Question

Below are the data collected from two random samples of 500 American adults on the number of hours they work per day (rounded to the nearest hour): Number of hours of work per day 6 7 8 9 10 Sample A: Number of adults 60 90 145 150 55 Sample B: Number of adults 70 80 140 145 65 Ryan concludes that adults spend a mean of 8 hours working each day. Malia thinks the mean is 9 hours. Who is correct—Ryan or Malia? Explain your answer in two or three sentences. Make sure to use facts to support your answer.

Answer 1

The mean of Sample A is 8.1
The mean of Sample B is 8.11
Therefore, Ryan is most correct!
Sample A and B were very close in percentages and ratios, hopefully this helps with a sentence  or two!

Answer 2

Sample A:

Equation:

(60 * 6) + (90 * 7) + (145 * 8) + (150 * 9) + (55 * 10) = 4050

4050 / 500 = 8.1

8.1 ≈ 8

8.1 rounded is 8

Explanation

For sample A The mean is 8. instead of adding 60 of 6s, i multiplied them, so it wouldn't be 6 + 6 + 6 + 6 and so on till i added 60 of 6s, I multiplied instead of add for each observation.

Secondly, Since we want to find the mean, i divided my sum by 500, because there were 500 observations.

4050 / 500 = 8.1

So,if rounded to nearest whole number for sample A, Ryan is correct. But we have not looked at sample B yet.

Sample B:

Equation:

(70 * 6) + (80 * 7) + (140 * 8) + (145 * 9) + (65 * 10) = 4055

4055 / 500 = 8.11

8.11 ≈ 8

8.11 rounded to 8

Explanation:

In sample B. The mean is 8 as well if rounded. I used to same stratgey as before and instead of adding the observations one by one, I multiplied. Example : instead of 70 of 6s being added one by one, just multiply 70*6, I did that to the other observations as well.

Secondly, Since we wanted the mean, we divided the sum by 500, So it is 4055/500 = 8.11, I could see why Malia thought it was 9, she has to keep in mind that the place of the second digit after the decimal is hundredth.

Hope it helps. :)