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# Descriptive Statistics Purpose for Measuring Central Tendency

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1. Explain the general purpose for measuring central tendency?

2. Explain what is meant by each of the following statements:
a. The mean is the balance point of the distribution.
b. The median is the midpoint of the distribution.

3. Identify the circumstances in which the median rather than the mean is the preferred measure of central tendency.

4. Under what circumstances will the mean, the median, and the mode all have the same value?
X f cf c%
10 1
9 3
8 7
7 6
6 2
5 1

5. Under what circumstances is the mode the preferred measure of central tendency?
10. Find the mean, median, and mode for the set of scores in the following frequency distribution table:
(See attached)

23. The following frequency distribution summarizes the number of absences for each student in a class of n=20:

a. Find the mode for this distribution.
b. Find the median number of absences for this class.
c. Explain why you cannot compute the mean number of absences using the data provided in the table.

15. for the following score: 1, 0, 4, 1,1,5
a. calculate the mean. (note that the value of the mean does not depend on whether the set of scores is considered to be sample or a population.)
b. Find the deviation for each score, and check that the deviations sum to zero.
c. Square each deviation and compute SS. (again note that the value SS is independent of whether the set of scores is a sample or a population.)

23. Calculate SS, variance, and standard deviation for the following population of N=6 scores: 11,0,8,2,4,5. (Note: the definitional formula for SS works well with these scores)

Number of Absence(X) f
5 or more 3
4 4
3 3
2 6
1 3
0 1

See attached file for full problem description.