Statistics Proficiency Exam Chapter 3

Find the values of n, ΣX, and M for the sample that is summarized in the following frequency distribution table. X, f 5, 1 4, 2 3, 2 2, 4 1, 1

For this sample n=10, ΣX=28, and M=28/10=2.8

A sample of n=8 scores has a mean of M=10. IF one new person with a score of X=1 is added to the sample, what will be the value for the new mean?

The original sample has n=8 and ΣX=80. The new sample has n=9 and ΣX=81. The new mean is M=9.

What general purpose is served by a good measure of central tendency?

The purpose of central tendency is to identify a single score that serves as the best representative for an entire distribution, usually a score from the center of the distribution.

It is possible for a distribution to have more than one mode. (True or false?)

True

It is possible for more than 50% of the scores in a distribution to have values greater than the mean. (True or false?)

True

The mode is the correct way to measure central tendency for data from nominal scale. (True or false?)

True

Explain why the mea is often not a good measure of central tendency for a skewed distribution.

With a skewed distribution, the extreme scores in the tail can displace the mean. Specifically, the mean is displaced away from the mean pile of scores and moved out toward the tail. The result is that the mean is often not a very representative value.

For the following sample a. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. b. Assume the the scores are measurements of a discrete variable and find the median. Scores: 1, 2, 2, 3, 4

a. Median =2.25 b. Median=2

An instructor recorded the number of absences for each student in a class of 20 and obtained the frequency distribution shown int he following table. Number of absences (X), f 7, 1 6, 0 5, 3 4, 3 3, 3 2, 5 1, 4 0, 1 a. Using the mean to define central tendency, what is the average number of absences for this class? b. Using the median to define central tendency, what is the average number of absences for this class? c. Using the mode to define central tendency, what is the average number of absences for this class?

a. The mean is 2.85 b. The median is 2.50 c. The mode is 2

Find the median for each distribution of scores: a. 3, 10, 8, 4, 10, 7, 6 b. 13, 8, 10, 11, 12, 10

a. The median is X=7. b. The median is X=10.5.

One sample has a mean of M=4 and a second sample has a mean of M=8. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n=7 scores? b. What is the mean for the combined set if the first sample has n=3 and the second sample has n=7? c. What is the mean for the combined set if the first sample has n=7 and the second sample has n=3?

a. The new mean is M=6 b. The new mean is (12+56)/10=6.8 c. The new mean is (28+24)/10=5.2

A population has a mean of μ=80. a. If 6 points were added to every score, what would be the value for the new mean? b. If every score were multiplied by 2, what would be the value for the new mean?

a. The new mean would be 86 b. The new mean would be 160

For each of the following situations, identify the measure of central tendency (mean, median, or mode) that would provide the best description of the "average" score: a. The college recorded the age of each student who graduated last spring. Although the majority of the students were in their early 20s, a few mature students were in their 40s, 50s, and 60s. b. A researcher asked each participant to select his or her favorite color from a set of eight color patches c. A professor uses a standardized test to measure verbal skill for a sample of new college freshman.

a. median (a few extreme scores would distort the mean) b. mode (nominal scale) c. mean

The ______ is the score that divides a distribution in half so that 50% of the individuals in a distribution have scores at or below the _______

median, median

In a frequency distribution, the ______ is the score or category that has the greatest frequency

mode

A sample of n=7 scores has a mean of M=5. What is the value of ΣX for this sample?

ΣX=35

Find the mean for the following sample of n=6 scores: 4, 10, 7, 5, 9, 7

ΣX=42 and M=7

A sample of n=8 scores has a mean of M=6. Wha tis the value of ΣX for this sample?

ΣX=48

A sample of n=7 scores has a mean of M=8. A second sample has n=3 scores with a mean of M=12. If the two samples are combined, what is the mean for the combined sample?

The combined mean is (56+36)/10=9.2

One sample has n=6 scores with a mean of M=4. A second sample has n=4 scores with a mean of M=9. If the two samples are combined, what is the mean for this combined sample?

The combined sample has n=10 scores that total ΣX=60. The mean is M=6.

Find the mean, median, and mode for the following sample of scores: 2, 3, 3, 1, 2, 5, 2, 3, 4, 2

The mean is 27/10=2.7, the median is 2.5, and the mode is 2

Find the mean, median, and mode for the set of scores in the following frequency distribution table: X, f 5, 1 4, 5 3, 4 2, 1 1, 1

The mean is 40/12=3.33, the median is 3.50, and the mode is 4

In a recent survey comparing picture quality for three brands of color televisions, 63 people preferred brand A, 29 people preferred brand B, and 58 people preferred brand C. What is the mode for this distribution?

The mode is brand A

A population of N=10 scores has a mean of μ=24. IF one person with a score of X=8 is removed from the sample, what will be the value for the new mean?

The new mean is 198/9=22.

A sample of n=6 scores has mean of M=10. If one score is changed from X=14 to X=2, what will be the value for the new sample mean?

The new mean is 48/6=8. Changing X=14 to X=2 subtracts 12 points from ΣX.

A sample of n=4 scores has a mean of 9. If one new person with a score of X=14 is added to the sample, what is the value for the new sample mean?

The original sample has n=4 and ΣX=36. The new sample has n=5 scores that total ΣX=50. The new mean is M=10.

A sample of n=7 scores has mean of M=5. After one new score is added to the sample, the new mean is found to be M=6. What is the value of the new score? (Hind: Compare the values for ΣX before and after the score was added).

The original sample has n=7 and ΣX=35. The new sample has n=8 and ΣX=48. The new score must be X=13.

Changing the value of a score in a distribution will always change the mean. (True or false?)

True

The goal of _______ is to find the single score that is most typical or most representative of the entire group.

central tendency

The _______ for a distribution is the sum of the scores divided by the number of scores

mean

_______ is a statistical measure to determine a single score that defines the center fo a distribution.

Central tendency

A distribution has a mean of 75 and a median of 70. This distribution is probably positively skewed. (True or false?)

False

If a graph is used to show the means obtained from an experiment, the different treatment conditions (the independent variable) should be listed on the vertical axis. (True or false?)

False

It is possible for more than 50% of the scores in a distribution to have values greater than the median. (True or false?)

False

Adding a new score to a distribution will always change the mean. (True or false?)

False. If the score is equal to the mean, it will not change the mean.

If you have a score of 52 on an 80-point exam, then you definitely scored above the median. (True or false?)

False. The value of the median would depend on where the scores are located.

Which measure of central tendency is most likely to be affected by one or two extreme scores in a distribution? (mean, median, or mode)

Mean

A sample of n=6 scores has a mean of M=40. One new scores is added to the sample and the new mean is found to be M=42. What can you conclude about the value of the new score? a. It must be greater than 40 b. It must be less than 40

a