Zoe is in a maths lesson at school. Her maths teacher chooses four numbers.
The mode of these four numbers is 8.
The range of the numbers is 7.
The mean of the numbers is 11.
Find the maths teachers four numbers.
Answer:
If the mode is 8, more than two of the number must equal 8
If the mean is 11 then:
(X + y + 16 )/ 4 = 11
X + y = 44 – 16
X + y = 28
If x or y = 8 the other number would be 20 and this would give a range > 7
So we know that both x and y must be greater than 8. The larger of the two must be 15 (ie 8 must be the smallest number and the range is 7, so 8 +7 = 15)
Substituting that back in:
X + 15 = 28
X = 13
So the numbers are 8, 8, 13 and 15