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 the television for 20 hours or less for the week. The 6th percentile of the data is 20 hours.

Step 1 of 5: Based on the given information, determine if the following statement is true or false.The 56th percentile is less than 30 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

Answer:

Multiple Answers

Step-by-step explanation:

We know that the mean is 35 and the median is 31.2 hours.

• Step 2: If we clear n of the percentil formule of the 6th percentile:

   (n)($\frac{6}{100}$)=  24 families   →     n=400 families.

• Step 3: true. The half of the population is 200. Therefore the 50% of the sample(the 50th percentile) is under or equal 31.2

• Step 4: By definition the median is the 50th percentil. So the 50 percentil   →     31.2.

• Step 1: If we considerate that the 50th percentil is 31.2, a bigger percentil had to be bigger too.

• Step 5: False. At the beggining we have that the 6% of the population were below or equal to 20 hours, therefore the 25% of the data have to be greater or equal to 20.

Answer 2

Using statistical concepts such as percentiles and median, it is found that:

• 1. False.
• 2. There are 400 families in the sample.
• 3. False.
• 4. The value of the 50th percentile is of 31.2 hours.
• 5. True

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• A measure is said to be in the xth percentile if it is greater than x% of the measures.
• The median is the 50th percentile.

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Statement 1:

• The median is of 31.2 hours, thus, the 50th percentile is 31.2 hours.
• The 56th percentile is above the 50th percentile, thus, it is above 31.2 hours, and statement 1 is false.

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Item 2:

• 24 families turned on the TV for 20 or less hours, corresponding to 6% of the sample, as it is the 6th percentile.

Thus, the size of the sample is:

$0.06n = 24$

$n = \frac{24}{0.06}$

$n = 400$

There are 400 families in the sample.

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Statement 3:

• The median is of 31.2 hours.
• Thus, 0.5(400) = 200 families turned on the TV for less than 31.2 hours, and statement 3 is false.

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Item 4:

• The median is of 31.2 hours, and thus, the value of the 50th percentile is of 31.2 hours.

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Statement 5:

• 20 hours is the 6th percentile.
• The first quartile, that is, the 25th percentile, is above the 6th percentile.
• Thus, the first quartile is greater than 20 hours, and the statement is true.

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