What numbers have the mean of 10 and the range of 12?

four and sixteen

16 - 4 = 12

16 + 4 = 20 then 20 / 2 = 10

Half of 12 is 6, therefore the two numbers 10 - 6 = 4 and 10 + 6 = 16 will have a mean of 10 and a range of 12.

Further numbers can be added between 4 and 16 as long as their mean is still 10, eg the data sets:

• {4, 16}
• {4, 10, 16}
• {4, 8, 12, 16}
• {4, 8, 10, 12, 16}
• {4, 7, 9, 14, 16}

all have a mean of 10 and a range of 12. There is an infinity of such sets.