1. For the following data set make the boxplot and find any outliers:
2, 3, 4, 6, 8, 10, 13, 15, 16, 19, 37
The 5 number summary is min:2 lowerQ: 4 Median:10 UpperQ: 16 Max : 37
The IQR is 12. The boundary for outlier is 18 + 1.5 x 12= 34
2
19
4
10
37
16
4. 40% of the chairs in the cafeteria are wood. 30% of the wooden chairs are broken. What proportion of
the chairs in the cafeteria are broken wooden chairs?
Multiply because the second sentence talks about the wooden chairs only – 12%
5. I took a walk of 13 random steps in the morning and another walk in the afternoon of 7 random steps.
How far am I likely to be away from my starting point altogether?
The time of day doesn’t matter it’s square root of 20
6. What is the mean and standard deviation of the following data set:
2, 3, 6, 7, 7
Show work
Mean is 5 so take 32 22 12 22 22 (the square distances to the mean) average them by dividing by 5 and
square root the result: 2.09
How many of the points are within one standard deviation of the mean?
Add and subtract 2.09 with 5 to get 2.91 and 7.09. There are 4 points between 2.91 and 7.09
5. 40% of the cars are Toyotas. 30% of the cars are silver Toyotas. What proportion of the Toyotas are
silver?
30 out of 40 is 75%
6. The standard deviation of this data set: 5, 8, 9, 10, 13 is about 2.6
a) what would be the standard deviation of 7, 10, 11, 12, 15
the new distribution is just the old one plus 2 so the standard deviation doesn’t change
b) what would be the standard deviation of 10, 16, 18, 20 , 26
Multiplying all the data points does spread the points out more so the answer is 5.2 which is 2 x 2.6