# Statistics: Standard Deviation

## Introduction

The Standard Deviation is a statistical formula that measures how far values are on average from the mean. In other words, this operation tells how great the spread of data is around the mean. The greater the spread, the higher the standard deviation. In real terms this is important because it tells you about the shape of the data (whether it is normally distributed or not) which makes drawing statistical inferences more accurate.

As this formula is statistical, it is often used in the math and statistical fields. Its principals also lend themselves to teaching, marketing, and sales. More generally however, it helps get an understanding for the shape of the data which is applicable in all types of statistical questions. In Excel, the standard deviation is a formula that has six variations to calculate values for samples and populations with the help of an additional letter. These are: STDEV.S, STDEVA, and STDEV for the sample, and STDEV.P, STDEVPA, and STDEVP for the population.

## Functions

Syntax

=STDEV.S(number1, [number 2], …)

Simplified syntax

=STDEV.S(requires at least one number, optional from here)

This formula function offers some flexibility and depends entirely on your desired results. This function can calculate the mean of a list or a single digit. However, if you want to calculate the standard deviation of a list you must use the colon (i.e. STDEV(A1:A30) or input the list individually (A1, B3, B4, C7, G2, …).

- Exam scores to see if students are performing at the same level.
- Short situational write up
- List of 25 test scores (55 -100). One cell with the standard deviation field.

## Practice

Practice using STDEV by answering the following question in the highlighted cell.

- What is the standard deviation of current health expenditure around the world?

## Answer:

1846.79

## Conclusion

The standard deviation function allows you to calculate the range of differences in data from your average (mean). The statistical feature is used in many fields and instances and is a basic statistical tool.