# Case Measures of Central Tendency (Math Problem Sample)

Case Assignment

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Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

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

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

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.

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

Name any outliers.

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?

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 4 7 6 3 5 6 2 6 5 3 7 2

Number of books read Frequency

1–2

3–4

5–6

7–8

9–10

Complete the frequency table.

Find the mean of the raw data.

Find the median of the raw data.

The chart below represents the number of inches of snow for a seven-day period.

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

2 5 3 10 0 4 2

Find the mean, median, and mode.

Which is the best measure of central tendency?

Remove Wednesday from the calculations. How does that impact the three measures of central tendency?

Describe the effect outliers have on the measures of central tendency.

A dealership sold 15 cars last month. The purchase price of the cars, rounded to the nearest thousand, is represented in the table.

Purchase price Number of cars sold

$15,000 3

$20,000 4

$23,000 5

$25,000 2

$45,000 1

Find the mean and median of the data.

Which measure best represents the data? Use the results to support your answer.

What is the outlier and how does it affect the data?

8. What do the letters represent on the box plot?

Box plot

9. The test scores from a math final exam are as follows:

64 85 93 55 87 90 73 81 86 79

Create a box plot using the data.

Label the five points on the box plot and include numerical answers from part "a."

10. Using the data and results from Question 9, answer the following questions.

What is the median?

What is the range?

What is the interquartile range?

In a short paragraph, describe the data in the box plot.

Module 2 - Case Measures of Central Tendency

Name

Course

Instructor

Date

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

The measures of central tendency are measures of location and include the mean, mode and median and all are suitable under different situations. The mode is the most common number occurring, and when none occurs more than once then all the numbers are the mode. The mode is mostly used in categorical data when in need to know the frequency in different categories. The median is the middle value in the data set when the data is rearranged from the smallest value to the largest value. When the frequency is an even number the median is the average of the two values at the middle. The median is less affected by extreme values and skewness compared to the mean and is more suitable in these circumstances. The mean is the average value in a data set and depends on the sum of the values and frequency of a data set. The mean takes into account all the values, but it is also susceptible to extreme values and unsuitable in such cases. The mean is illustrated as

INCLUDEPICTURE "https://statistics.laerd.com/statistical-guides/img/measures-of-central-tendency-1.png" \* MERGEFORMATINET and then INCLUDEPICTURE "https://statistics.laerd.com/statistical-guides/img/measures-of-central-tendency-4.png" \* MERGEFORMATINET

(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

Stem plot

55 6 962 3 4 4 4 977 785Mean= INCLUDEPICTURE "https://statistics.laerd.com/statistical-guides/img/measures-of-central-tendency-4.png" \* MERGEFORMATINET = (55+56+59+62+63+64+64+64+69+77+77+85)/12= 795/12 =66 years

[3] 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.

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

Name any outliers.

(a)Mean= INCLUDEPICTURE "https://statistics.laerd.com/statistical-guides/img/measures-of-central-tendency-4.png" \* MERGEFORMATINET = = [27+30+21+62+28+18+23+22+26+28] = 285/10 = =28.5

Median= [10+1]/2 hence the median of the 5th and 6th value

Data in increasing order = 18, 21, 22, 23, 26, 27, 28, 28, 30, 62

= (26+27)/2 = 26.5

Mode

Data in ascending order = 18, 21, 22, 23, 26, 27, 28, 28, 30, 62= 28.

(b) Assuming that the data is grouped in classes with class limits10-20 up to the 60- 70 class limit, and the highest frequency is in the 20-30 class, with no data in classes 40-50 and 50-60. The median is the best measure of central tendency in the case as it is not affected by the outlier.

(C) Outliers

Outliers are the extreme values in a data set and depend on the interquartile range, with the first quartile being the middle point in the lower half the data while the third quartile is the second midpoint in upper half.

18, 21, 22, 23, 26, 27, 28, 28, 30, 62

First quartile= 22

The lower half is {18, 21, 22, 23, 26}

Third quartile=28

The upper half is {27, 28, 28, 30, 62}

Interquartile range (IQR) = 28-22=6

Outliers l...

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