Questions: The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 12th percentile of the data is 15 hours. Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The 12th percentile of the data is 15 hours.

Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

Transcript text: The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 30 hours and the median is 26.2 hours. Twenty-four of the families in the sample turned on the television for 15 hours or less for the week. The $12^{\text {th }}$ percentile of the data is 15 hours. Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

Solution

Solution Steps

To determine the approximate number of families in the sample, we can use the information given about the 12th percentile. The 12th percentile means that 12% of the families watched TV for 15 hours or less. We know that 24 families watched TV for 15 hours or less. Therefore, we can set up a proportion to find the total number of families in the sample.

Step 1: Understanding the Given Data

We are given that the 12th percentile of the data is 15 hours, meaning 12% of the families watched TV for 15 hours or less. Additionally, we know that 24 families watched TV for 15 hours or less.

Step 2: Setting Up the Proportion

To find the total number of families in the sample, we set up the proportion: \[ \frac{12}{100} = \frac{24}{\text{Total Families}} \]

Step 3: Solving for Total Families

Rearranging the proportion to solve for the total number of families: \[ \text{Total Families} = \frac{24}{\frac{12}{100}} = \frac{24}{0.12} \]

Step 4: Calculating the Total Number of Families

Performing the division: \[ \text{Total Families} = 200.0 \]

Step 5: Rounding to the Nearest Integer

Since the problem asks for the answer to be rounded to the nearest integer: \[ \text{Total Families Rounded} = 200 \]