Question

consider the means of the samples shown in the table. which value is least likely to be the mean of the population from which the samples were taken?
sample | sample mean
1 | 15.2
2 | 17.1
3 | 16.9
4 | 12.2
5 | 18.0
6 | 16.3
7 | 17.4

options: 12.2, 15.3, 16.4, 17.5

Explanation:

Step1: Calculate overall sample mean

First, sum all sample means, then divide by the number of samples.
Sum of sample means: $15.2 + 17.1 + 16.9 + 12.2 + 18.0 + 16.3 + 17.4 = 113.1$
Number of samples: $7$
Overall sample mean: $\frac{113.1}{7} = 16.16$

Step2: Compare options to the mean

Calculate the absolute difference between each option and the overall sample mean:

• $|12.2 - 16.16| = 3.96$
• $|15.3 - 16.16| = 0.86$
• $|16.4 - 16.16| = 0.24$
• $|17.5 - 16.16| = 1.34$

Step3: Identify the farthest value

The value with the largest difference is the least likely to be the population mean.

Answer:

12.2