91Ó°ÊÓ

In the output, the median for the variable $X$is given:

${MEDIAN}_X=8.5$

Ms. Hall multiplies the number of correct answers $X$by $10$:

$G=10X$

Property median (same as for the mean, because both are measures of center):

${MEDIAN}_{aX+b}=a{MEDIAN}_X+b$

Then we can determine the median for $G$:

localid="1649909519882" $$\begin{gathered} {MEDIAN}_G={\text{MEDIAN}}_{10X} \\ =10{\text{MEDIAN}}_X \\ =10(8.5) \\ =85 \end{gathered}$$

The interquartile range is the difference between the third and the first quartile:

${IQR}_X=Q_3-Q_1=9-8=1$

Ms. Hall multiplies the number of correct answers $X$by $10$:

$G=10X$

Property IQR (same as for the standard deviation, because both are measures of spread):

${\mathrm{IQR}}_{aX+b}=a{\mathrm{IQR}}_X$

Then we can determine the interquartile range for $G$:

localid="1649909558629" $$\begin{gathered} {\mathrm{IQR}}_G={\mathrm{IQR}}_{10X} \\ =10{\mathrm{IQR}}_X \\ =10\left(1\right) \\ =10 \end{gathered}$$

Given

$\begin{array}{llllllll}\mathrm{N}& \text{Mean}& \text{Median}& \text{StDev}& \text{Min}& \text{Max}& Q_1& Q_3\\ 30& 7.6& 8.5& 1.32& 4& 10& 8& 9\end{array}$

Result exercise $39a-40a-40b:$

$$\begin{gathered} MEA{N}_G=76 \\ MEDIA{N}_G=85 \\ IQ{R}_G=10 \end{gathered}$$

The fact that the mean is lower than the median suggests that the distribution is skewed to the left (since the mean is influenced by outliers, which have to be very small because the mean is less than the median).