Question

The distribution of text message usage by age group, broken down by daily message volume, is shown in the table.
Number of Text Messages
0–200 201–500 Over 500
Age 12–15 24 47 78
16–19 20 35 97
20–23 55 67 177
Given the data in the table about the number of text messages per day, what is the relative frequency of the people age 12–15 who had over 500 messages? Round the percentage to the nearest tenth.

Answer 1

To find the relative frequency of the people aged 12–15 who had over 500 messages, we can use the following formula:

\[
\text{Relative Frequency} = \frac{\text{Number of people in the specific category}}{\text{Total number of people in that age group}}
\]

From the table, we can see that the number of people aged 12–15 who had over 500 messages is 78.

Next, we need to find the total number of people aged 12–15. We do this by adding up all the categories for that age group:

\[
\text{Total for age 12–15} = 24 + 47 + 78 = 149
\]

Now we can calculate the relative frequency:

\[
\text{Relative Frequency} = \frac{78}{149}
\]

Calculating this gives:

\[
\text{Relative Frequency} \approx 0.5235
\]

To express this as a percentage, we multiply by 100:

\[
0.5235 \times 100 \approx 52.35
\]

Rounding to the nearest tenth of a percent:

\[
\text{Relative Frequency} \approx 52.4\%
\]

Therefore, the relative frequency of the people age 12–15 who had over 500 messages is approximately **52.4%**.