(All work must be shown on a separate sheet. You may use a calculator, but I need to be able to follow the steps you used.)
1. For the following frequency distribution: (5 points)
|
Distribution 1 |
|
|
X |
f |
|
9 |
1 |
|
8 |
2 |
|
7 |
3 |
|
6 |
4 |
|
5 |
5 |
|
4 |
4 |
|
3 |
3 |
|
2 |
2 |
|
1 |
1 |
a.
Determine the mean, median and mode.
b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.
c.
Insert the mean, median and mode of the frequency distribution at the
appropriate points.
2. For the following frequency distribution: (5 points)
|
Distribution 1 |
|
|
X |
f |
|
9 |
0 |
|
8 |
1 |
|
7 |
1 |
|
6 |
2 |
|
5 |
2 |
|
4 |
3 |
|
3 |
4 |
|
2 |
5 |
|
1 |
7 |
a. Determine the mean, median and mode.
b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.
c. Insert
the mean, median and mode of the frequency distribution at the appropriate
points.
3. For the following frequency distribution: (5 points)
|
Distribution 1 |
|
|
X |
f |
|
9 |
7 |
|
8 |
5 |
|
7 |
4 |
|
6 |
3 |
|
5 |
2 |
|
4 |
2 |
|
3 |
1 |
|
2 |
1 |
|
1 |
0 |
a. Determine the mean, median and mode.
b. Construct a frequency polygon and superimpose a smooth curve on the frequency polygon.
c.
Insert the mean, median and mode of the frequency distribution at the
appropriate points.
4. Which of the distributions above is normally distributed, positively skewed, negatively skewed? (6 points)
5. If
these scores represent scores on a 10-item spelling test designed for 8th
graders, which distribution would likely result from: a. 5th graders;
b .11th graders; c. 8th graders. (6 points)
6. Calculate the mean, median, mode, standard deviation and range of the following sets of measurements: (20 points)
a. 9, 7, 6, 6, 2
b. 12,10,9, 8, 6
c. 82,82,82,82,82
d. 12, 10, 9, 8,
6, 45
7. Use question number 6 to help answer the following questions:
(8 points)
a. Why is
the standard deviation in (d) so large compared to the standard deviation for question (b)?
b. Why is the mean so much higher in (d) than
in (b)?
c. Why is the median relatively unaffected?
d. Which measure of central tendency best
represents the set of scores in (d)?
8. Given, a mean of 50, and a standard deviation of 5 calculate the raw score, z-scores, T- scores, and percentile ranks where appropriate. (20 points)
a. Given a raw score
of 35, find the z, T and %tile
b. Given the z score
of 1.2, find the raw score, T, and %tile
c. Given the T score
of 35, find the raw score, the z score and the %tile
d. Given the %tile
of 16, find the raw score, z, and T.
9. The Graduate Record Examination (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200. Scores range from 200 to 1600 and are approximately normally distributed. (25 points)
For
each of the following problems:
1.
Draw a rough sketch, darkening the portion of the cure that relates to the
answer,
2. Indicate the percentage or score called for by the problem.
a. What percentage of persons who take the test score above
1300?
b. What percentage score above 800?
c. What percentage score below 1200?
d. Above what score do about 20 percent of the test-takers
score?
e. Above what score do about 30 percent of the test-takers
score?
Since the assignment is worth 20 points overall, take the score you earn and divide it by 5 to get the number of points earn toward your final grade.