Mean, median, mode, range, and standard deviation

Learning objectives

• Compute mean, median, mode, range and sample standard deviation in a free spreadsheet.
• Choose the summary that fits the data shape and question.
• Report centre and spread with units and sample size.

Core idea

Mean is the balance point, median the middle order statistic, mode the most frequent value, range the extreme gap and standard deviation the typical distance from the mean.

Spreadsheet lab

• =AVERAGE(A2:A31) for the sample mean.
• =MEDIAN(A2:A31) for the middle value.
• =MODE.SNGL(A2:A31) for the most frequent reading.
• =MAX(A2:A31)-MIN(A2:A31) for the range.
• =STDEV.S(A2:A31) for the sample standard deviation (never =STDEV.P for a sample).

Variables and units

Seam-strength readings in newtons (N); n = 30; report mean ± SD with units.

Garment-factory example

Thirty seam-strength readings on a knit polo give mean 168 N and SD 12 N. One outlier of 210 N pulls the mean above the median (163 N), which flags a skew and prompts the analyst to also report median and IQR.

Method

1. Plot the data before summarizing.
2. Compute mean and median; large gap = skew.
3. Report centre + spread + n + units together.

Common mistakes

• Averaging category codes as if they were numbers.
• Reporting SD without the mean it was calculated around.
• Using =STDEV.P when the data are a sample.