# Descriptive Statistics

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

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

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

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

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

c Name any outliers.

d

4 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?

5 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

a Complete the frequency table.

b Find the mean of the raw data.

c Find the median of the raw data.

6 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

a Find the mean, median, and mode.

b Which is the best measure of central tendency?

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

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

7 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

a Find the mean and median of the data.

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

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

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

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

64 85 93 55 87 90 73 81 86 79

a Create a box plot using the data.

b 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.

a What is the median?

b What is the range?

c What is the interquartile range?

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

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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.

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MEASURES

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

Answer

Mean

Mean is defined as the arithmetic average of data, that is, the sum of all the numbers divided by the number of observations contributing to that sum. The mean represents the balance point, or centre of gravity of the distribution and it is the most common measure of central tendency.

Mean is the best measure of central tendency when the data distributed approximately normal.

Median

Median is the middle most observation of the data, determined after all items are arranged in ascending or descending order of magnitude. In other words, median is that observation above which and below which lie 50% of all the data.

Median is the best measure of central tendency when the data distribution is skewed.

Mode

The Mode is simply the most frequently occurring item in a distribution.

Mode is the best measure of central tendency when the data is categorical and we want to know the most common category.

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

Answer

Frequency Stem Leaf

3 5 5 6 9

6 6 2 3 4 4 4 9

2 7 7 7

1 8 5

12

Mean = = 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

Answers

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

Mean = = 28.5

Median = item when the items are arranged in ...

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