What is the Interquartile Range (IQR) of the pumpkin weights?

A) 10

B) 8

C) 4

D) 15

What is the range of the pumpkin weights?

a) 8

b) 14

c) 6

d) 11

What percent of the pumpkins weigh between 16 and 24 pounds?

a) 50%

b) 25%

c) 75%

- The Interquartile Range (IQR) of the pumpkin weights is 4.

Option C is correct.

- The range of the pumpkin weights is 14.

Option B is correct.

- The percent of the pumpkins that weigh between 16 and 24 pounds is 25%.

Option B is correct.

Step-by-step explanation:

The box and whiskers plot representing the distribution of pumpkin weight is missing from the question, but it was obtained from the internet and is attached to this solution of the question.

Note that a box and whiskers plot shows 5 major information about the distribution of data. It shows:

- The maximum variable

This is easily read from the whiskers, the tail end on the whiskers on the right hand side. For this distribution, the maximum value is 24.

- The minimum variable

This is also easily read from the whiskers, the very beginning of the whiskers on the left. For this distribution, the minimum value is 10.

- The first Quartile or the 25th percentile

This is the beginning of the boxplot. For this distribution, it is 12.

- The third quartile or the 75th percentile

This is the end of the boxplot. For this distribution, it is 16.

- The Median

This is represented by the point that thay coincides to the line drawn on the boxplot. For this distribution, the Median is 15.

1) The Interquartile Range (IQR)

The IQR is a measure of the spread of the distribution and it is given mathematically as the difference between the third and first quartile.

IQR = (Third quartile or 75th percentile) - (First quartile or 25th percentile)

IQR = 16 - 12 = 4

2) The range.

The range is given as the difference between the maximum and minimum values of a distribution.

Range = (Maximum value) - (Minimum Value) = 24 - 10 = 14.

3) What percent of the pumpkins weigh between 16 and 24 pounds?

16 is third quartile or 75th percentile of the distribution; meaning that, the weight 16 is bigger than 75% of the different weights of the pumpkins.

24 is the maximum weight of pumpkin in the distribution. The weight 24 is bigger than any other weight of pumpkin in the distribution.

Hence, the percent of the distribution that will weigh between 16 and 24 pounds is the percent of the distribution that will lie between the third quartile or 75th percentile and the maximum value of the distribution. That is easily 25% of the distribution.

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