The number of hours per weeek that the television is turned on is determined for each family in a sample. The mean of the data is 33 hours and the median is 29.2 hours. Twenty four of the families the sample turned on the television for 18 hours or less for the week. The 16th percentile of the data is 18 hours. Step 2 of how many familles are in the sample? Round your answer to the nearest Integer

Well, Step 1 was clearly deciding to watch less TV, and Step 2 is figuring out how many families are in the sample. Let me grab my calculator and do some math while juggling some bananas…

Alright, so we know that the 16th percentile is 18 hours, which means 16% of the families in the sample watch 18 hours or less. And we also know that 24 families i.e. 24% watch 18 hours or less.

Now, if we assume a linear relationship, we can calculate the total percentage of families in the sample. So, we have:

16% ------------------- 18 hours (24 families)
100% ------------------ x hours (total families)

Using this proportion, we can solve for x:

(16/100) * x = 24

If we solve this equation, we find that x is equal to 150. So, there are approximately 150 families in the sample.

Just remember, watching less TV not only improves your math skills but also gives you more time to learn to juggle bananas! 🍌

Step 2: Calculate the number of families in the sample.

From the given information, we know that 24 families in the sample turned on the television for 18 hours or less for the week, which corresponds to the 16th percentile of the data.

To find the total number of families in the sample, we need to determine the position of the 16th percentile within the data. Since the median is given as 29.2 hours, we can infer that it is the 50th percentile. This means that 16% of the data is below the 16th percentile.

Let's set up a proportion to find the position of the 16th percentile:

(16% of the data) / (total number of families in the sample) = (position of the 16th percentile) / (total number of data points)

16% / 100% = (16th percentile position) / (total number of data points)

0.16 = (16th percentile position) / (total number of data points)

Since we know that the 16th percentile corresponds to 18 hours, we can set up another proportion to find the position of this data point:

(18 hours) / (total number of families in the sample) = (position of the 16th percentile) / (total number of data points)

18 hours / total number of families in the sample = 0.16

Solving for the total number of families in the sample:

total number of families in the sample = 18 hours / 0.16

total number of families in the sample ≈ 112.5

Rounding to the nearest integer, the estimated total number of families in the sample is 113.

Therefore, there are approximately 113 families in the sample.

To find the number of families in the sample, we need to determine the 16th percentile of the data. The 16th percentile represents the value below which 16% of the data lies.

Given that 24 families in the sample turned on the television for 18 hours or less, we can conclude that these 24 families constitute 16% of the total number of families in the sample.

So, we can set up the following equation:

16% = 24/x

To solve for x (the total number of families), we can cross-multiply and solve for x:

0.16x = 24

Dividing both sides of the equation by 0.16 will give us the value of x:

x = 24 / 0.16

By performing the calculation, we find that x ≈ 150.

Therefore, there are approximately 150 families in the sample.