Download AP Statistics Unit 1 Review 1. Which of

Name ________________________________________________________________ Period __________
AP Statistics
Unit 1 Review
1.
Which of the following are examples of categorical variables?
I.
method of payment for purchases (cash, check, credit card,…)
II.
zip code of a customer’s mailing address
III.
number of items purchased
IV.
amount of sales tax on a purchase
V.
customer’s driver’s license number
a) I
2.
b) I and II
b) Upper Quartile
c) Median
d) Lower Quartile
e) Minimum
Ms. Myers’ class is more homogeneous than Ms. Gentry’s class.
Ms. Gentry’s class is more homogeneous than Ms. Myers’ class.
Ms. Gentry’s class did less well on the test than Ms. Myers’ class.
Ms. Myers’ class performed twice as well on the test as Ms. Gentry’s class.
Ms. Myers’ class performed 1.2 points better on the test than Ms. Gentry’s class.
The following is a statistical summary of the gold medal performance in the men’s long jump (measured
in inches) for the modern Olympic series starting in 1900. Approximately what percent of the data lie
between 298 and 334.64?
a)
b)
c)
d)
e)
5.
e) all
Ms. Myer’s pre-calculus class had a standard deviation of 2.4 on a trigonometry test, while Ms. Gentry’s
pre-calculus had a standard deviation of 1.2 on the same test. What can be said about these two classes?
a)
b)
c)
d)
e)
4.
d) I, II and V
The statement: “The mean of a sample always divides the data into two equal portions – half larger and
half smaller in value than itself” is incorrect. Which of the following must replace the term mean to
make the statement correct?
a) Maximum
3.
c) I, II, IV and V
25%
33%
50%
67%
75%
Summary of Long Jump Mean 314.096
Median 312.781
StdDev 20.7055
Min 281.5
Max 350.5
Upper Quartile 334.64
Lower Quartile 298
In a frequency distribution of 3000 scores, the mean is 78 and the median is 95. One would expect this
distribution to be:
a)
b)
c)
d)
e)
skewed to the right
skewed to the left
symmetrical and mound-shaped
symmetrical and uniform
bimodal
6.
The mean age of 12 of the members attending a mathematics department faculty meeting is 37. Mr.
Myers, who is 50, arrives late. What is the average of all 13 members.
a) 37
7.
c) 39
d) 40
e) 41
Which of the following are true statements?
I.
The standard deviation is the square root of the variance.
II.
The standard deviation is zero only when all values are the same.
III.
The standard deviation is strongly affected by outliers.
a) I and II
8.
b) 38
b) I and III
c) II and III
d) I, II, and III
e) none
The stemplot displays the 1988 per capita income in (hundreds of dollars) of the 50 states. Which of the
following best describes the data?
11 7 a)
Skewed distribution, mean greater than median
12 2256677788 b)
Skewed distribution, median greater than the mean
13 2345677789 c)
Symmetric distribution, mean greater than the median
d)
Symmetric distribution, median greater than the mean
14 12667889 e)
Symmetric distribution with outliers on the high end
15 244559 16
17
18
19
20
9.
6889 667 9 9 9 Vocabulary:
Individuals variables Skewed right symmetric categorical variable quantitative variable distribution range spread frequency outlier dot plot histogram stemplot split stems back‐to‐back stemplot mean 
center shape skewed left x nonresistant median 10.
In statistics, what is meant by individuals?
11.
In statistics, what is meant by variable?
12.
What is meant by exploratory data ananlysis?
resistant quartiles Q1 and Q3 IQR five‐number summary minimum maximum boxplot modified boxplot standard deviation variance density curve  mu  sigma outcomes normal curve normal distribution standard normal distribution inflection point 68‐95‐99.7 rule percentile N   ,   standardize value z‐scores 13.
What is the difference between a categorical variable and a quantitative variable?
14.
When is it useful to use a bar chart?
15.
What is meant by a distribution?
16.
Define range:
17.
When is it better to use a histogram rather than a dotplot?
18.
What is meant by frequency in a histogram?
19.
When setting a window for constructing a histogram on the TI-84:
a)
What is the significance of Xscl?
b)
How do you choose the values of Xmin and Xmax?
c)
what is the significance of Ymax?
20.
Define outlier:
21.
If a distribution is symmetric, what does its histogram look like?
22.
If a distribution is skewed right, what does its histogram look like?
23.
If a distribution is skewed left, what does its histogram look like?
24.
When is it advantageous to split stems on a stemplot?
25.
What is the purpose of a back-to-back stemplot?
26.
In statistics, what is the most common measurement of center?
27.
Explain how to calculate the mean, x .
28.
Explain how to calculate the median, M.
29.
Explain why the median is resistant to extreme observations, but the mean is nonresistant.
30.
In statistics, what is meant by spread?
31.
Explain how to calculate Q1 and Q3 .
32.
What is the five-number summary?
33.
What does standard deviation measure?
34.
What is the relationship between variance and standard deviation?
35.
When does standard deviation equal zero?
36.
Is standard deviation resistant or nonresistant to extreme observations? Explain.
37.
What is a percentile?
38.
Is there a difference between the 80th percentile and the top 80%? Explain
39.
Is there a difference between the 80th percentile and the lower 80%? Explain
40.
Explain how to standardize a variable
41.
What is the purpose of standardizing a variable?
42.
What is the standard normal distribution?
43.
What information does the standard normal table give?
44.
How do you use the standard normal table (Table A) to find the area under the standard normal curve to
the left of a given z-value? Draw a sketch.
45.
How do you use Table A to find the area under the standard normal curve to the right of a given zvalue? Draw a sketch.
46.
How do you use Table A to find the area under the standard normal curve between two given z-values?
Draw a sketch.
47.
The figure show the distributions of number of births in Toronto, Canada, on each of the 365 days in a
year, grouped by day of the week. Based on these plots, give a more detailed description of how births
depend on the day of the week.
48.
Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the
college each morning. Here are the times (in minutes) for 42 consecutive weekdays, with the date in
order along the rows:
8.25 9.00 8.33 8.67 49.
7.83 8.50 7.83 10.17 8.30 9.00 7.92 8.75 8.42 7.75 8.58 8.58 8.50
7.92
7.83
8.67
8.67
8.00
8.42
9.17
8.17
8.08
7.75
9.08
9.00
8.42
7.42
8.83
9.00 8.75 6.75 8.67 8.17 8.08 7.42 7.92
9.75
8.50
a)
Make a histogram of these drive times. Describe the distribution. Are there any clear outliers?
b)
Would you consider this data to be approximately normal? Justify your response using the
information provided in part (a), as well as, the 68 – 95 – 99.7 rule and normal probability plots
A set of test scores had a mean of 84 and a standard deviation of 12. The instructor decided to adjust the
scores, so that the mean is 72 with a standard deviation of 5. Michael’s original score of 81 will be
converted to what adjusted score? (Show your work)
50.
The army reports that the distribution of head circumference among soldiers is approximately Normal
with mean 22.8 inches and standard deviation 1.1 inches. Helmets are mass-produced for all except the
smallest 5% and the largest 5% of head sizes. Soldiers in the smallest or largest 5% get custom-made
helmets. What head sizes get custom-made helmets? Show your work.
51.
Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose
osteoporosis, an elaborate apparatus measure bone mineral density (BMD). BMD is usually reported in
standardized form. The standardization is based on a population of healthy young adults. The World
Health Organization (WHO) criterion for osteoporosis is a BMD score that is 2.5 standard deviations
below the mean for young adults. BMD measurements in a population of people similar in age and sex
roughly follow a Normal distribution.
a)
What percent of healthy young adults have osteoporosis by the WHO criterion?
c)
Women aged 70 to 79 are of course not young adults. The mean BMD in this age group is about
–2 on the standard scale for young adults. Suppose that the standard deviation is the same as for
young adults. What percent of this older population has osteoporosis?
Selected Answers
Multiple Choice
1. D
5. B
2. C
6. B
Free Response
48.
a) Remember – shape, center and spread outliers
b) Yes it is approximately normal
49. 70.75
50. Less than 20.991 inches and greater than 24.609 inches
51 a. 0.6%
b. 31%
3. B
7. D
4. C
8. A