Sigma Notation and Calculating the Arithmetic Mean · Exercise 9

A sample of 10 prices is chosen from a population of 100 similar items. The values obtained from the sample, and the values for the population, are given in and respectively.

(a) Is the mean of the sample within $1 of the population mean?
(b) What is the difference in the sample and population means?

\begin{array}{|c|}\hline \text{Prices of the sample} \\ \hline \text{$21} \\ \hline \text{$23} \\ \hline \text{$21} \\ \hline \text{$24} \\ \hline \text{$22} \\ \hline \text{$22} \\ \hline \text{$25} \\ \hline \text{$21} \\ \hline \text{$20} \\ \hline \text{$24} \\ \hline\end{array}

\begin{array}{|c|c|}\hline \text{Prices of the population} & \text{Frequency} \\ \hline \text{$20} & \text{20} \\ \hline \text{$21} & \text{35} \\ \hline \text{$22} & \text{15} \\ \hline \text{$23} & \text{10} \\ \hline \text{$24} & \text{18} \\ \hline \text{$25} & \text{2} \\ \hline\end{array}

OpenStax, Introductory Business Statistics 2e · §2.4 Sigma Notation and Calculating the Arithmetic Mean · Exercise 9