Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
Math 256, Hallstone Review for Final Exam Spring 2024
Part I (Chapters 1-6)
1. A sample of 10 high school seniors was asked to record the amount of time they spent studying during a one
week period. The ranked data is given here: 0,1,1,3,4,4,5,5,5,8. Which one of the following statements is
correct concerning this data?
1) The sample mean is 7.
2) The sample mean is 4.
3) The sample median is 4.
4) All of the above are correct.
5) None of the above are correct.
2. Shown below are estimates of the mileage recorded for thirteen 1982 model cars:
Miles per Gallon 32 33 30 40
Number of Cars 3 2 5 3
Compute the following for these data:
1) Mean miles per gallon
2) Median miles per gallon
3) Mode miles per gallon
4) Standard deviation (miles per gallon)
3. From the beginning of the class to the end, we have discussed “distributions” of data. What three things are
we usually interested in when we discuss “distributions”?
a. Mean, median, mode
b. Center, spread, shape
c. Range, standard deviation, variance
d. Sex, drugs, rock and roll
4. Which of the following random variables would be considered continuous?
a. the number of brothers a randomly chosen person has
b. the time it takes for a randomly chosen woman to run 100 yards
c. the number of cars owned by a randomly chosen adult male
d. number of orders received by a mail order company in a randomly chosen week
5. Identify the following as true (T) or false (F).
1)_____ An average alone does not completely describe the characteristics of a set of data; measures of
spread are also needed.
2)_____ If the original measurements are expressed in feet, the variance would also be expressed in feet.
3)_____ The employees of a company are classified by religious preference. The company is asked to
name the religion practiced by the greatest number of its employees. The mode would be the most
appropriate measure of center in this case.
6. A set of experimental data has a mean x of 40 pounds and a standard deviation s of 8 pounds. Find the
value of any piece of data that has a standard z-score of -1.25.
1) 30
2) 32
3) 50
4) There is not enough information to answer the question.
5) None of the above are correct.
7. A class of third grade students, when given a nationally used standardized examination, was found to have a
mean score of 75 with a standard deviation of 4. Each child's score was changed to a standard z-score, for
1
, Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
comparison with his/her classmates. What is the z-score (to the nearest hundredth) for a child who scored 81?
8. Data where numbers 1-5 are used to represent categories like “strongly disagree”, “disagree”, “neutral”, etc.
are referred to as ________________________ data. (Two answers possible.)
9. a) The fact that you can have females accepted at a higher rate in every program at a university, but still be
accepted at a lower rate overall at that university is known as _____________________
b) The person responsible for both the concept and name of the stem and leaf display is ______________
A study by the university if Texas Southwestern Medical Center examined 626 people to see if there was a
relationship between tattoo status (tattoo from commercial parlor, tattoo done elsewhere, or no tattoo) and Hepatitis
C status (whether or not you have Hepatitis C). The data is given in the following table:
Tattoo done in a Tattoo done No Tattoo
commercial parlor elsewhere Total
Has Hepatitis C 17 8 18
No Hepatitis C 35 53 495
Total
10. a) How many variables are there in the above data? ________
b) List them:
c) What percentage of people with Hepatitis C had no tattoo?
d) What percentage of people with a tattoo done in a commercial parlor had no hepatitis C?
e) Give the conditional distribution of having hepatitis C for those who had their tattoos done elsewhere?
Has Hepatitis C ______ No Hepatitis C ______
f) Does it appear that having hepatitis C is independent of your tattoo status? Give an appropriate picture to
help with your answer
The table below shows how a company’s employees commute to work.
Transportation Mode
Car Bus Train Total
26 20 44 90
Management
56 106 168
Labor
Job Class 126 8 212 420
Total
2
11. a. How many variables are there in the above table? 2 3 4 5 6
b. What percentage of management employees take their car?
c. What percentage of people who commute in their car are management?
d. What is the conditional distribution (in %) of mode of transportation for management?
car _____ bus _____ train _____
12. a. Draw a display of the commuting data in the previous problem above that would show whether or not
there is an association between job class and mode of transportation
2
,Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
b. Do Job classification and mode of transportation appear to be independent? Give a statistical argument
based on your graph to support your conclusion.
13. The following data is from the April 2005 Nutrition Action Newsletter, in an article that says that strong
bones require more than calcium. Potassium is one of several minerals that is discussed, and the data is how
much potassium is the listed foods. (I changed the data from milligrams to centigrams to make it easier on
you.)
Potassium
Food (centigrams)
Potato (1) 94
Sweet potato (1) 54
Banana (1) 49
Halibut (3 oz. cooked) 49
Lima beans 49
Fresh tuna (3 oz. cooked) 48
Swiss chard 48
Acorn squash 45
Spinach 42
Salmon (3 oz. cooked) 39
Cantaloupe (1/4 melon) 37
Lentils 37
Milk (1 cup) 37
Watermelon (2 cups) 32
Grapes (1 cup) 31
Pork (3 oz. cooked) 31
Raisins (1/4/ cup) 31
a) Draw a stem and leaf display (stemplot) of the data in the above problem. Use the space to the right of the
data
b) If you were asked by your friend, “What is the average amount of potassium in the foods listed?”, what
should your response be? (Remember, you have now had the benefit of taking part of a statistics class.)
Explain your answer.
14. What must be true about a set of data when its standard deviation is zero (s = 0)?
1) All values of the data appear with the same frequency.
2) All of the data have the same value.
3) The mean value of the data is also zero.
4) All of the above are correct.
5) None of the above are correct.
15. The security Department of the college is taking a survey of the number of people in each car parking at the
college. If x represents the number of people in each car then x is an example of
1) a categorical variable.
2) a continuous variable.
3) a discrete variable.
16. A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective
in killing roaches. 79% of the respondents agreed that the roach disk would be effective. The number 79% is
what? a. parameter . b. population. c. statistic. d. sample
The March 2006 Nutrition Action Health Letter has an article on frozen seafood. The data table below is part of the
data presented on battered or breaded fillets, with all numbers being for a serving closest to 4 ounces. I changed
sodium figures to centigrams to make it easier on you.
3
, Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
Product Name Number of fillets Calories Total Fat (g) Sodium (cg)
Natural Sea Breaded Cod Fish 2 240 10 40
Dr. Praeger’s Fish- Breaded 2 220 8 42
Whole Catch Lightly Breaded Fish 1 250 9 33
Trader Joes’s Breaded Alaskan Cod 1 280 10 37
Ian’s Lightly Breaded Fish 1 260 8 41
Gorton’s Garlic Breaded Fish 2 230 12 77
Tiger Thai Tempura Cod 1 220 14 16
Gorton’s Fish - Beer Batter 2 240 13 57
Mrs. Paul’s Crispy Battered Fish 1 190 9 61
Van de Kamp’s Beer Battered Fish 2 260 12 70
17. a) Draw a stemplot (stem and leaf display) for the fish sodium data.
b) Some brands are cod fish, and the others are not. Draw an appropriate display to see if there is a
difference in sodium for the two types of fish (cod and not cod). (With only this partial data, it would be hard
to come to a conclusion. I just want the display.)
18. Using the data for total fat above, find the mean, median, standard deviation, and variance. Be sure to give
units.
19. Give the name of all the variables/identifiers and their type (categorical, discrete, continuous, or identifier).
See the previous frozen fish problem.
a. ________________________________________ ________________________
b. ________________________________________ ________________________
c. ________________________________________ ________________________
d. ________________________________________ ________________________
e. ________________________________________ ________________________
A poll conducted about potential voters came up with the data in the following table.
Democrat Republican Independent Total
Male 40 80 30 150
Female 90 50 20
Total 130 310
20. a) How many variables are there in this problem? ________
b) List them:
c) What percentage of Democrats were male?
d) What percentage of males were Democrats?
21. a) Give the conditional distribution (in %) of gender for Democrats? (See above.)
Male ______ Female ______
b) Does it appear that political party affiliation is independent of gender? Give an appropriate picture to help
with your answer?
22. What does a standard z-score of -1.3 indicate about a particular value of x?
4
Math 256, Hallstone Review for Final Exam Spring 2024
Part I (Chapters 1-6)
1. A sample of 10 high school seniors was asked to record the amount of time they spent studying during a one
week period. The ranked data is given here: 0,1,1,3,4,4,5,5,5,8. Which one of the following statements is
correct concerning this data?
1) The sample mean is 7.
2) The sample mean is 4.
3) The sample median is 4.
4) All of the above are correct.
5) None of the above are correct.
2. Shown below are estimates of the mileage recorded for thirteen 1982 model cars:
Miles per Gallon 32 33 30 40
Number of Cars 3 2 5 3
Compute the following for these data:
1) Mean miles per gallon
2) Median miles per gallon
3) Mode miles per gallon
4) Standard deviation (miles per gallon)
3. From the beginning of the class to the end, we have discussed “distributions” of data. What three things are
we usually interested in when we discuss “distributions”?
a. Mean, median, mode
b. Center, spread, shape
c. Range, standard deviation, variance
d. Sex, drugs, rock and roll
4. Which of the following random variables would be considered continuous?
a. the number of brothers a randomly chosen person has
b. the time it takes for a randomly chosen woman to run 100 yards
c. the number of cars owned by a randomly chosen adult male
d. number of orders received by a mail order company in a randomly chosen week
5. Identify the following as true (T) or false (F).
1)_____ An average alone does not completely describe the characteristics of a set of data; measures of
spread are also needed.
2)_____ If the original measurements are expressed in feet, the variance would also be expressed in feet.
3)_____ The employees of a company are classified by religious preference. The company is asked to
name the religion practiced by the greatest number of its employees. The mode would be the most
appropriate measure of center in this case.
6. A set of experimental data has a mean x of 40 pounds and a standard deviation s of 8 pounds. Find the
value of any piece of data that has a standard z-score of -1.25.
1) 30
2) 32
3) 50
4) There is not enough information to answer the question.
5) None of the above are correct.
7. A class of third grade students, when given a nationally used standardized examination, was found to have a
mean score of 75 with a standard deviation of 4. Each child's score was changed to a standard z-score, for
1
, Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
comparison with his/her classmates. What is the z-score (to the nearest hundredth) for a child who scored 81?
8. Data where numbers 1-5 are used to represent categories like “strongly disagree”, “disagree”, “neutral”, etc.
are referred to as ________________________ data. (Two answers possible.)
9. a) The fact that you can have females accepted at a higher rate in every program at a university, but still be
accepted at a lower rate overall at that university is known as _____________________
b) The person responsible for both the concept and name of the stem and leaf display is ______________
A study by the university if Texas Southwestern Medical Center examined 626 people to see if there was a
relationship between tattoo status (tattoo from commercial parlor, tattoo done elsewhere, or no tattoo) and Hepatitis
C status (whether or not you have Hepatitis C). The data is given in the following table:
Tattoo done in a Tattoo done No Tattoo
commercial parlor elsewhere Total
Has Hepatitis C 17 8 18
No Hepatitis C 35 53 495
Total
10. a) How many variables are there in the above data? ________
b) List them:
c) What percentage of people with Hepatitis C had no tattoo?
d) What percentage of people with a tattoo done in a commercial parlor had no hepatitis C?
e) Give the conditional distribution of having hepatitis C for those who had their tattoos done elsewhere?
Has Hepatitis C ______ No Hepatitis C ______
f) Does it appear that having hepatitis C is independent of your tattoo status? Give an appropriate picture to
help with your answer
The table below shows how a company’s employees commute to work.
Transportation Mode
Car Bus Train Total
26 20 44 90
Management
56 106 168
Labor
Job Class 126 8 212 420
Total
2
11. a. How many variables are there in the above table? 2 3 4 5 6
b. What percentage of management employees take their car?
c. What percentage of people who commute in their car are management?
d. What is the conditional distribution (in %) of mode of transportation for management?
car _____ bus _____ train _____
12. a. Draw a display of the commuting data in the previous problem above that would show whether or not
there is an association between job class and mode of transportation
2
,Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
b. Do Job classification and mode of transportation appear to be independent? Give a statistical argument
based on your graph to support your conclusion.
13. The following data is from the April 2005 Nutrition Action Newsletter, in an article that says that strong
bones require more than calcium. Potassium is one of several minerals that is discussed, and the data is how
much potassium is the listed foods. (I changed the data from milligrams to centigrams to make it easier on
you.)
Potassium
Food (centigrams)
Potato (1) 94
Sweet potato (1) 54
Banana (1) 49
Halibut (3 oz. cooked) 49
Lima beans 49
Fresh tuna (3 oz. cooked) 48
Swiss chard 48
Acorn squash 45
Spinach 42
Salmon (3 oz. cooked) 39
Cantaloupe (1/4 melon) 37
Lentils 37
Milk (1 cup) 37
Watermelon (2 cups) 32
Grapes (1 cup) 31
Pork (3 oz. cooked) 31
Raisins (1/4/ cup) 31
a) Draw a stem and leaf display (stemplot) of the data in the above problem. Use the space to the right of the
data
b) If you were asked by your friend, “What is the average amount of potassium in the foods listed?”, what
should your response be? (Remember, you have now had the benefit of taking part of a statistics class.)
Explain your answer.
14. What must be true about a set of data when its standard deviation is zero (s = 0)?
1) All values of the data appear with the same frequency.
2) All of the data have the same value.
3) The mean value of the data is also zero.
4) All of the above are correct.
5) None of the above are correct.
15. The security Department of the college is taking a survey of the number of people in each car parking at the
college. If x represents the number of people in each car then x is an example of
1) a categorical variable.
2) a continuous variable.
3) a discrete variable.
16. A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective
in killing roaches. 79% of the respondents agreed that the roach disk would be effective. The number 79% is
what? a. parameter . b. population. c. statistic. d. sample
The March 2006 Nutrition Action Health Letter has an article on frozen seafood. The data table below is part of the
data presented on battered or breaded fillets, with all numbers being for a serving closest to 4 ounces. I changed
sodium figures to centigrams to make it easier on you.
3
, Statistics Final Exam Practice – Math 256 (Solved Problems + Formulas)
Product Name Number of fillets Calories Total Fat (g) Sodium (cg)
Natural Sea Breaded Cod Fish 2 240 10 40
Dr. Praeger’s Fish- Breaded 2 220 8 42
Whole Catch Lightly Breaded Fish 1 250 9 33
Trader Joes’s Breaded Alaskan Cod 1 280 10 37
Ian’s Lightly Breaded Fish 1 260 8 41
Gorton’s Garlic Breaded Fish 2 230 12 77
Tiger Thai Tempura Cod 1 220 14 16
Gorton’s Fish - Beer Batter 2 240 13 57
Mrs. Paul’s Crispy Battered Fish 1 190 9 61
Van de Kamp’s Beer Battered Fish 2 260 12 70
17. a) Draw a stemplot (stem and leaf display) for the fish sodium data.
b) Some brands are cod fish, and the others are not. Draw an appropriate display to see if there is a
difference in sodium for the two types of fish (cod and not cod). (With only this partial data, it would be hard
to come to a conclusion. I just want the display.)
18. Using the data for total fat above, find the mean, median, standard deviation, and variance. Be sure to give
units.
19. Give the name of all the variables/identifiers and their type (categorical, discrete, continuous, or identifier).
See the previous frozen fish problem.
a. ________________________________________ ________________________
b. ________________________________________ ________________________
c. ________________________________________ ________________________
d. ________________________________________ ________________________
e. ________________________________________ ________________________
A poll conducted about potential voters came up with the data in the following table.
Democrat Republican Independent Total
Male 40 80 30 150
Female 90 50 20
Total 130 310
20. a) How many variables are there in this problem? ________
b) List them:
c) What percentage of Democrats were male?
d) What percentage of males were Democrats?
21. a) Give the conditional distribution (in %) of gender for Democrats? (See above.)
Male ______ Female ______
b) Does it appear that political party affiliation is independent of gender? Give an appropriate picture to help
with your answer?
22. What does a standard z-score of -1.3 indicate about a particular value of x?
4
