Chapter 6, Problem 5E

To determine

To find the new summary statistics.

Explanation of Solution

Given:

Lowest score = 19

Mean = 27

Standard deviation = 3

Third quartile = 30

Median = 28

IQR = 6

Formula:

The convenient rule of thumb is,

  $SAT=40\times ACT+150$

As per rule, only 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,

  $\begin{array}{l}\begin{array}{l}Lowestscore=\text{ 40}\times 19+150=910\hfill \\ Mean=\text{40}\times 27+150=1230\hfill \\ Standarddeviation=\text{40}\times 3=120\hfill \\ Thirdquartile=\text{40}\times 30+150=1350\hfill \\ Median=\text{40}\times 28+150=1270\hfill \end{array}\\ IQR=\text{40}\times 6=240\end{array}$