Question

looking at the means of these samples, which value is most likely to be the mean of the population from which the samples were taken?
sample number|sample mean
1|11.8
2|12.5
3|15.1
4|14.3
5|13.0
6|12.9
10.2
11.5
12.9
15.4

Explanation:

Step1: Recall the concept of sample - mean as an estimator

The sample means are estimates of the population mean. The population mean is likely to be close to the values of the sample means.

Step2: Analyze the given sample means

The sample means are 11.8, 12.5, 15.1, 14.3, 13.0, 12.9. We need to find the option that is closest to these values.

Step3: Calculate the differences

For option 10.2:

11.8 - 10.2

= 1.6,

12.5 - 10.2

= 2.3,

15.1 - 10.2

= 4.9,

14.3 - 10.2

= 4.1,

13.0 - 10.2

= 2.8,

12.9 - 10.2

= 2.7

For option 11.5:

11.8 - 11.5

= 0.3,

12.5 - 11.5

= 1,

15.1 - 11.5

= 3.6,

14.3 - 11.5

= 2.8,

13.0 - 11.5

= 1.5,

12.9 - 11.5

= 1.4

For option 12.9:

11.8 - 12.9

= 1.1,

12.5 - 12.9

= 0.4,

15.1 - 12.9

= 2.2,

14.3 - 12.9

= 1.4,

13.0 - 12.9

= 0.1,

12.9 - 12.9

= 0

For option 15.4:

11.8 - 15.4

= 3.6,

12.5 - 15.4

= 2.9,

15.1 - 15.4

= 0.3,

14.3 - 15.4

= 1.1,

13.0 - 15.4

= 2.4,

12.9 - 15.4

= 2.5

The option 12.9 has the smallest overall differences from the sample - means.

Answer:

12.9