Questions: Male and female populations of tortoises under 80 years old are represented by age in the table below. Complete parts (a) through (d). Age Males Females 0-9 10 6 10-19 13 6 20-29 12 12 30-39 15 20 40-49 24 22 50-59 24 22 60-69 16 20 70-79 13 14 (d) Which gender has the higher dispersion in age?

Solution Steps

To determine which gender has the higher dispersion in age, we can calculate the standard deviation for the male and female populations across the given age groups. The standard deviation is a measure of the amount of variation or dispersion in a set of values. We will compute the standard deviation for both males and females and compare the results.

The standard deviation for the male population across the age groups is calculated as follows: \[ \sigma_{\text{males}} = 4.9859 \]

The standard deviation for the female population across the age groups is calculated as follows: \[ \sigma_{\text{females}} = 6.3196 \]

To determine which gender has the higher dispersion, we compare the standard deviations:

• \(\sigma_{\text{males}} = 4.9859\)
• \(\sigma_{\text{females}} = 6.3196\)

Since \(6.3196 > 4.9859\), the female population has a higher dispersion in age.

Final Answer