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

From the table for age group 12–15, we have the following data:

  • Number of messages in the range 0–200: 24
  • Number of messages in the range 201–500: 47
  • Number of messages in the range Over 500: 78

Now we can calculate the total number of people aged 12–15:

\[ \text{Total} = 24 + 47 + 78 = 149 \]

Next, we find the number of people age 12–15 who sent over 500 messages, which is 78.

Now, we can calculate the relative frequency:

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

Now, calculating this value:

\[ \frac{78}{149} \approx 0.5221 \]

To convert this to a percentage, we multiply by 100:

\[ 0.5221 \times 100 \approx 52.21 % \]

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

52.2%