The frequency distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 

1. (5 points) The frequency distribution below summarize the home sale prices in a city for a specific month. Determine the width of each class.

1. 20
2. 28
3. 30
4. 31

1. (5 points) The following frequency distribution analyzes the scores on a test. Find the class boundaries of scores interval 95-99.

1. 95.5, 99.5
2. 95.5,100.5
3. 94.5,99.5
4. 94.5,100.5

1. (5 points) The histogram below represents the number of television sets per household for a sample of U.S. households. What is the maximum number of households having the same number of television sets?

1. 20
2. 100
3. 5
4. 50

1.  (5 points) The students in John’s math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score.

528   505  342  348  492

346   349  643  470  482

A. 450.5

B. 459.7

C. 460.5

D. 441.7

1. (5 points) Listed below are the amounts of time in months that the employees of a restaurant have been working at the restaurant. Find the median.

12  4   6  8.5  12  16  17  32  53  85  99  123   140  167

A. 24.5 months

B. 58.7 months

C. 17 months

D. 32 months

1. (5 points) Listed below are the lengths in inches of each snake in the Atlanta Zoo’s reptile house. Find the mode.

9  15  78  13  16  101  19  10  14  17  102

A. 17 inches

B. 13.9 inches

C. no mode

D. 78 inches

1. (5 points) The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height.

.

A. 78.2 in.

B. 76.4  in.

C. 74.4 in.

D. 13.2 in.

1.  (5 points) A survey of the 9854 vehicles on the campus of State University yielded the following pie chart. Find the number of hatchbacks. Round to the nearest whole number.

A. 657

B. 36

C. 6307

D. 3547

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.  Express percents as decimals. Round dollar amounts to the nearest cent.

9. There are 31 participants in a special high-adventure camp. Following is a list of the age of the participants.

16, 18, 13, 24, 17, 17, 18, 14, 14, 16, 14, 20, 22, 21, 15
11, 13, 26, 27, 13, 16, 17, 17, 14, 19, 15, 17, 16, 19, 19, 28

1. (10 points) Prepare a frequency distribution of the participants' ages with a class width of 2, and another with class width of 5.

Frequency distribution:                   Frequency distribution

Class width = 2                               Class width = 5

Class   Frequency                           Class       Frequency

11-12         1                                   11-15            10

13-14         7                                   16-20            15

15-16         6                                   21-25              3

17-18         7                                   26-30              3

19-20         4

21-22         2

23-24         1

25-26         1

27-28         2

b. (10 points) Construct a histogram of the participants' age with a class width of 2 and another with a class width of 5.

10. I have a collection of 5 ancient gold coins. Their weights, in ounces, are 23.1, 18.6, 33.5, 12.4, and 27.1.

a. (5 points) What is the mean weight of my ancient gold coins?

b. (5 points) How do you consider this collection, a population or a sample? Why?

c. (10 points) What is the variance and standard deviation in weight of my coin collection?

Answers:

a)      Mean = (23.1+18.6+…27.1)/5 = 22.94

b)      It is a sample since we have only 5 ancient gold coins and surely there were more than that

c)      Variance =  [(23.1-22.94)²+ …..(27.1-22.94)²]/4 = 64.693

Standard deviation = Övariance = Ö64.693 =  8.043

11. Below is a summary of test score in two sections. The questions and possible maximum scores are different in these two sections. We notice that Student A4 in Section A and Student B2 in Section B have the same numerical score.

a. (15 points) How do these two students stand relative to their own classes based on their z-scores?

b. (5 points) Which student performed better? Explain your answer based on z-score.

a)

Section A scores:

Mean = 56.29

Standard deviation = 20.62

z-score of 61 = (61-56.29)/20.62 = 0.228

Section B scores:

Mean =57.38

Standard deviation = 25.85

z-score of 61 = 0.14

Based on the z-scores student A4 is 0.228 standard deviations above the mean and student B2

Is 0.14 standard deviations above the mean

b)

Student A4 performed better than student B2 since the z-score of A4 (0.228) is greater than the z-score of B2 (0.14)