# Descriptive Statistics and Measures of Central Tendency

For my personal study guide.

Refer to the enclosed chart which represents 10 days and the number of questions asked in the AM and PM on Day 1 through Day 10. Given the data answer the following:

1. Calculate and report the mean, median, and mode of the data.

2. Now calculate the standard deviation of the data. For this calculation compute the difference between each one of the observations and the mean, (this number may be positive or negative), then multiply each of these differences by itself, then add all of these products, and finally divide the sum total by the number of observations. You'll get the "VARIANCE". Now take the square root of this number and you get what is called the "STANDARD DEVIATION" that measures the dispersion of the data from their mean.

3. Label the "Variance" and the "Standard Deviation"

DAY AM (Number of Q's) PM (Number of Q's)

1 6 4

2 4 5

3 1 7

4 3 2

5 8 1

6 2 5

7 4 7

8 1 1

9 3 6

10 7 12

~Please show your work, so I understand the concept.

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#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics. Formula for the calculation and Interpretations of the results are also included.

Statistics Questions

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.

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