Question

A distribution has the five-number summary shown below. What is the

Answer 1

Answer:

The interquartile range(IQR) is 31.

Step-by-step explanation:

Given:

A distribution has the five-number summary shown below:

24, 36, 42, 57, 65.

Now, to find the interquartile range (IQR).

So, to get the IQR we need to find the quartile 1 and quartile 3:

As, 42 is the median.

Quartile 1 is the average of first half.

24, 36, 42, 57, 65.

Q1 = $\frac{24+36}{2}$

Q1 = $\frac{60}{2}$

Q1 = $30$

Quartile 3 is the average of last half.

24, 36, 42, 57, 65.

Q3 = $\frac{57+65}{2}$

Q3 = $\frac{122}{2}$

Q3 = $61$

Thus, by putting the formula we get IQR:

IQR = Q3 - Q1.

$IQR=61-30$

$IQR=31.$

Therefore, the interquartile range(IQR) is 31.