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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