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 35 hours and the median is 31.2 hours.  Twenty-four of the families in the sample turned on the television for 20 hours or less for the week.  The 15th percentile of the data is 20 hours.

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

To find how many families are in the sample, we can use the information about the 15th percentile. Specifically, we know that:

- The 15th percentile corresponds to 20 hours of television watching per week.
- This means that 15% of the families watched 20 hours or less of television.

We are also told that 24 families watched 20 hours or less of television.

Let \( n \) represent the total number of families in the sample. Since 15% of the total families represent those who watched 20 hours or less, we can express this relationship as:

\[
0.15 \times n = 24
\]

To solve for \( n \):

\[
n = \frac{24}{0.15} = 160
\]

Therefore, the approximate number of families in the sample is **160**.

Would you like more details on any part of the solution?

Here are 5 related questions for further exploration:
1. What does it mean for a data point to be at the 15th percentile?
2. How is the median different from the mean in this context?
3. What would be the effect if the 15th percentile had been 25 hours instead?
4. How can we use percentiles to estimate the distribution shape?
5. What does the difference between mean and median suggest about data skewness?

**Tip**: When interpreting percentiles, remember that they indicate the percentage of data points below a given value.

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 35 hours and the median is 31.2 hours. Twenty-four of the families in the sample turned on the television for 20 hours or less for the week. The 15th percentile of the data is 20 hours. Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.

Learn how to estimate the number of families in a sample based on the 15th percentile and provided data. This problem covers key statistical concepts such as percentiles and uses basic algebra to solve for the total sample size. The mean, median, and other descriptive statistics are also discussed.

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