Statistics
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Econ 302 Summer 1 2021 Midterm

Midterm Exam

· There are 4 parts:

**In the first three parts, you are able to choose your best questions to be graded.**

Part A (Do 6): Fill in the Blank (1-12)

Part B (Do 6): True or False (13-23)

Part C (Do 12): Multiple Choice (24-46)

Part D (Do All): Answer the Following Questions (47-53)

Part E (Do All): Work Problems (54-63) **Must show your work step by step to get full credit**

· There are 2 different ways to submit your answer sheet:

1. Scan your answer sheet and place it in ONE FILE in the drop box. (preferable)

2. Use Ms-Word and place it in the drop-box.

· Deadline: June 21st at 1:00 pm CST

· All work must be shown step by step in order to receive credit.

Part A (Do 6): Fill in the Blank (1-12)

1. The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making effective decisions is called ________________.

2. Methods of organizing, summarizing, and presenting data in an informative way are called ________________.

3. The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest are called the ________________.

4. List the two types of variables. ________________ ________________

5. The number of bedrooms in a house is an example of a ________________. (discrete variable, continuous variable, qualitative variable — pick one)

6. The jersey numbers of Major League Baseball players are an example of what level of measurement? ________________

7. The classification of students by eye color is an example of what level of measurement? ________________

8. What percent of the values in a data set are always larger than the median? ________________

9. The square of the standard deviation is the ________________.

10. The standard deviation assumes a negative value when ________________. (all the values are negative, at least half the values are negative, or never — pick one)

11. Which of the following is least affected by an outlier? ________________. (mean, median, or range — pick one)

12. If the mean > median > mode, then the data are skewed to the right or left. (pick one) ________________

Part B (Do 6): True or False (13-23)

13. ____ The random sample is the most important, because statistical theory applies to it alone.

14. ____ Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations.

15. ____ The sum of the class frequencies is equal to the number of observations made.

16. ____ Planning is the most important step in statistical studies.

17. ____ A relative frequency distribution describes the proportion of data values that fall within each category.

18. ____ There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations.

19. ____ The median always exists in a set of numerical data.

20. ____ Pk to Kth percentile so K can be any number between 0 and 100, although usually K is an integer.

21. ____ The values of the variance and the standard deviation are never negative.

22. ____ If the mean = median = mode, then the data are symmetric

23. ____ The value of variance is in a different unit, whereas the value of standard elevation is in the same units.

Part C (Do 12): Multiple Choice (24-46)

24. For the data values, 20,31,45,54,38,33,22,45, and 17, the mode is

a) 33 b) 34 c) 38 d) 45

25. The simplest measure of dispersion is the

a) Standard deviation b) Variance c) Quartile deviation d) Range

26. For the values 10, 20, 30, 40, and 50, the average absolute deviation from the mean is

a) 10 b) 15 c) 12 d) 14

27. A simple random sample for five executives who went on a diet on their doctor’s order report the following numbers of pounds lost during their first two weeks on the diet: 5, 8, 3, 7, 8. What is the variance for this sample?

a) 4.7 b) 3.76 c) 1.94 d) 2.17

28. The following are the ages, in year, of 6 people who applied for a job: 21, 39, 23, 25, 36, 34. The median age is _____________.

a) 29.7 b) 28.5 c) 24 d) 18

29. For the value 10, 40, 20, 50, and 40, the value of the arithmetic mean is _____________.

a) 32 b) 40 c) 30 d) 34.5

30. The difference between the largest and smallest data values in the _____________.

a) Variance b) Range

c) Coefficient of Variation d) Interquartile Range

31. We ask a sample of 6 students from college freshman class the question: “How many movies did you see at the movie theater during the past month?”. The 6 students said: 4, 0, 2, 3, 1, 2, respectively. Find the sample standard deviation _____________.

a) 4.0 b) 199973 c) 1.4142 d) 10

32. We select a sample of 5 households from a certain geographic area. The following are the number of cars owned by the residents of each of the 5 households: 4, 3, 2, 3, 3. The sample variance is _____________.

a) 3.0 b) 2.0 c) 0.7071 d) 0.5

33. The value of the middle term in a ranked data set is called the

A) Mean B) Median C) Mode

34. Which of the following summary measures is/are influenced by extreme values?

A) Mean B) Median C) Mode D) Range

35. Which of the following summary measures can be calculated for qualitative data?

A) Mean B) Median C) Mode

36. Which of the following can have more than one value?

A) Mean B) Median C) Mode

37. Which one of the following is obtained by taking the difference between the largest and the smallest values of a data set

A) Variance B) Range C) Mean

38. Which of the following is the mean of the squared deviations of x values from the mean?

A) Standard Deviation

B) Population Variance

C) Sample Variance

39. The values of the variance and standard deviation are

A) Never Negative

B) Always positive

C) Never zero

40. A summary measure calculated for the population data is called

A) A population parameter

B) A Sample Statistic

C) An outlier

41. A summary measure calculated for the sample data is called a

A) A population parameter

B) A sample statistic

C) An outlier

42. Chebyshev’s theorem can be applied to

A) Any distribution

B) Bell-shaped distributions only

C) Box-and-whisker plot

43. The empirical rule can be applied to

A) Any distribution

B) Bell-shaped distributions only

C) Box-and-whisker plot

44. The first quartile is a value in a ranked data set such that about

A) 75% of the values are smaller and about 25% are larger than this value

B) 50% of the values are smaller and about 50% are larger than this value

C) 25% of the values are smaller and about 75% are larger than this value

45. The third quartile is a value in a ranked data set such that about

A) 75% of the values are smaller and about 25% are larger than this value

B) 50% of the values are smaller and about 50% are larger than this value

C) 25% of the values are smaller and about 75% are larger than this value

46. The 75th percentile quartile is a value in a ranked data set such that about

A) 75% of the values are smaller and about 25% are larger than this value

B) 25% of the values are smaller and about 75% are larger than this value

Part D (Do All): Answer the following questions (47-53)

47. What are the measures of central tendency?

48. What is the sampling error?

49. Name 6 reasons why we use samples instead of an entire population.

50. Name measures of variability.

51. What is the regression analysis? How does it differ from correlation analysis?

52. Name the three types of sample.

53. What are four types of random sample?

Part E (Do All): Work Problems (54-63)

54. Suppose that the average contribution to the company’s profit sharing plan is $42.32, with a standard deviation of $8.53. At least what percent of the contributions lie between $22.34 and $62.30?

55. Use the following data to find P??, P??, P??

5 7 8 9 33 22 14 12 0 0

56. The following data give the numbers of times 10 persons used their credit cards during the past three months.

9 6 28 14 2 18 7 3 16 6

Please answer the following questions:

Mean

Median

Mode

Range

Variance

Standard Deviation

57. The cars owned by all people living in a city are, on average, 7.3 years old with a standard deviation of 2.2 years.

a. Using Chebyshev’s theorem, find at least what percentage of cars in this city are

i. 1.8 to 12.8 years old ii. .7 to 13.9 years old

b. Using Chebyshev’s theorem, find the interval that contains the ages of at least 75% of the cars owned by all people in this city.

58. The following random sample of annual salaries was recorded. Units are in thousands of dollars.

45

50

40

42

30

51

46

10

52

47

1. Calculate the mean and standard deviation.

1. Using Chebyshev’s, between what two bounds will at least 68.26% of the data lie?

1. Using Chebyshev’s, between what two bounds will at least 75% of the data values lie?

59. According to Chebyshev’s theorem, at least what proportion of the data will fall within ? ± k? for each value of k?

a. k = 5

b. k = 3.5

c. k = 2.6

d. k = 4.2

60. The fuel capacity in gallons of 50 randomly selected 2018 cars is shown below .

Class

Frequency

10 – 12

6

13 – 15

4

16 – 18

14

19 – 21

15

22 – 24

8

25 – 27

2

28 – 30

1

50

Please answer the following questions:

a) Mean

b) Median

c) Mode

d) Range

e) Variance

f) Standard deviation

g) 3rd Quartile

h) 45th Percentile

61. Facing declining revenues, the owner of a video club arbitrarily selected 68 files from his membership list to determine the number of videos rented per household last month. He obtained these data:

X

0

1

2

3

4

5

6

7

8

10

14

f

10

9

11

7

13

9

5

1

3

4

2

a. Find the median number of videos rented.

b. The profit per rented video is roughly $0.50. If there are a total of 2648 members, estimate the monthly profit using the median number from the survey.

62. Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times recorded for each method are shown. Times are in minutes.

Public Transportation

18

15

13

20

22

17

11

9

3

16

Automobile

12

24

19

21

19

25

23

14

17

10

a. Compute the sample mean time to get to work for each method.

b. Compute the sample standard deviation for each method.

c. On the basis of your results from a) and b), which method of transportation should be preferred? Explain.

63. In a class of 29 students, this distribution of quiz scores was recorded.

Grade

Frequency

0-2

1

3-5

3

6-8

5

9-11

14

12-14

6

Find the mean, median, mode, variance, and standard deviation.

a. Mean =

b. Median =

c. Mode =

d. Variance =

e. Standard Deviation =

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