Question

Consider a sample data set with the following summary

statistics: s= 95, Q_L = 72, Q_U = 195.

a. Calculate IQR.

b. Calculate IQR/s.

c. Is the value of IQR/sapproximately equal to 1.3? Whatdoes this imply?

Short answer

a. The value of IQR is 123

b. The value of IQR/s is 1.3

c. The value of IQR/s is approximately 1.3, implies that the data is normally distributed.

Step-by-step solution

Given Information

The summary statistics are given by,

$s=95,Q_L=72,Q_U=195$

Calculating IQR

a.

The IQR is,

$$\begin{gathered} IQR=Q_U-Q_L \\ =195-72 \\ =123 \end{gathered}$$

Thus, the IQR is 123.

Calculating IQR/s

b.

$$\begin{gathered} \frac{IQR}{s}=\frac{123}{95} \\ =1.294737 \\ 𝆏1.3 \end{gathered}$$

Thus, the IQR/s is 1.3.

Interpretation of IQR/s

C.

Here the value of IQR/s is approximately 1.3. This means that the data is normally distributed.