Question

HELP ASAP PLSSSSS

(picture of graph is below)
Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per day (rounded to the nearest hour):


Number of hours spent doing leisure and sports activities per day 1 2 3 4 5
Sample A: Number of adults 70 90 135 140 65
Sample B: Number of adults 80 80 130 135 75


Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct—Dan or Bret? Explain your answer in two or three sentences. Make sure to use facts to support your answer.

Answer 1

Dan is correct

Explanation:

Mean = the sum of all data values divided by the total number of data values

Number of adults in Sample A:

= 70 + 90 + 135 + 140 + 65 = 500

Mean of Sample A:

= [ (1 × 70) + (2 × 90) + (3 × 135) + (4 × 140) + (5 × 65) ] ÷ 500

= 1540 ÷ 500

= 3.08

Number of adults in Sample B:

= 80 + 80 + 130 + 135 + 75 = 500

Mean of Sample A:

= [ (1 × 80) + (2 × 80) + (3 × 130) + (4 × 135) + (5 × 75) ] ÷ 500

= 1545 ÷ 500

= 3.09

Mean of the two samples:

= (3.08 + 3.09) ÷ 2

= 3.085 hours

= 3 hours (nearest hour)

The mean of Sample A is 3.08 hours and the mean of Sample B is 3.09 hours, so the mean of the entire sample is 3.085 hours. If we round this to the nearest hour, then the mean is 3 hours. Therefore, Dan is correct in concluding that the adults spend a mean of 3 hours each day doing leisure and sports activities.