Question

The pounds of produce purchased at a grocery store on Friday between 1:00 p.m. and 6:00 p.m. is

shown:
8, 14, 15, 20, 9, 7, 5, 10, 12, 16, 9, 11, 13, 8, 14, 7, 11, 18, 20, 24, 15, 10, 8, 5, 4, 6, 10, 7, 9, 11, 13, 12, 11, 14, 13,
10, 8, 17, 9, and 11.
Which set of sample data is needed to best represent the population mean?
the first five customers
the first ten customers
the first twenty customers
the first twenty-five customers

Answer 1

The correct option is;

The first twenty-five customers

Explanation:

For the given data, by calculation, we have;

The population average = 11.45

The average of the first five customers = 13.2

The average of the first ten customers = 11.6

The average of the first twenty customers = 12.5

The average of the first twenty-five customers = 11.72

Therefore both the first ten customers and the first twenty-five customers have good representation of the population mean with the mean of the first ten customers having a value of 11.6 is more closer to the population mean than the mean of the first twenty-five customers

However, by the central limit theorem, as the size of the sample continues to be increasingly larger, it becomes more and more representative of the population mean, this is more so because when the data is sorted, the population mean will be better represented by the mean of a large sample size

Hence the set of sample data needed to best represent the population mean is the first twenty-five customers.