes it more accessible and useful to a wider range of people.

5. Robustness: A good measure of dispersion should be robust, meaning it should not be easily affected by outliers or extreme values in the data. For example, if a dataset has a few outliers that are much higher or lower than the majority of the data points, a robust measure of dispersion should not be significantly affected by these outliers.

In conclusion, a good measure of dispersion should be sensitive, have a wide range, be reliable, simple to understand and calculate, and be robust to outliers. These characteristics ensure that the measure accurately reflects the variability in a dataset and can be used to make informed decisions and predictions based on the data.

## Chapter 5 Measures of Dispersion

. The mean absolute deviation is also known as the mean deviation and average absolute deviation. . It should be based on all observations in the data set. This implies that data set B is more variable than data set A.

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## 2 What are the characteristics of good measures of dispersion 3 What are

Computation of mean deviation. What is the effect of shift of origin and change of scale on standard deviation? So, it has fixed value. It should be noted that the standard deviation of a set of data is a non-negative number. Therefore it is better to use relative measure of dispersion obtained as ratios or % and are thus pure numbers independent of the unit of measurement. Twenty randomly chosen people are asked to rank a product on scale 0 to 100.

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## Measures of dispersion Characteristics of good measures of dispersion range QD

Sample standard deviation has same unit of measurement as of the data. Two distinct What are Absolute and Relative Measures of Dispersion? Thus, if x is measured in centimetres cm , then the unit of measurement of the sample variance is cm 2 and that of sample standard deviation is cm. In What are the 5 Measures of Dispersion? рд╡рд┐рджреНрдпрд╛ рдирд╛рдо рдирд░рд╕реНрдп рдХреАрд░реНрддрд┐рд░рддреБрд▓рд╛ рднрд╛рдЧреНрдпрдХреНрд╖рдпреЗ рдЪрд╛рд╢реНрд░рдпреЛ рдзреЗрдиреБрдГ рдХрд╛рдорджреБрдзрд╛ рд░рддрд┐рд╢реНрдЪ рд╡рд┐рд░рд╣реЗ рдиреЗрддреНрд░рдВ рддреГрддреАрдпрдВ рдЪ рд╕рд╛редред рд╕рддреНрдХрд╛рд░рд╛рдпрддрдирдВ рдХреБрд▓рд╕реНрдп рдорд╣рд┐рдорд╛ рд░рддреНрдиреИрд░реНрд╡рд┐рдирд╛ рднреВрд╖рдгрдореН рддрд╕реНрдорд╛рджрдиреНрдпрдореБрдкреЗрдХреНрд╖реНрдп рд╕рд░реНрд╡рд╡рд┐рд╖рдпрдВ рд╡рд┐рджреНрдпрд╛рдзрд┐рдХрд╛рд░рдВ рдХреБрд░реБрее рдЕрд░реНрдерд╛рдд:- рд╡рд┐рджреНрдпрд╛ рдЕрдиреБрдкрдо рдХреАрд░реНрддрд┐ рд╣реИ, рднрд╛рдЧреНрдп рдХрд╛ рдирд╛рд╢ рд╣реЛрдиреЗ рдкрд░ рд╡рд╣ рдЖрд╢реНрд░рдп рджреЗрддреА рд╣реИ, рдХрд╛рдордзреЗрдиреБ рд╣реИ, рд╡рд┐рд░рд╣ рдЕрднрд╛рд╡ рдореЗрдВ рд░рддрд┐ рдЖрдирдВрдж рд╕рдорд╛рди рд╣реИ, рддреАрд╕рд░рд╛ рдиреЗрддреНрд░ рд╣реИ, рд╕рддреНрдХрд╛рд░ рдХрд╛ рдордВрджрд┐рд░ рд╣реИ, рдХреБрд▓-рдорд╣рд┐рдорд╛ рд╣реИ, рдмрдЧреИрд░ рд░рддреНрди рдХрд╛ рдЖрднреВрд╖рдг рд╣реИ, рдЗрд╕рд▓рд┐рдП рдЕрдиреНрдп рд╕рдм рд╡рд┐рд╖рдпреЛрдВ рдХреЛ рдЫреЛрдбрдХрд░ рд╡рд┐рджреНрдпрд╛ рдХрд╛ рдЕрдзрд┐рдХрд╛рд░реА рдмрди. Range: Given a data set, the Variance: The average squared deviation from the mean of the given data set is known as the Standard Deviation: The square root of the variance gives the Mean Deviation: The Quartile Deviation: Relative Measures of Dispersion If the data of separate data sets have different units and need to be compared then relative measures of dispersion are used. It should be based on all observations in the data set. EXERCISE FOR PRACTICE 1. It is like asking how tall icy water is, or how cold your height is! Range, interquartile range, and standard deviation are the three commonly used measures of dispersion.

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## PROPERTIES OF A GOOD MEASURE OF DISPERSION

Conversely, lower values correspond to data points bunching closer to it. So their presence should not affect the calculation to a large extent. The inter-quartile range is sometimes used as a measure of dispersion. Give different formulae for variance. Statistical dispersion means the extent to which a numerical data is likely to vary about an average value. This question could not make less less.

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## What are the characteristics of a good measure of dispersion?

The inter-quartile range of a set of data is the difference between the upper and lower quartiles of the data. Absolute measures of dispersion have the same units as the data itself while relative measures of dispersion are dimensionless. Here is how to calculate the mean absolute deviation. Thus, measures of dispersion are certain types of measures that are used to quantify the dispersion of data. Not based on all observations 2.

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## 6 properties of a good Measure of Dispersion

Calculate standard deviation and variance from the following data: Class 1-3 3-5 5-7 7-9 9-11 Frequency 2 3 5 3 2 NMIMS N O T E S 142 BUSINESS STATISTICS NMIMS Global Access тАФ School for Continuing Education 3. The mean and standard deviation for yield are 50 kg and 10 kg respectively. The Standard Deviation SD tells the mean distance of the scores in the data set from the mean. Dispersion is a statistical term that can be used to describe the extent to which data is scattered. Measures of dispersion help to describe the variability in data. Find the standard deviation. Extreme Absolute and Relative Measures of Dispersion 4.

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## How do you measure dispersion?

Like, Kilograms, Rupees, Centimeters, Marks, etc. Range is used in meteorological department for forecast. It should be easy to understand and compute. Computation of HM, GM of frequency distribution with Equal and Unequal class intervals. Arora: Comprehensive Statistical Methods.

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## Characteristics of a good Measure of Dispersion

Thus to describe data, one needs to know the extent of variability. Severely affected by sampling fluctuations. What do you understand by mean deviation? Thus, good measure of dispersion should be based on the entire data. Cannot be used for open end classes. This is given by the measures of dispersion. What is dispersion and its measures? Explain the concept of standard deviation of combined means. Some of the relative measures of dispersion are given below: Coefficient of Range: It is the Coefficient of Variation: It is the ratio of the standard deviation to the Coefficient of Mean Deviation: This can be defined as the ratio of the mean deviation to the value of the central point from which it is calculated.

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## Measures of Dispersion

For a set of 100 items, the mean and SD are 60 and 6 respectively. It means that the average difference between the values obtained from the sample and the corresponding values from the population should be the least. Standard deviation is the best and the most commonly used measure of dispersion. Relative measures of dispersion are obtained as ratios or percentages of the average. Types of Measures of Dispersion The measures of dispersion can be classified into two broad categories. Statistics 34 of 45 B. It should be affected by fluctuations of sampling.

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## What are the characteristics of a good measure of dispersion?

What fraction of a kg is 100m? Characteristics of a good measure of dispersion The properties of a good ideal measure of dispersion are the same as those of measure of central tendency. Is rigidly defined 2. What do measures of dispersion assess? Extreme items, many times, are not true representatives of the data. In continuous series, the following two methods are followed. In other words, dispersion is the extent to which values in a distribution differ from the average of the distribution. So complicated definitions and calculations are not desirable.

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