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 11th percentile of the data is 15 hours.
Step 4 of 5 : What is the value of the 50th percentile?
Median = 50th percentile
To find the value of the 50th percentile, also known as the median, we can use the information given:
1. The mean of the data is 30 hours.
2. The median is 26.2 hours.
Since the median is the value that splits the data into two equal parts, we can start with the assumption that the data follows a normal distribution. In a normal distribution, the mean and median would be the same.
However, we have information that contradicts this assumption - there are 24 families in the sample who turned on the television for 15 hours or less for the week. This indicates that the data is skewed or has outliers pulling the median below the mean.
Given this information, we can conclude that the median (50th percentile) is less than the mean of 30 hours.
Unfortunately, based on the information provided, we cannot determine the exact value of the 50th percentile.