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AP Statistics / Mr. Hansen |
Name: _______________________ |
General Instructions: Raise your hand if you have a question. Write answers in the space provided. If you need additional room, write “OVER” and use reverse side. You may find the provided formula sheet and z table to be helpful.
|
# |
Description |
Customary Name |
Notation |
|
(1.) |
The number that forms the right edge of the box (not the whisker) in a boxplot |
third quartile |
Q3 |
|
2. |
Number of data points (observations) |
|
|
|
3. |
A dispersion statistic that is resistant to outliers |
|
|
|
4. |
What a dot represents in a modified boxplot |
|
N/A (leave blank) |
|
5. |
A measure of dispersion that equals the square root of the mean squared deviation from the population mean (note: this is a parameter, not a statistic) |
|
|
[to make correction, cross out “Chebyshev’s Theorem” and write “Empirical
Rule”]
(6.) According to Chebyshev’s Theorem, approximately 95% of the values in a
normal distribution will lie within ± 2
standard deviations of the mean.
7. The “1.5 IQR” rule should be used in all cases where determination of outliers is needed. Human judgment does not play a role.
8. The median is a measure of central tendency that is strongly influenced by outliers.
9. In a typical chemistry test having a low score of 63 and a high score of 97, one of the statistics we could compute would be the range, which in this example would be 63 to 97.
10. A modified boxplot is a useful diagram for showing the essential characteristics of a two-peaked (bimodal) distribution.
|
(11.) |
Consider the distribution of heights (inches) in adult males. What type of distribution is this? NORMAL 6 | 035 |
|
12. |
Consider the distribution of mean marathon speeds for runners in the Marine Corps Marathon. For example, one runner may have a mean speed of 10 mph during the race, and another (less competitive) runner may have a mean speed of 8.5 mph. What type of distribution is this? _____________________ In the space to the right, |
Part IV. Free Response (6 pts. each, except 10 pts. for #15, 5 pts. ea.
for #17-20).
Use your knowledge of statistical methods and the graphing calculator to solve
the following problems. Remember that in any problem in which you use a
formula, you should (1) show me the formula, (2) show me the plugged-in
formula, and (3) show some work leading to a circled answer.
|
Height (in.) |
Shoe size (units) |
|
68 |
10 |
|
65 |
6 |
|
72 |
12 |
|
71 |
12 |
|
67 |
10.5 |
|
68 |
9 |
|
73 |
9.5 |
|
74.5 |
12.5 |
|
72 |
11.5 |
|
73 |
10.5 |
|
70 |
11 |
|
66 |
10 |
13. For the data set shown above, compute the r value. Identify it by its full name (all the words) and state the
strength, direction, and linearity of
the association that is seen.
14. Would an r value close to 0
suggest a lack of patterns in the data (answer “yes” or “no”)? ____ Give two
reasons to support your answer.
15.(a)(6 pts.) Describe, in two or three literate, intelligible sentences, how to apply the rule of thumb we learned for determining whether or not a data value is an outlier.
15.(b)(4 pts.) The median household income in Loudoun County, VA, is $98,483, according to the latest U. S. Census Bureau figures released on August 29, 2006. Is the mean higher or lower than this? Explain how you know.
For questions 16-20, assume that the College Board has decided to replace the SAT with a new test that is designed to follow the N(1050, 150) distribution.
16. The new test will have a mean of _____________________ points, a standard deviation of _____________________ points, and a median of _____________________ points. If you don’t know the answers, raise your hand, because you need these answers in order to proceed.
17. Suppose that Joe Bulldog scores 1220 on the new test. What is this in terms
of a z score? Show your work.
18. What is Joe Bulldog’s score of 1220 expressed as a percentile? No work
required, but at least show a sketch.
19. What score would Bill Beauvoir need on the new test in order to be at the
45th percentile? Show a sketch.
20. What fraction of students taking the new test will receive scores between
1200 and 1300? Work is optional, but at least show a sketch.
Part V. Short Answer (2 pts./blank, 16 pts. total).
Fill in each blank with the word or phrase that best fits.
21. For males, greater height is associated with reduced
comfort in airplane seats. If both quantities are expressed as quantitative
variables, we would say that height and comfort level are _____________________
associated.
22. In mathematics, the term parameter
means an “adjustable constant” or a value that determines the shape of a
relationship between quantities. In statistics, the term parameter means __________________________________________
.
23. The two parameters of a normal distribution, in the mathematical
sense, are ______________ , which measures central
tendency, and ______________ , which
measures dispersion.
24. In this week’s “Quick Study” section of the Post Health insert, the study involving young people was a meta-analysis (i.e., an analysis based
on other studies). Summarize the finding of that meta-analysis (max. of 10
words):
______________________________________________________________
Was a cause-and-effect relationship sought by the
design of the experiments? ____ How can you tell?
______________________________________________________________
Was the cluster headache study also a meta-analysis?
____