Consider the ordered data set {a,b,c,d}where a,b,c,∈ Z+.

Given that the mode is 3, the median is 2.5, and the range is 2 find the mean of the data set correct to 3 significant figures.

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1 Answer

(a+b+c+d)/4 is the mean, where d≥c≥b≥a. The median is (b+c)/2=2.5; the range d-a=2. So b+c=5, therefore (a+5+d)/4 is the mean. And d=a+2, so (a+5+a+2)/4=(2a+7)/4 is the mean. The value 3 is repeated. Since the median is 2.5, b and c can’t both be 3. If c=d=3, then b=5-c=2; if a=b=3, then c=2.  Since c must be greater than b by definition, then the former must be true: (a,b,c,d)=(a,2,3,3). Therefore a=3-2=1, so the dataset is 1,2,3,3 and the mean is 9/4=2.25.

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