# Finding the Mean, Median, and Standard Deviation

Question 1

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

Enter your responses for the following calculations:

1. The arithmetic mean age of the senior citizens to the nearest hundredth is Blank years.

3. The median age of the senior citizens is Blank years.

5. The standard deviation of the ages of the senior citizens, calculated to the nearest hundredth of a year, is Blank years.

Question 2

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92.

Identify which of the following is the correct statement.

A. One-fourth of the senior citizens sampled are below 64 years of age.

B. The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age.

C. 24% of the senior citizens sampled are older than 81.5 years of age.

D.All of the above are correct.

Question 3

The data below represent the amount of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings: 11, 15, 23, 29, 19, 22, 21, 20 ,15, 25, 17.

Enter your responses for the following calculations:

1. The arithmetic mean carbohydrates in this sample is Blank grams.

3. The median carbohydrate amount in the cereal is Blank grams.

5. The first quartile of the carbohydrate amounts is Blank grams.

7. The third quartile of the carbohydrate amounts is Blank grams.

9. The range in the carbohydrate amounts is Blank grams.

11. The standard deviation of the carbohydrate amounts is Blank grams.

Question 4

Which of the following statistics is NOT a measure of central tendency?

A. arithmetic mean

B. median

C. mode

D. Q3

Question 5

Which measure of central tendency can be used for both numerical and categorical variables?

A. arithmetic mean

B. median

C. mode

D. standard deviation

Question 6

According to the empirical rule, if the data form a “bell-shaped” normal distribution, ________ percent of the observations will be contained within 2 standard deviations around the arithmetic mean.

A. 68.26

B. 88.89

C. 93.75

D. 95.44

Question 7

According to the Chebyshev rule, at least 75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

A. 1

B. 2

C. 3

D. 4

Question 8

True or False: The Z scores can be used to identify outliers.

Question 9

Which of the following is NOT sensitive to extreme values?

A. the range

B. the standard deviation

C. the interquartile range

D. the coefficient of variation

Question 10

The following set of data is from a sample of n=6: 7 4 9 7 3 12

Compute your answers for each computation listed below using Excel and then insert the data into the spaces provided in the table below.

Part a) Compute the mean, median, and mode.

Part b) Compute the range, variance, standard deviation, and coefficient of variation.

Part c) Compute the minimum, maximum, sum, count, first quartile, third quartile and interquartile ranges.

You are encouraged to use Excel for all/most of this!

* PART A

* Mean Blank 1

* Median Blank 2

* Mode Blank 3

* PART B

* Range Blank 4

* Variance Blank 5

* Standard Deviation Blank 6

* Coefficient of Variation Blank %

* PART C

* Minimum Blank 8

* Maximum Blank 9

* Sum Blank 10

* Count Blank 11

* First Quartile Blank 12

* Third Quartile Blank 13

* Interquartile Range Blank 14

Question 11

The following set of data is from a sample of n=6: 7 4 9 7 3 12

Answer both of these questions:

1. Compute the Z scores. Are there any outliers? Explain why or why not.

2. Describe the shape of the data set.