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 = [tex]\frac{24+36}{2}[/tex]
Q1 = [tex]\frac{60}{2}[/tex]
Q1 = [tex]30[/tex]
Quartile 3 is the average of last half.
24, 36, 42, 57, 65.
Q3 = [tex]\frac{57+65}{2}[/tex]
Q3 = [tex]\frac{122}{2}[/tex]
Q3 = [tex]61[/tex]
Thus, by putting the formula we get IQR:
IQR = Q3 - Q1.
[tex]IQR=61-30[/tex]
[tex]IQR=31.[/tex]
Therefore, the interquartile range(IQR) is 31.
