Statistics
Grade 1-3Mean, Median & Mode
Mean, median and mode are three different ways of describing the "typical" value in a set of data, and each is found using a different method. This lesson covers finding the mode, median and mean, finding a missing value when the mean is known, and comparing the means of two data sets.
What you need to know
- Mean is the total of the values divided by how many values there are.
- Median is the middle value when the data is in order; average the middle two if there is an even number.
- Mode is the most common value; there can be none, one, or more than one.
- The mean is affected by extreme values; the median is not.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Finding the mode
The mode is the value that appears most often in a list of data. There can be more than one mode, or no mode at all if every value appears the same number of times.
In the list 3, 7, 5, 7, 2, 7, 9, the number 7 appears three times, more than any other value, so the mode is 7.
Finding the median
The median is the middle value once the data has been put in order. If there is an odd number of values, the median is the single middle value. If there is an even number of values, the median is the mean of the two middle values.
For the list 5, 2, 9, 4, 7, ordering gives 2, 4, 5, 7, 9, so the median is the middle value, 5. For the list 8, 3, 6, 1, ordering gives 1, 3, 6, 8, so the median is (3 + 6) ÷ 2 = 4.5.
Finding the mean
The mean is found by adding up all the values and dividing by how many values there are.
For the list 4, 8, 6, 10, 2, the sum is 4 + 8 + 6 + 10 + 2 = 30, and there are 5 values, so the mean is 30 ÷ 5 = 6.
Finding a missing value and comparing means
If the mean and all but one value are known, multiply the mean by the total number of values to find the total sum, then subtract the sum of the known values to find the missing one.
To compare two data sets, find the mean of each one separately, then compare these two mean values directly, rather than comparing the totals or individual values.
Worked examples
Three exam-style questions, fully solved
Find the mode of this list of numbers: 3, 7, 5, 7, 2, 7, 9.
Easy- 1.Count how many times each number appears: 7 appears three times, more than any other number
Answer: 7
The mean of 5 numbers is 8. Four of the numbers are 6, 9, 7 and 10. Find the fifth number.
Medium- 1.Find the total sum of all 5 numbers: 5 × 8 = 40
- 2.Find the sum of the four known numbers: 6 + 9 + 7 + 10 = 32
- 3.Subtract to find the fifth number: 40 − 32
Answer: 8
Team A scored these points in 5 matches: 12, 15, 9, 18, 21. Team B scored these points in 5 matches: 14, 16, 10, 20, 10. Which team had the higher mean score?
Hard- 1.Find the mean for Team A: (12 + 15 + 9 + 18 + 21) ÷ 5 = 15
- 2.Find the mean for Team B: (14 + 16 + 10 + 20 + 10) ÷ 5 = 14
- 3.Compare the two means: 15 is greater than 14
Answer: Team A had the higher mean score
Practice
6 questions, marked instantly
Type an answer and check it. The worked solution appears once you have had a go. No login needed, and your progress saves in this browser.
Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Work out the mean of 4, 8, 6, 10, 7.
Work out the median of 3, 9, 1, 7, 5.
Work out the mode of 2, 5, 3, 5, 8, 5, 2.
Work out the median of 6, 2, 9, 4.
Five numbers have a mean of 12. Work out the total of the five numbers.
Four numbers have a mean of 15. Three of them are 12, 18 and 14. Work out the fourth number.
Avoid these
The mistakes students make most often
Forgetting to order the data before finding the median, which can give the wrong middle value.
For an even number of values, forgetting to average the two middle values, and instead picking just one of them as the median.
Confusing the mode, median and mean with each other, such as giving the most frequent value when the mean was asked for.
When finding a missing value from the mean, forgetting to multiply the mean by the total count first, and instead just subtracting the known values from the mean itself.
When comparing two means, comparing the totals instead of the means, which gives the wrong answer if the two data sets have different numbers of values.
FAQ
Questions students and parents ask
Before this topic, make sure you know
What to learn next
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