# Module 2 Assignment: Background Measures of Central Tendency (Math Problem Sample)

# Module 2 - Background

## Measures of Central Tendency

You can download the full, digital version of a statistics book using the link below. (Version in PDF, on the left side)

Lane, D. M. (n.d.). *Online Statistics Education: A multimedia course of study.* Retrieved from http://onlinestatbook.com/2/index.html

### Required Materials

**Digital Readings**

Read sections A–C from

Lane, D. M. (n.d.). *Online Statistics Education: Graphing distributions*. Retrieved from http://onlinestatbook.com/2/graphing_distributions/graphing_distributions.html

Read sections A (parts 1–9) and B from

Lane, D. M. (n.d.). *Online Statistics Education: Summarizing distributions*. Retrieved from http://onlinestatbook.com/2/summarizing_distributions/summarizing_distributions.html

Read section I (Distributions)

Lane, D. M., & Ziemer, H. (n.d.). *Online Statistics Education: Introduction*. Retrieved from http://onlinestatbook.com/2/introduction/introduction.html

**Videos and Exercises**

Using the websites below, watch the videos and complete the practice exercises for the topics in **BOLD**:

Khan Academy. (2014). Descriptive statistics. Retrieved from https://www.khanacademy.org/math/probability/descriptive-statistics

**Measures of central tendency**(6 videos, 4 practice exercises)**Box-and-whisker plots**(4 videos, 1 practice exercise)

Khan Academy. (2014).Statistical studies. Retrieved from https://www.khanacademy.org/math/probability/statistical-studies

**Categorical data**(3 videos, 2 practice exercises)

Measures of Central Tendency

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Measures of central tendency

Name

Institution

Measures of Central Tendency

1 Describe the measures of central tendency. Under what condition(s) should each one be used?

A measure of central tendency is considered to be a value that provides a description of a given set of data by showing a central position in the given data. The three measures of central tendencies include mean, mode and median. The mean is obtained by adding the total value of the data set then divide it by the number of values of the data. Mean therefore, represents an average value of the data set; hence, it should be used when dealing with an interval and ratio scales of measurement. The median is central value of an ordered distribution; is well used when dealing with an ordinal scale of measurement. The mode of a data set is the value that occurs most frequently; it is widely used at the nominal scale of measurement.

2 Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year.

55 77 64 77 69 63 62 64 85 64 56 59

Solution

Arranging the data in order

10147303204210055, 56, 59, 62, 63, 64, 64, 64, 69, 77, 77, 85

61264823253700StemLeaf

5 5 6 9

6 2 3 4 4 4 9

7 7 7

8 5

Mean = 55+56 + 59+ 62+63+ 64+ 64+ 64+69+ 77+ 77+ 85

=795/12= 66.25

Mean= 66 years (to the nearest a year)

1 A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below.

27 30 21 62 28 18 23 22 26 28

* Find the mean, median, and mode of newspapers sold over the 10-week period.

Solution

Mean = (27+30+21+62+28+18+23+22+26+28)/10

=285/10

Mean =28.5

Median

Arranging the data in the ascending order

18 21 22 23 (26 27) 28 28 30 62

Median = (26+27)/2 the data is even therefore, there are two values in the middle 26 and 27; hence I shall get their average.

Median =26.5

Mode

28 it appears more often (twice) than the other values

* Which measure(s) of central tendency best represent the data?

Mean

* Name any outliers.

62 It is not close to other values

1 Joe wants to pass his statistics class with at least a 75%. His prior four test scores are 74%, 68%, 84% and 79%. What is the minimum score he needs on the final exam to pass the class with a 75% average?

To have an average of 75% in five subjects, the total marks needs to be 75×5 =375 marks

The sum for the four subjects is 74+68+84+79 = 305 marks

Therefore, to get at least an average of 75% he has to score (375-305) = 70 marks to pass the class

2 Nancy participated in a summer reading program. The number of books read by the 23 participants are as follows:

10 9 6 2 5 3 9 1 6 3 10 ...

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