Components of a Statistical Study (College Board AP® Statistics): Study Guide

A common mistake is to confuse a population with a sample. Ask yourself "who or what does the researcher want to know about?" — the answer is the population, not the sample. The sample is just the subset of the population that the researcher was actually able to collect data from.

AP exam questions require responses to be in context. A response that just gives a number or a generic statement (e.g. "the median is greater than the mean") will not earn full credit without also identifying what the values represent in the real-world scenario.

A researcher wants to investigate the average number of hours per week that adults in a city volunteer in their local community. There are 138,000 adults living in the city. The researcher randomly selects 500 of them to take part in a survey, and finds that the average number of hours per week these 500 adults volunteer is 2.3 hours.

(a) Identify the population.

(b) Identify the sample.

(c) State the values of and .

(d) Is "2.3 hours per week" a parameter or a statistic? Justify your answer.

Answer:

(a)

The population is all items or individuals of interest

The researcher wants to know about adults in the city

The population is all 138,000 adults living in the city

(b)

The sample is the subset of the population that data are obtained from

The sample is the 500 adults selected by the researcher to take part in the survey

(c)

is the population size and is the sample size

and

(d)

A parameter describes a characteristic of the population; a statistic is computed from the sample

2.3 hours is the average for the 500 adults in the sample, not for all 138,000 adults in the city

2.3 hours per week is a statistic, because it is the mean computed from the sample of 500 adults rather than the mean of the entire population of 138,000 adults