$18$ . Use the data in the table. Describe the shape of the distribution, and tell the measures of center and variation that best represent the data. $\newline$ \begin{tabular}{|l|c|c|c|c|c|c|c|} $\newline$ \hline Interval & $1-10$ & $11-20$ & $21-30$ & $31-40$ & $41-50$ & $51-60$ & $61-70$ \\ $\newline$ \hline Frequency & $21$ & $28$ & $21$ & $15$ & $12$ & $6$ & $3$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ (A) skewed left; median and standard deviation $\newline$ (B) symmetric; mean and five-number summary $\newline$ (C) skewed right; median and five-number summary $\newline$ (D) symmetric; mean and standard deviation

Full solution

18

. Use the data in the table. Describe the shape of the distribution, and tell the measures of center and variation that best represent the data.

\newline

\begin{tabular}{|l|c|c|c|c|c|c|c|}

\newline

\hline Interval &

1-10

11-20

21-30

31-40

41-50

51-60

61-70

\newline

\hline Frequency &

21

28

21

15

12

6

3

\newline

\hline

\newline

\end{tabular}

\newline

(A) skewed left; median and standard deviation

\newline

(B) symmetric; mean and five-number summary

\newline

\newline

(D) symmetric; mean and standard deviation

Analyze Data Shape: Analyze the frequency distribution to determine the shape of the data. The frequencies decrease as the intervals increase, indicating a concentration of data on the lower end and fewer frequencies as the values increase. This suggests a right-skewed distribution.
Identify Center and Variation: Identify the measures of center and variation that best represent the data. For skewed distributions, the median is a better measure of center because it is less affected by extreme values. The five-number summary $\left(\text{minimum}, \text{first quartile}, \text{median}, \text{third quartile}, \text{maximum}\right)$ provides a good representation of the spread and central tendency in skewed data.