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

deliredejoker7m

deliredejoker7m

Answered question

2021-11-30

The amount of time each household in a sample watches television each week is calculated. The mean of the data is 31 hours and the median is 27.2hours. Twenty-four of the families in the sample turned on the television for 16 hours or less for the week. The 8th percentile of the data is 16 hours. 
Based on the given information, determine if the following statement is true or false. 
The first quartile is less than 16 hours.

Answer & Explanation

May Dunn

May Dunn

Beginner2021-12-01Added 12 answers

Step 1 
Given: 
- Mean of the data is, μ=31 hours 
- Median, x=27.2 hours 
- The percentage of families who watched television for no more than 16 hours per week is, n=24
- The 8-th percentile of the data is 16 hours. 
Finding out whether the given statement—that the first quartile is less than 16 hours—is true or false—is the goal.
Step 2 
The median is 27.2 hours, so that is a given.
So, the 50th percentile is 27.2 hours. 
Also given that the 8th percentile is 16 hours. 
So, P50P8 
Then, the first quartile P25 will lies between P50  and  P8 
So, the condition can be represented as, 
P50P25P8=27.2P2516
Thus, P25 cannot be less than 16 hours. 
Hence, the given statement is false.

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