The number of hours per week that the television is turned on is determined for

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 35 hours and the median is 31.2 hours. Twenty-four of the families in the sample turned on 20 hours for the week. The 6h percentile of the data is 20 hours. Step 1. The 5Sth percentile is less than 30 hours. (2 Points) A) Truc B) False Step 2. Approximately how many families are in the sample? Round your answer to the nearest integer. (2 Points) Step 3. Approximately 200 families turned on their televisions for less than 35 hours. (2 Points) A) True B) False Step 4. What is the value of the so" percentile? (2 Poins) Step 5. The first quartile is less than 20 hours. (2 Points) A) True B) False

Explanation / Answer

Step 1: Median = 50th Percentile --> that value which is greater than 50% of the overall data.

Median = 31.2 --> 31.2 is greater than 50% of the data.

55th percentile --> that value which is greater than 55% of the data --> this has to be greater than the 50th percentile value (Median)

So, 55th percentile value > 31.2

Thus, it can't be less than 30 hours.

Ans: B) False

Step 2: Since 24 families used less than 20 hours in a week and the 6th percentile value is 20.

That means, 20 is larger than 6% of the overall data set that has less than 20 hours.

That 6% of data set = 24 families

Therefore, if total families = N --->

6% x N = 24

6/100 x N = 24

N = 2400/6 = 400 families.

Ans: N = 400 families

Step 3. If the statement was: If less than 200 families turned on their television for less than 31.2 (median) hours, this statement would have been correct. As that is the definition of the median itself, as 50% of the data (50% of 400 = 200) is less than the median.

We don't know if it's true for 35 hours. 100 families may use less than 35 and 200 use more than 35 or vice versa. Or even 50 families may use less than 35 and 350 remaining may use more than 35 in order to keep the average constant.  

Hence, this statement is categorized false.

Step 4. The value of the 50th percentile = Median = 31.2

Step 5. The first quartile = 25th percentile.

Given that 6th percentile is 20 hours, then 25th percentile HAS to be greater than or equal to 20 hours, but it can't be less than 20 hours.

Therefore, statement is false.

Cheers!

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