Chapter 6, Problem 6E

To determine

To find the new summary statistics.

Explanation of Solution

Given:

Maximum temperature = 11⁰C

Range = 33⁰C

Mean = 1⁰C

Standard deviation = 7⁰C

Median = 2⁰C

IQR = 16⁰C

Formula:

The conversion formula is,

  ${}^{0}F=9/5^{0}C+32$

As per rule, only range, standard deviation and IQR will be unaffected by constant addition. But these things will be affected by multiplication factor. The new summary statistics after applying the convenient rule of thumb is,

  $\begin{array}{l}\begin{array}{l}Maximumtemperature=\frac{9}{5}\times 11+32={51.8}^{0}F\hfill \\ Range=\frac{9}{5}\times 33={59.4}^{0}F\hfill \\ Mean=\frac{9}{5}\times 1+32={33.8}^{0}F\hfill \\ Standarddeviation=\frac{9}{5}\times 7={12.7}^{0}F\hfill \\ Median=\frac{9}{5}\times 2+32={35.6}^{0}F\hfill \end{array}\\ IQR=\frac{9}{5}\times 16+32={60.8}^{0}F\end{array}$