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 people age 12–15 who had over 500 text messages, we'll first need to determine the total number of people in the 12–15 age group and then calculate the relative frequency of those who fall into the over 500 messages category.

From the table, the number of text messages for the age group 12–15 is as follows:

  • 0–200 messages: 24
  • 201–500 messages: 47
  • Over 500 messages: 78

Now, we calculate the total number of people in the 12–15 age group:

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

Next, we find the number of people in this age group who had over 500 messages, which is 78.

Now, we calculate the relative frequency:

\[ \text{Relative frequency} = \frac{\text{Number of people with over 500 messages}}{\text{Total number of people in age group}} = \frac{78}{149} \]

Now we compute the relative frequency:

\[ \frac{78}{149} \approx 0.5235 \]

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

\[ 0.5235 \times 100 \approx 52.35% \]

Finally, rounding to the nearest tenth, the relative frequency of the people age 12–15 who had over 500 messages is:

\[ \boxed{52.4%} \]