PCALC III Statistics  International Maritime College
Question 1.
In testing a braking system, the distance required to stop a car, was measured in 120 trials. The results are shown in the following distribution table.
Stopping distance (ft.)

Times car stopped



155  159

2



160  164

15



165  169

32



170  174

36



175  179

24



180  184

10



185  189

1







(a) Form a cumulative frequency distribution for the above data in Column 3.
(b) For the given data, draw an ogive and represent median on it.
Question 2.
Compare the variability of the following two sets of data by using both the sample standard deviation and the sample coef?cient of variation.
Data Set 1

149

82

77

54

Data Set 2

159

121

138

152

(a) Compute the measure of central tendency (mean) and standard deviation for data set 1.
(b) Compute the measure of central tendency (mean) and standard deviation for data set 2.
(c) Use a coefficient of variation to compare which data is more consistent. Explain.
Question 3.
The following table represents the number of deliveries of Al Seer Logistics LLC containers which were received by Al Meera and Al Maya in 2018. Data for 5 months of deliveries is given below.
Month

Number of Al Meera containers

Number of Al Maya containe

January

75

100

February

80

55

March

55

65

April

70

75

May

60

45

(a) Draw a multiple bar diagram for the above data.
(b) Explain the above diagram that you have drawn (not less than 100 words) and compare the delivery consistency of the above two companies.
Question 4.
The Automobile Fuel Ef?ciency was tested in 15 automobiles (in miles per gallon). The data is given below.
41 , 31 , 25 , 23 , 22 , 30 , 20 , 16 , 23 , 27 , 38 , 34 , 24 , 29 , 23
(a) Write five number summary and point out any outliers for the above data.
(b) Use Pearson's coef?cient of skewness to check the skewness of the data.
Question 5.
The ages of 35 Assistance manager working in Sohar Aluminium are given below.
Age in years

30  34

35  39

40  44

45  49

50  54

Number of Employees

8

10

6

7

4

(a) Calculate the average age of the employees working in Sohar Aluminium.
(b) Calculate the standard deviation of the employees working in Sohar Aluminium.
(c) Determine the coefficient of variation in their ages.
Question 6.
The director of an alumni association for a small college wants to determine whether there is any type of relationship between the amount of an alumnus's contribution (in dollars) and the years the alumnus has been out of school.
Year (x)

1

5

3

10

7

6

Contribution (y)

500

100

300

50

75

80

(a) Draw the scatter plot for the above variables.
(b) Compute the correlation coefficient for the above data.
(c) What type of the relation exits after result of part (b)? Explain.
(d) Find the least square regression line in the form y^= a + bx.
(e) Predict the amount of an alumnus's contribution (in dollars) for ?? = 10
Attachment: Statistics.rar