Answers (Review of 1st midterm exam)

A. The number of visitors to the Historic Museum for 25 randomly selected hours is shown below.

15 19 26 28 31 35 38 38 39 41 47 48 53 53 54 62 63 67 68 76 79 86 88 89 98

For your convenience,

1. Compute the mean, the mode, the median, and the midrange.

(mean = 53.6; mode = 38 and 53; MD=53; MR=56.5)

2. Compute the range, the variance, and the standard deviation.

(R=83, variance=543.6, SD=23.3)

3. Compute the z score for the values of 15 and 98.

(For x=15, z=-1.7; for x=98, z=1.9)

4. From part 3, can you conclude that 15 and 98 are outliers? Why?

(No because they are neither less than -3 nor greater than 3.)

5. Find the 1st quartile and the 3rd quartile. (Q1=36.5; Q3=72)

6. What is the percentile of 39? (P39 = 34th %)

7. What is the score of the 60th percentile? (c=15, step 3B, x=58)

8. Construct a Boxplot and describe the shape. (Construct the boxplot by yourself. The distribution is skewed to the right)

9. Find the outliers, if any, in the data set.

(The interval for none outliers is -16.75 and 125.25. No outliers because there is none falls below -16.75 and 125.25)

10. Construct a stem and leaf plot. (Do it yourself)

B. The data shown below indicate the number of tournaments and the earnings in thousands of dollars of 10 randomly selected LPGA golfers. Construct a scatter plot and comment on the nature of the relationship.

x

27

30

24

21

18

32

25

32

25

27

y

956

757

583

517

104

173

252

303

355

405

(Construct a scatter plot by yourself. From the scatter plot, there is no clear relationship between x and y.)

C. In a sample of 29 students, the following distribution of quiz scores was recorded.

Grade

Frequency

Xm

f Xm

f Xm^2

0 - 2

1

1

1

1

3 - 5

3

4

12

48

6 - 8

5

7

35

245

9 - 11

14

10

140

1400

12 - 14

6

13

78

1014

 Total

29

 

266

2708

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

(mean = 9.2; model class = 9-11; variance = 9.6, s = 3.1)