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 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 7th percentile of the data is 16 hours. 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 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 7th percentile of the data is 16 hours.

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 31 hours and the median is 27.2 hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The $7^{\text {th }}$ percentile of the data is 16 hours. Step 2 of 5 : Approximately how many families are in the sample? Round your answer to the nearest integer. Answer How to enter your answer (opens in new window) Tables Keypad Keyboard Shortcuts

Solution

Solution Steps

Step 1: Identify Given Data

We are given:

The $7^{\text{th}}$ percentile of the data is 16 hours.
24 families turned on the television for 16 hours or less.

Step 2: Set Up the Proportion

To estimate the total number of families in the sample, we use the given percentile information and the number of families at or below that percentile. The proportion can be set up as follows: \[ \frac{24}{\text{Total Families}} = \frac{7}{100} \]

Step 3: Solve for the Total Number of Families

Rearrange the proportion to solve for the total number of families: \[ \text{Total Families} = \frac{24 \times 100}{7} \]

Step 4: Calculate the Total Number of Families

Perform the calculation: \[ \text{Total Families} = \frac{2400}{7} \approx 342.8571 \]

Step 5: Round to the Nearest Integer

Round the result to the nearest integer: \[ \text{Total Families} \approx 343 \]