Question

identifying an unlikely estimate
sample | sample mean
1 | 16.8
2 | 12.3
3 | 19.0
4 | 17.5
5 | 18.2
6 | 17.5
looking at the means of the samples, which of these values is least likely to be the mean of the population the samples were taken from?
12.3
18.4
19.0
19.5

Explanation:

Step1: Calculate mean of sample means

First, sum all sample means: $16.8 + 12.3 + 19.0 + 17.5 + 18.2 + 17.5 = 101.3$
Then divide by number of samples: $\frac{101.3}{6} \approx 16.88$

Step2: Find value farthest from sample mean average

Calculate absolute differences:

• $|12.3 - 16.88| = 4.58$
• $|18.4 - 16.88| = 1.52$
• $|19.0 - 16.88| = 2.12$
• $|19.5 - 16.88| = 2.62$

The largest difference is for 12.3.

Answer:

12.3