Before the change
6, 8, 10 has mean 24 ÷ 3 = 8.
Before this page: add and divide numbers, and read a list as a collection of separate values.
The mean is the equal share of the total
The mean gives every value in a list an equal share of the total. Add the values, then divide by how many values there are.
Mean = total of the values ÷ number of values
- The divisor is the count of values, not the largest value.
- The mean has the same units as each value in the list.
Mean of 6, 8 and 10
Add the values and divide the total by the count.
- 6 + 8 + 10 = 24The total is 24.
- 24 ÷ 3 = 8There are three values, so each equal share is 8.
The mean is 8, which is also the middle value because 6 and 10 are equally far from 8. That coincidence does not make the mean and the median the same method.
A mean can lie between the listed values
The total need not divide into whole-number shares. Keep the units and calculate the decimal answer.
Mean time for four journeys
The times are 1.2 hours, 1.5 hours, 1.8 hours and 2.1 hours.
- 1.2 + 1.5 + 1.8 + 2.1 = 6.6The total time is 6.6 hours.
- 6.6 ÷ 4 = 1.65The mean journey takes 1.65 hours.
The answer is between 1.2 hours and 2.1 hours, and it keeps the unit hours. A mean does not have to be one of the values in the list.
An extreme value pulls the mean towards it
Changing one value changes the total, so it changes the equal share. The effect is larger when the changed value is far from the other values.
After the change
Replacing 10 with 30 gives 6, 8, 30, whose mean is 44 ÷ 3 = 14.6….
The mean moves from 8 towards 30, but it does not reach 30 because 6 and 8 are both less than 30. The mean describes the whole list, so one extreme value can affect it strongly.
Use the list to check the mean
A mean of a list lies between its smallest and largest values. Multiplying the mean by the count must also recover the total.
Check 6, 8 and 10
6 ≤ 8 ≤ 10, and 8 × 3 = 24, the original total. Both checks agree with the calculation.
Common mistakes
- Dividing by the largest value For 6, 8 and 10, dividing 24 by 10 gives 2.4. The divisor is the count 3, so the mean is 8.
- Leaving out a value from the total Adding 6 + 8 and dividing by 3 gives 4.6…, but 10 is still in the list. The complete total is 24, so the mean is 8.
- Assuming the mean must be listed The mean of 1.2, 1.5, 1.8 and 2.1 is 1.65 hours, even though 1.65 is not one of the four times.
Summary
- Add every value and divide by the number of values.
- The mean has the same units as the values and can be a decimal not present in the list.
- An extreme value pulls the mean towards it.
- Check that the mean lies between the smallest and largest values, and that mean × count gives the total.