91影视

Number of IQ scores$=10$

The IQ scores are$145,139,126,122,125,130,96,110,118,118$

Inter quartile range

$$\begin{gathered} IQR=Q_3鈭�Q_1 \\ {Q}_3=3脳{(\frac{n+1}{4})}^{th}term \\ {Q}_1={(\frac{n+1}{4})}^{th}term \end{gathered}$$

Arranging in ascending order

$96,110,118,118,122,125,126,130,139,145$

The IQR for the $10$scores can be calculated as follows

$$\begin{gathered} Q_3=3脳{(\frac{10+1}{4})}^{th}term \\ {Q}_3=3脳{2.75}^{th}term={8.25}^{th}term \\ {Q}_3=8^{th}term+\frac{1}{4}脳(9^{th}term鈭�8^{th}term) \\ {Q}_3=130+\frac{1}{4}脳(139鈭�130)=132.25 \end{gathered}$$

The lower quartile is

$$\begin{gathered} Q_1={(\frac{10+1}{4})}^{th}term \\ {Q}_1={2.75}^{th}term \\ {Q}_1=2^{th}term+\frac{3}{4}脳(3^{th}term鈭�2^{th}term) \\ {Q}_1=110+\frac{3}{4}脳(118鈭�110)=116 \end{gathered}$$

Therefore the IQR for $10$scores is

$132.25鈭�116=16.25$

After deleting $96$, find the IQR.

The updated set of results is as follows:

$110,118,118,122,125,126,130,139,145$

The IQR for the $9$scores can be calculated as follows

$$\begin{gathered} Q_3=3脳{(\frac{9+1}{4})}^{th}term \\ {Q}_3=3脳{2.5}^{th}term={7.5}^{th}term \\ {Q}_3=7^{th}term+\frac{1}{2}脳(8^{th}term鈭�7^{th}term) \\ {Q}_3=130+\frac{1}{2}脳(139鈭�130)=134.5 \end{gathered}$$

The lower quartile is

$$\begin{gathered} Q_1={(\frac{9+1}{4})}^{th}term \\ {Q}_1={2.5}^{th}term \\ {Q}_1=2^{th}term+\frac{1}{2}脳(3^{th}term鈭�2^{th}term) \\ {Q}_1=118+\frac{1}{2}脳(118鈭�118)=118 \end{gathered}$$

Therefore the IQR for $9$scores is

$134.5鈭�118=16.5$

As a result, the IQR of scores after deleting $96(=16.5)$ is somewhat higher than the original$(=16.25)$ invalidating the subpart statement (e).