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?

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?

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

Solution

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.

Step 1: Calculate Standard Deviation for Males

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

Step 2: Calculate Standard Deviation for Females

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

Step 3: Compare Standard Deviations

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