Question

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.

Step 1 of 5: Based on the given information, determine if the following statement is true or false. The 54th percentile is less than 26 hours.
Step 2 of 5: Approximately how many families are in the sample? Round your answer to the nearest integer.
Step 3 of 5: Based on the given information, determine if the following statement is true or false. Approximately 200 families turned on their televisions for less than 35 hours.
Step 4 of 5: What is the value of the 50th percentile?
Step 5 of 5: Based on the given information, determine if the following statement is true or false.The first quartile is greater than or equal to 20 hours.

Answer 1

Explanation:

The mean of the data is 31 hours and the median of the data 27.2 hours.

24 of the families in the sample turned on the television for less than 16 hours for the week.

The 7th percentile = 16 hours

Step 1:

The median is a value that divides the whole data into two equal parts. It implies that the median represents the 50th percentile of the data.

Given that the median is 27.2 hours, thus the 54th percentile should be greater than 27.2 hours.

Thus, the given statement is false.

Step 2:

Let assume that N is the total number of families

24 of the families in the sample turned on the television for less than 16 hours for the week.

The 7th percentile = 16 hours

It means that 7% of N = 24

N = 24/0.07

N = 343

Step 3:

From (2), N = 343

Given that median= 27.2 hours.

It means 200 families turned on their television for less than 27.2 hours.

We don't know if this is true for 35 hours. 100 families may use less than 35 hours and 200 may use more than 35 or vice versa. In addition to that, even 50 families might use less than 35 and 350 may use more than 35 hours.

Hence, the statement is false.

Step 4:

The median is the 50th percentile value which is = 27.2 hours

Step 5:

The statement is false

The 25th percentile is the first quarter of the data and if the 7th percentile is 16 hours, then the 25th percentile should be greater than that.