Standard deviation

Although range and interquartile range are a measure of spread both of them have issues as they only take into account two values in the calculation. So we need to consider other measures of spread, this includes standard deviation.

For Extension students, you may wish to investigate the standard deviation below to explore what it actually is:

Standard Deviation

Standard deviation has a complex formula so instead of doing it by hand, we use our calculators.

Example:

Using your calculator and the videos above lets find the standard deviation of the following data sets:

Answers

a) 5.75

b) 2.26

Comparing mean and standard deviation

The mean and standard deviation are really important statistical calculations that help us to easily analyse and compare different data sets. Have a look at the question below:

Solutions

ai. Girls: mean = 163 cm and standard deviation = 7.6

ii. Boys: mean = 168.33 cm and standard deviation = 8.64

iii. Class: mean = 165.76 cm and standard deviation = 8.58

b) The group of boys have a greater spread of heights as the standard deviation is the largest.

c) The mean height of the boys was higher, but the girls had a smaller spread of data.

Technology: Google Sheets

We can also calculate the standard deviation in google sheets.

Interdisciplinary Component

For your data set can you use technology to calculate the standard deviation. Compare this to your range and interquartile range from before, what can you deduce about the data. Have you got any outliers in your data and has that affected your range more than your standard deviation.

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