AP Statistics / Mr. Hansen
Test #1, 9/25/2000 (Chapters 1 and 2, plus §3.1)

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.

Part I. Terminology (2 pts./box, 14 pts. total).
Fill in the customary name and notation for each. The first one has been filled in as an example.

#

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 measure of central tendency which is resistant to outliers and which is not pulled very much to the left or right by left or right skewness

 

[optional; 2-pt. bonus if you fill in this box]

4.

The sum of observations in a sample, divided by n

 

 

5.

The average squared deviation from the population mean. Although this parameter can be used as a measure of dispersion, it is more common to use its square root instead. What parameter (whose units are square units of the underlying data measurements) are we talking about?

 

 

 

Part II. The False-True Challenge (4 pts. each, 16 pts. total).
All of the numbered statements (6-10 below) are false. That’s right; all of them are false. In each case, make some minor changes (such as adding a word or two, crossing a few words out, or changing the wording) to make the statement true. However, do not simply add or subtract the word "not" (since, obviously, that would be too easy). Likewise, do not change the word "useful" to "useless" in #10. Make changes that demonstrate some actual knowledge. The first one has been done for you as an example.

[to make correction, cross out 2.5 IQR and write 1.5 IQR]
(6.) Although human judgment is better, the "2.5 IQR" ^ rule is useful in cases where automated determination of outliers is needed.

7. According to Chebyshev’s Theorem, approximately 95% of the values in a normal distribution will lie within ± 2 standard deviations of the mean.

8. The standard deviation is a resistant measure of dispersion.

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 boxplot is a useful diagram for showing the essential characteristics of a two-peaked (or "bimodal") distribution.

Part III. Creative Answers (8 pts. each, 24 pts. total).
Categorize each of the following distributions as uniform, skew left, skew right, normal, or other. Then provide a believable chart of the type requested. You will need to fabricate some data in a believable manner. The first problem has been done for you as an example.

(11.)
Consider the distribution of heights (inches) in adult males.
What type of distribution is this? NORMAL
Draw a believable sample stemplot:
6 | 035
6 | 77889
7 | 000011235
7 | 67
8 | 0
12.
The distribution of rolls of a single fair die.
What type of distribution is this? _____________________
In the space to
the right, make
a rough sketch
of a histogram
and indicate
numbers and units
on both axes:
13.
Consider the distribution of lifespans (or projected lifespans) for Americans born in the year 1950.
What type of distribution is this? _____________________
In the space to the right,
draw a believable boxplot
or modified boxplot (your
choice) and label the values
in the 5-number summary:
14.
Consider the distribution of sale prices for single-family houses sold in Montgomery County, MD, during 1999.
What type of distribution is this? _____________________
In the space to the right,
make a rough sketch of a
normal quantile plot and
mark dollar values on the horizontal axis:
 

Section IV. Free Response (6 pts. each, 36 pts. total).
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.

15. Compute (a) the interquartile range and (b) the standard deviation for the sample data presented in problem #11. No work is required, but for full credit you must label your answers using standard notation and state the units.
(a)
(b)

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(1250, 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 1440 on the new test. What is this in terms of a z score? Show your work.




18. What is Joe Bulldog’s score of 1440 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 your work.





20. What fraction of students taking the new test will receive scores between 1300 and 1550? Work is optional, but at least show a sketch.




Part V. Short Answer (2 pts./blank, 10 pts. total).
Fill in each blank with the word or phrase that best fits.

21. For males, height and weight are _____________________ associated, though the association is not linear.

22. GPA and hours spent watching TV are negatively associated, or so your parents would have you believe. They would likely claim that TV time (in hours) constitute the explanatory variable and that GPA is the _____________________ variable. However, the linear correlation coefficient, denoted by the letter _____________________ , is probably not very close to –1.

23. Estimate the linear correlation coefficient (no work required) for each of the scatterplots shown below:
(a) _____________________
(b) _____________________