There are seven cousins together at a family reunion. The youngest is 5 years old and the range between ages is 7. Three of the other cousins are 7, 10, and 12 years old. The mean and median age of cousins is 9 years old. The mode is 12 years old.

Find the ages of all seven cousins. Show how you found them.

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abidemiokin abidemiokin · Answer 1 · 2021-09-28T07:12:26+02:00

The ages of all the seven cousins are 5, 7, 8, 9, 10, 12, 12.

The following parameters are given in the question as shown.

Youngest age = 5 years

Range between ages = 7 years

Three of the other cousins are 7, 10 and 12 years old.

Mean = 9 years

Median = 9 years

Mode = 12 years

First need to get the highest Age.

Range = Highest Age - Lowest Age

Substitute the given values

7 = Highest Age - 5

Highest Age = 7 + 5

Highest Age = 12 years

Since mode is 12 years, this means that 12 years will occur most.

The possible ages of the seven cousins will be

5, 7, x, 9, 10, 12, 12 where x is unknown

Get the unknown.

Recall that the mean Age is 9

Mean = Sum of data/ sample size

9 = 5+7+x+9+10+12+12/7

9 × 7 = 5+7+x+9+10+12+12

63 = 55 + x

x = 63 - 55

x = 8

Therefore the ages of all the seven cousins are 5, 7, 8, 9, 10, 12, 12.

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