AP Statistics
Chapter 1 Extra Practice
Name: ____________________________________
Use the following information for numbers 1 & 2:
Nitrates are organic compounds that are a substantial component of agricultural fertilizers. When those fertilizers run off into streams,
the nitrates can have a toxic effect on animals that live in those streams. An ecologist studying nitrate pollution in two streams collects
data on nitrate concentrations at 42 places on Stony Brook and 42 places on Mill Brook. His results are given in the dotplots and
computer output below.
Variable Total Count
Stony Brook
42
Mill Brook
42
Mean
5.524
7.929
SE Mean
0.451
0.711
StDev
2.922
4.607
Minimum
0.000
0.000
Q1
3.500
4.500
Median
5.400
8.250
Q3
7.500
10.500
Maximum
12.000
20.000
1. Determine if there are any outliers in each distribution. Show your work.
For Stony Brook: Q1 = 3.5 and Q3 = 7.5; 1.5 x IQR = 6.
Q1 – 6 < 0 so no low outliers; Q3 + 6 = 13.5, so no high outliers.
For Mill Brook: Q1 = 4.5 and Q3 = 10.5; 1.5 x IQR = 9.
Q1 – 9 < 0 so no low outliers; Q3 + 9 = 19.5, so 20 is a high outlier.
2. Write a few sentences comparing the nitrate concentrations in Stony Brook and Mill Brook.
Shape: Stony Brook’s distribution is slightly skewed right, while Mill Brook’s is roughly symmetric.
Center and Spread: The median and IQR in Stony Brook (5 mg/l and 4 mg/l, respectively) are much lower than in Mill Brook (8.25
mg/l and 6 mg/l, respectively).
Outliers: answered in question number 1.
3. Do people’s opinion of the alt-rock band Coastal Surface depend on their age? Here are some data that address this question.
Age
11-14 years
15-18 years
19-22 years
Total
Like
18
38
40
96
Opinion of band
Dislike
30
10
67
107
Uncertain
15
17
15
47
Calculate three conditional distributions for opinion of the band, one for each age group.
Age
11-14 years
15-18 years
19-22 years
Like
28.5%
58.5%
32.8%
Dislike
47.6%
15.4%
54.9%
Uncertain
23.8%
26.2%
12.3%
Total
63
65
122
250
Use the following information for numbers 4 & 5:
Below is a box plot of the amounts of oil recovered from 38 wells (in thousands of barrels) in the Devonian Richmond Dolomite area
of the Michigan basin.
4. The mean of this distribution is 50.39 and the median is 47. Explain why you could have predicted that the mean would be higher
than the median by looking at the boxplot.
The high outlier will cause the mean to be higher, but will have no effect on the median.
5. The largest amount of oil recovered was 157,000 barrels. Suppose that it was replaced with another basin that had 254,000 barrels.
Without performing any calculations, indicate whether each of the following measures of center and spread would increase, decrease,
or remain the same.
a) mean
Increase
b) median
No change
c) standard deviation
Increase
d) interquartile range
No change