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Range

**Range** is the simplest measure of variation in a set of data. It is equal to the largest value minus the smallest value. Range = maximum value - minimum value.

Standard Deviation

**Standard Deviation** is another measure of the spread of data. It is derived from the distance of each point in the sample from the sample mean. These distances are called deviations. Standard deviation is calculated by first calculating the sum of the square of the deviations (called sum of squares SS). SS is then divided by one less than the sample size. Now if we take the square root of this value, we arrive at the standard deviation (s). In other words, standard deviation is the positive square root of the variance Standard deviation cannot be less than zero. If it is zero, then all sample values are the same.

Variance

**Variance** is another measure of the spread of data. It is derived from the distance of each point in the sample from the sample mean. These distances are called deviations. Standard deviation is calculated by first calculating the sum of the square of the deviations (called sum of squares SS). SS is then divided by one less than the sample size to give us the variance of the data set.

Inter Quartile Range

**Interquartile Range (IQR)** is the difference between the third and the first quartile (Q3-Q1). Quartiles divides the sample into four equal parts. First quartile has 25% of the points below it and 75% above it. Similarly, third quartile will have 75% points below it and 25% above it.

IQR = value of point at Q3 - value of point at Q1.

An application oriented question on the topic along with responses can be seen below. The best answer was provided by Mohan P B on 31st August 2018.

## Question

## Vishwadeep Khatri 265

Q. 88

Is standard deviation a superior measure of dispersion as compared to range and interquartile range? Are there any specific scenarios where you will choose to use range instead of standard deviation?Note for website visitors- Two questions are asked every week on this platform. One on Tuesday and the other on Friday.All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening as per Indian Standard Time.The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term.## Link to post

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