# 4.3.8 Standard Deviation

### Standard Deviation

#### Mean

• A mean value is what is usually meant when the term “average” is used in biology

Mean = sum of all measurements ÷ number of measurements

• Problems with the mean occur when there are one or two unusually high (or low) values in the data (outliers) which can make the mean too high (or too low) to reflect any patterns in the data
• The mean is sometimes referred to as X̄ in calculations

#### Standard Deviation

• The mean is a more informative statistic when it is provided alongside the standard deviation
• Standard deviation measures the spread of data around the mean value
• It is very useful when comparing consistency between different data sets
• The mean must be calculated before working out the standard deviation

#### Worked Example

15 rats were timed how long it took them to reach the end of a maze puzzle. Their times, in seconds, are given below. Find the mean time.

12, 10, 15, 14, 17,

11, 12, 13, 9, 21,

14, 20, 19, 16, 23

Step 1: Calculate the mean

12 + 10 + 15 + 14 + 17 + 11 + 12 + 13 + 9 + 21 + 14 + 20 + 19 + 16 + 23 = 226

226 ÷ 15 = 15.067

Step 2: Round to 3 significant figures

Mean (X̄) = 15.1 seconds

#### Worked Example

The ear lengths of a population of rabbits was measured.

Ear lengths (mm): 62, 60, 59, 61, 60, 58, 59, 60, 57, 56, 59, 58, 60, 59, 57

Calculate the mean and standard deviation.

Step 1: Calculate the mean

Mean = 885 ÷ 15 = 59 mm

Step 2: Find the difference between each value and the mean

Subtract the mean from each value to find the difference

Example: 62 – 59 = 3

Step 3: Square each difference

Square the difference for each value

Example: 32 = 9

Step 4: Total the differences

Step 5: Divide the total by (n-1) to get value A

37 ÷ (15 – 1) = 37 ÷ 14 = 2.642

Step 6: Get the square root of value A

Standard Deviation = 1.63

#### Exam Tip

Constructing a table like the one above can help you to keep track of all your calculations during the exam!

Close