Year 6 Maths reasoning (SATs): Mean, median, mode and range
Part of the Year 6 Maths reasoning (SATs) statistics and data chapter. Chapter overview · whole chapter on one page
Mean, median, mode and range
Rule
The mean is the total divided by the number of values. The median is the middle value when they are in order. The mode is the most common value. The range is the largest minus the smallest.
Key ideas
- Mean = total / number of values.
- Median: order the values first; with an even number, take halfway between the middle two.
- Range = largest - smallest.
Method. The mean is the total divided by the number of values.
- Add the values. Add up all 5 values.4 + 6 + 8 + 10 + 12 = 40
- Share equally. Divide the total by the number of values, 5.40 / 5 = 8
- Write the answer. 8 cm
Check. 8 x 5 = 40. ✓
Watch out. Check that the total of the values is the mean times the number of values.
Method. Order the values, then find the middle one.
- Put the values in order. Write them from smallest to largest.1, 3, 5, 7, 9
- Find the middle. With 5 values, the middle value is 5.5
- Write the answer. 5
Check. There are 2 values on each side of 5. ✓
Watch out. Always order the values first. The median is not the first or the last value.
Method. Count how often each value appears, and choose the most common.
- Count how many times each value appears. 2 appears 2 time(s), 3 appears 1 time(s), 5 appears 3 time(s), 8 appears 1 time(s)5 appears 3 times
- Choose the most common. The mode is the value that appears most often.5
- Write the answer. 5
Check. 5 appears 3 times, which is the most. ✓
Watch out
Watch out. The median is found after putting the values in order. The first value you see is not the median.
Exam tip
Practice guide. Write the values in order first, then the median, mode and range are easy to see.
Exercise 8D Practice: mean, median, mode and range
Non-calculatorMethod. The mean is the total divided by the number of values.
- Add the values. Add up all 4 values.3 + 5 + 7 + 9 = 24
- Share equally. Divide the total by the number of values, 4.24 / 4 = 6
- Write the answer. 6 cm
Check. 6 x 4 = 24. ✓
Watch out. Check that the total of the values is the mean times the number of values.
Method. The mean is the total divided by the number of values.
- Add the values. Add up all 6 values.10 + 12 + 14 + 16 + 18 + 20 = 90
- Share equally. Divide the total by the number of values, 6.90 / 6 = 15
- Write the answer. 15 kg
Check. 15 x 6 = 90. ✓
Watch out. Check that the total of the values is the mean times the number of values.
Method. Multiply the mean by the number of values, then take away the known values.
- Total needed. The mean is 8 for 5 values, so the total is 8 x 5.8 x 5 = 40
- Subtract the known values. Take away the values you already know.40 - 31 = 9
- Write the answer. 9
Check. 31 + 9 = 40. ✓
Watch out. Find the total first, then the missing value.
Method. Multiply the mean by the number of values, then take away the known values.
- Total needed. The mean is 12 for 4 values, so the total is 12 x 4.12 x 4 = 48
- Subtract the known values. Take away the values you already know.48 - 36 = 12
- Write the answer. 12
Check. 36 + 12 = 48. ✓
Watch out. Find the total first, then the missing value.
Method. Order the values, then find the middle one.
- Put the values in order. Write them from smallest to largest.2, 3, 6, 8, 9, 11, 14
- Find the middle. With 7 values, the middle value is 8.8
- Write the answer. 8
Check. There are 3 values on each side of 8. ✓
Watch out. Always order the values first. The median is not the first or the last value.
Method. Order the values, then find the middle one.
- Put the values in order. Write them from smallest to largest.3, 8, 10, 13
- Find the middle. With 4 values, the middle two values are 8 and 10, so the median is halfway between them.9
- Write the answer. 9
Check. Each side has 2 values. ✓
Watch out. Always order the values first. The median is not the first or the last value.
Method. Count how often each value appears, and choose the most common.
- Count how many times each value appears. 2 appears 1 time(s), 4 appears 2 time(s), 7 appears 1 time(s), 9 appears 3 time(s)9 appears 3 times
- Choose the most common. The mode is the value that appears most often.9
- Write the answer. 9
Check. 9 appears 3 times, which is the most. ✓
Method. Range = largest value minus smallest value.
- Find the largest and smallest values. The largest is 20 and the smallest is 4.20 and 4
- Subtract. The range is the largest minus the smallest.20 - 4 = 16
- Write the answer. 16
Check. 4 + 16 = 20. ✓
Method. Range = largest value minus smallest value.
- Find the largest and smallest values. The largest is 31 and the smallest is 18.31 and 18
- Subtract. The range is the largest minus the smallest.31 - 18 = 13
- Write the answer. 13
Check. 18 + 13 = 31. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. One large value raises the total, so the mean goes up a lot.the mean fits
- Reject the other choices. The median and mode depend on the middle or most common values, not the total.the median and the mode do not fit
- Write the answer. the mean
Check. the mean is the one that fits. ✓
Method. Work out the mean and the median.
- Mean. (10 + 20) / 2 = 15.15
- Median. With two values the median is halfway between them: (10 + 20) / 2 = 15.15
- Write the answer. Because the mean is (10 + 20) / 2 = 15, and with two values the median is halfway between them, which is also 15.
Check. (10 + 20) / 2 = 15. ✓
Method. Find the total from the mean, then take away the four known heights.
- Total. 140 x 5 = 700.700
- Known. 136 + 142 + 138 + 144 = 560.560
- Fifth child. 700 - 560 = 140 cm.140
- Write the answer. 140
Check. 560 + 140 = 700. ✓
Method. With seven values, the median is the fourth value after ordering.
- Position. With 7 values, the median is the 4th value.4th
- Value. The median is 9, so the 4th value is 9.9
- Write the answer. 9
Check. The 4th of 7 values is the middle. ✓
Method. Count how often each value appears, and choose the most common.
- Count how many times each value appears. 2 appears 1 time(s), 5 appears 2 time(s), 8 appears 3 time(s), 9 appears 1 time(s)8 appears 3 times
- Choose the most common. The mode is the value that appears most often.8
- Write the answer. 8
Check. 8 appears 3 times, which is the most. ✓
Method. Range = largest value minus smallest value.
- Find the largest and smallest values. The largest is 17 and the smallest is 3.17 and 3
- Subtract. The range is the largest minus the smallest.17 - 3 = 14
- Write the answer. 14
Check. 3 + 14 = 17. ✓