Statistics Measures Of Dispersion

Statistics Measures Of Dispersion!!!

It is important to understand measures of Dispersion in Statistics. This equips the Manager with a more powerful analysis skill as compared to just understanding measures of Central Tendency.

A basic measure used to summarize data is the measure of “Dispersion”

Dispersion measures indicate the spread of data points around the central tendency measure
(say mean), and give an idea of variability in the data.

There are different ways to measure Dispersion as well, and we need to use the
appropriate measure, given a situation.

Some popular measures of Dispersion are:

1)Range

2)Standard Deviation

3)Inter-Quartile Range

4)Coefficient of Variation

RANGE

Measure of dispersion

Difference between largest & smallest observations

Case Study

Mr. X had to cross five different states on his way from Delhi to Bangalore. The petrol prices were different across states. What is the range of petrol prices?

          Rs. 45 Rs. 47.50 Rs. 48 Rs. 46.50 Rs. 49.50

Ordering the data from least to the greatest, we get:

          Rs. 45 Rs. 46.50 Rs. 47.50 Rs. 48 Rs. 49.50

Highest – Lowest = Rs. 49.50 – Rs. 45 = Rs. 4.50.

The range of petrol prices is Rs. 4.50

Interquartile Range

Difference between third & first quartiles

e.g. If you have 100 numbers (not 1 to 100 but some 100 numbers), the number that falls between the 25th & 26th position when the numbers are ranked in ascending order is called the 1st quartile(Q1); the one that falls between the 50th & 51st position is the 2nd quartile; and the one that falls between the 75th & 76th position is called the 3rd quartile (Q3). Basically, you order the data and break into four parts containing equal number of observations

Inter-quartile range measures the spread in the middle 50% of the data   Interquartile Range  =  Q3 – Q1

Caveat: Not affected by extreme values (as values below Q1 and beyond Q3 are not used in calculating IQR). This makes the IQ range a very important measure Of Dispersion in Statistics

For Case Study on understanding Interquartile Ranges using a BOX Plot refer our article here on Box Plot

Interesting Note: The second quartile is also called the Median (Q2) – This number will be in the middle with 50% of observations above & below

Variance & Standard Deviation

  • Most commonly used measures
  • These measures take into account the distribution of data between the extreme values, unlike the Range
  • These measures indicate the spread of the data around the mean (x- in case of sample mean or mpopulation mean)

Coefficient Of Variation

  1. Measure of relative dispersion
  2. Always a %
  3. Shows variation relative to mean
  4. Used to compare 2 or more groups

Skewness

Skewness gives an idea of how far to the left, or how far to the right is the data distribution skewed, as compared to a symmetrical distribution. Left skew is also called positive skew, and right skew is called a negative skew. Some graphical examples are given below.

Kurtosis

Kurtosis is another measure of shape that indicates if the distribution is sharp & peaked or if it is flat, when compared to a normal distribution.

KeyTakeaways:

In a lot of practical situations, understanding the Central Tendency & Dispersion to a large extent explains the entire distribution of data – around what value is the data grouped (mean, median etc.), and what is the spread around that value (Standard Deviation, IQR etc.)

However, in some cases, just knowing measures of central tendency measure and dispersion does not help in understanding the distribution of the data completely. In addition to these, we also need to know shape measures to understand the data distribution completely. Two such shape measures are “Skewness” & “Kurtosis”.

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