Mean, median and mode
Mean, median and mode are three kinds of average. The mean shares the total out equally, the median is the middle value in order, and the mode is the most common value.
Maths · Ages 11–12 · 55 minutes
Mean, median, mode and range
Pupils calculate the mean, median, mode and range of a small data set and explain what each one tells you about the data.
Success criteria
- I can find the mode and the range
- I can find the median by ordering the data
- I can calculate the mean and say which average fits best
Key vocabulary
- data
- average
- mean
- median
- mode
- range
- order
- outlier
- spread
You will need
- cards with numbers for ordering
- a set of class data (for example, hand spans in cm or shoe sizes)
- mini whiteboards
- calculators for checking
Curriculum links
- Year 7· England
- Grade 6· United States
- JSS 1· Nigeria
- Class 7· India
- Common Core 6.SP.A.3: Understand that a measure of centre summarises a data set with one number, while a measure of variation describes how values vary.
- Common Core 6.SP.B.5.C: Summarise numerical data with measures of centre (median, mean) and of variability.
- England NC Y6.MA.ST.2: Calculate and interpret the mean as an average.
- England NC KS3.MA.STA.1: Describe and compare distributions using the mean, mode and median and the range.
Practice sheets
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Finding the mode
Finding the range
Finding the median
Finding the mean
Averages and range
1.Starter
8 minutesSeven pupils each measure their hand span and write it on a card: for example 16, 18, 15, 18, 17, 21, 14. Hold them up, unsorted. "What is a typical hand span in this group?" Take answers and ask how they decided. Some will pick the most common number, some the middle one, some will try to "even them out". All three are averages.
2.Teach
15 minutesUse the hand-span cards.
"Mode: the most common value. 18 appears twice, so the mode is 18."
"Median: the middle value once the data is in order." Pupils at the front arrange themselves: 14, 15, 16, 17, 18, 18, 21. "The middle one is the 4th of 7: 17. With an even number of values, there are two middle values, and the median is halfway between them."
"Mean: share the total out equally. Add them all: 119. Divide by how many: 119 ÷ 7 = 17."
"Range: not an average. It tells us how spread out the data is. Biggest minus smallest: 21 − 14 = 7."
Step by step
- Order the data firstIt makes the median, mode and range much easier.
- ModeThe value that appears most often. There can be more than one, or none.
- MedianThe middle value. For an even count, the halfway point between the two middle values.
- MeanAdd all the values and divide by how many there are.
- RangeLargest minus smallest.
Then add a new pupil with a hand span of 45 (a teacher, perhaps). "What happens to each average?" The mean jumps to 20.5; the median moves only to 17.5. "An unusual value, called an outlier, pulls the mean but barely moves the median."
