Mean, median, mode and range explained (with examples)

Test scores: 7, 3, 9, 7, 4, 10.

• In order: 3, 4, 7, 7, 9, 10 (6 values)
• Mean: $(3 + 4 + 7 + 7 + 9 + 10) \div 6 = 40 \div 6 \approx 6.67$
• Median: six values, so halfway between the 3rd and 4th: $(7 + 7) \div 2 = 7$
• Mode: 7
• Range: $10 - 3 = 7$

Check your own data with our mean, median and mode calculator.

Exam questions often ask you to compare two groups. Make two comparisons, one of an average and one of spread, and say what they mean in context:

"Class A had a higher median score (72 vs 65), so they generally did better. Class B had a smaller range (20 vs 35), so their scores were more consistent."

For data in a frequency table, multiply each value by its frequency to find the total:

Mean $= 9 \div 10 = 0.9$ goals. The mode is 1 (highest frequency). With 10 values, the median is halfway between the 5th and 6th values, both 1, so it's 1.

• Finding the median without ordering the values.
• Giving the frequency as the mode instead of the value.
• Dividing by the wrong count (the number of rows instead of the total frequency).
• Writing the range as "3 to 10" instead of one number.

For 5, 8, 2, 8, 6, 1, find the mean, median, mode and range. Answers: mean 5, median 5.5, mode 8, range 7. More in the averages and spread topic guide.

When data are grouped into classes, you don't know the exact values, so you estimate the mean using the midpoint of each class:

Estimated mean $= 110 \div 10 = 11$ cm. It's an estimate because each value is assumed to sit at the middle of its class. For grouped data you give the modal class ($10 \le h < 20$) rather than a single mode.