Question

the parallel dotplots below display the girths (belly circumference) of some male and female pigs. which of the following statements is true? 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.

Explanation:

Step1: Analyze the range

• Range = maximum - minimum.
• For male pigs: maximum is 32, minimum is 24. Range = \(32 - 24=8\).
• For female pigs: maximum is 30, minimum is 21. Range = \(30 - 21 = 9\). So the range for female pigs is larger.

Step2: Analyze the IQR

• IQR = \(Q_{3}-Q_{1}\).
• For male pigs: \(Q_{1}\) is around 26, \(Q_{3}\) is around 28. IQR = \(28 - 26=2\).
• For female pigs: \(Q_{1}\) is around 24, \(Q_{3}\) is around 27. IQR = \(27 - 24 = 3\). So the IQR for female pigs is larger.

Step3: Analyze the standard deviation

• Standard deviation measures the spread.
• The data points for female pigs are more spread out (from 21 to 30) compared to male pigs (from 24 to 32). So the standard deviation for female pigs is larger.

Answer:

The IQR for the distribution of girths is larger in female pigs.