Question

the parallel dotplots below display the girths (belly circumference) of some male and female pigs. which of the following statements is true? pig girth by gender the iqr for the distribution of girths is larger in female pigs. the range for the distribution of girths is larger in male pigs. the standard deviation for the distribution of girths is smaller in female pigs. the standard deviation for the distribution of girths is about the same for both male and female pigs. gender m f 22 24 26 28 30 32 girth in inches

Explanation:

Step1: Recall definitions

IQR is the inter - quartile range (Q3 - Q1), range is max - min, and standard deviation measures spread.

Step2: Analyze range

For male pigs, the minimum girth is around 24 inches and the maximum is around 32 inches, so range = 32 - 24 = 8 inches. For female pigs, the minimum is around 22 inches and the maximum is around 30 inches, so range = 30 - 22 = 8 inches. So the ranges are equal.

Step3: Analyze IQR

Without exact data points, it's hard to calculate IQR precisely, but visually the spread of the middle 50% of data doesn't suggest a clear difference between male and female pigs.

Step4: Analyze standard deviation

Visually, the data points for male and female pigs are spread out in a similar way around their centers. The data for male pigs has a few more extreme values, but overall the spread of the data relative to the mean seems about the same for both genders.

Answer:

The standard deviation for the distribution of girths is about the same for both male and female pigs.