Problem 1
Consider the histogram shown below.
(a)
Is this data skewed to the right, symmetric, or skewed to the left?
The data is skewed to the left as the majority of the mass is on the right with a long tail going out to the left.
(b)
Which is bigger for this data set, the mean or the median, or are they about equal?
The median of the data set will be larger as the smaller values will skew the mean to a smaller value, which will affect the median less.
Problem 2
In a statistics class with 136 students, the professor records how much money each student has in their possession during the first class of the semester. The histogram below is of the data collected.
(a)
The percentage of students with over 20 dollars in their possession is
- [ ] A. over 40%.
- [ ] B. about 30%.
- [x] C. about 20%.
- [ ] D. about 10%.
(b)
The histogram
- [ ] A. has an outlier.
- [ ] B. is asymmetric.
- [ ] C. is skewed right.
- [x] D. all of the above.
(c)
The number of students with under 10 dollars in their possession is closest to
- [ ] A. 40
- [ ] B. 70
- [ ] C. 50
- [x] D. 60
Problem 3
The table below summarizes the number of surface flaws found on the paintwork of new cars following their inspection after primer paint was applied by a new method:
| No. of flaws | No. of cars |
|---|---|
| 0 | 5 |
| 1 | 9 |
| 2 | 14 |
| 3 | 12 |
| 4 | 6 |
| 5 | 3 |
| 6 | 1 |
(a)
Find the mean number of flaws per car. Please give your answer to two decimal places.
(b)
Find the variance of the number of flaws per car. Please give your answer to two decimal places.
Problem 4
A North American company manufactures rivets for use in car production. A sample of forty rivets from the production line had mean 6.574 and standard deviation 0.26 (both in 1/100 of an inch).
On communicating these results to the company headquarters in Europe, a request is made for the summary statistics to be converted into millimetres. Given that one inch is 2.538 centimetres, find the mean and standard deviation of the sample in millimetres.
(a)
What is the mean in millimeters? (Provide your answer to 3 significant figures.)
(b)
What is the standard deviation in millimeters? (Provide your answer to 3 significant figures.)