Question

1) Bob gets the following homework grades: 2, 2, 2, 2, 2, 10, 10, 10, 10, 10 Tom gets the following homework grades: 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 Pat gets the following homework grades: 1, 1, 8, 8, 8, 8, 8, 8, 10, 10 Find the mean homework grade for each student, find the median homework grade for each student, and estimate the standard deviation for each student. You should not find the actual standard deviation using a formula. Show all work and explain how you are getting each answer.

2) Dante records the height of 25 second graders, and Maria records the height of the first 25 people who walk into McDonalds at 6pm on a Friday night. Who do you expect will have a higher mean? Who do you expect will have a higher standard deviation? Explain.

Answer 1

1)

Mean for Bob = (5 * 2 + 5 * 10) / 10 = 6

All are same sumbers, so Mean for Tom = 7

Mean for Pat = (2 * 1 + 6 * 8 + 2 * 10) / 10 = 7

Median for Bob = Mean of 5th and 6th element = (2 + 10)/2 = 6

All are same sumbers, so Median for Tom = 7

Median for Pat = Mean of 5th and 6th element = (8 + 8)/2 = 8

Standard deviation for Bob = = 4

All are same sumbers, so Standard deviation for Tom = 0

Standard deviation for Pat = = 3.255764

2)

Since the second graders have low heights with most of the people who walk into McDonalds, the expected mean of the height of the first 25 people who walk into McDonalds will be higher.

All 25 second graders will almost have same heights with lesser variation. The height of the first 25 people who walk into McDonalds at 6pm on a Friday night can be both adults and kids and have greater variablility in heights. We expect the height of the first 25 people who walk into McDonalds to have higher standard deviation.