se the table to answer the 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.

1 answer

To find the relative frequency of the people aged 12–15 who sent over 500 messages, we first need to determine the total number of people in that age group, and then find the proportion of that total who sent over 500 messages.

From the table for the age group 12–15:

  • Number of people sending 0–200 messages: 24
  • Number of people sending 201–500 messages: 47
  • Number of people sending over 500 messages: 78

Total number of people aged 12–15: \[ 24 + 47 + 78 = 149 \]

Now, to find the relative frequency of those who sent over 500 messages: \[ \text{Relative Frequency} = \frac{\text{Number of people who sent over 500 messages}}{\text{Total number of people in that age group}} \]

Substituting the numbers we have: \[ \text{Relative Frequency} = \frac{78}{149} \]

Calculating this gives: \[ \text{Relative Frequency} \approx 0.5235 \]

To convert this to a percentage: \[ 0.5235 \times 100 \approx 52.35% \]

Rounding this to the nearest tenth: \[ \text{Relative Frequency} \approx 52.4% \]

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