Question

The following data are final marks for a Strategic Management Accounting course at a University.

30 74 41 65 51 54 36 56 68 57 70 64 76 67 83 61 81 77 60 38 84 68 72 94 71 86 71 75 91 55 90 82 83 54 79 62 68 58 41 49

a. Construct a frequency distribution and a relative frequency distribution for the data .

b. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data .

c. Plot a relative frequency histogram for the data (1 mark)

d. Construct an ogive for the data (1 mark)

e. What proportion of the marks is less than or equal to 60? (1 mark)

f. What proportion of the marks is more than 70? (1mark)

Use following class intervals to answer the above questions

Up to 40 Up to 50 Up to 60 Up to 70 Up to 80 Up to 90

Up to 100

Classes

Frequency

Relative Frequency

Cumulative Frequency

Cumulative Relative Frequency

Answer 1

a)

frequency distribution-

class interval	frequency
30-39	3
40-49	3
50-59	7
60-69	9
70-79	9
80-89	6
90-99	3

relative frequency distribution-

class interval	frequency	relative frequency=fi/N
30-39	3	0.075
40-49	3	0.075
50-59	7	0.175
60-69	9	0.225
70-79	9	0.225
80-89	6	0.150
90-99	3	0.0750

b)

class interval	frequency	relative frequency=fi/N	cumulative frequency			cumulative relative frequnecy
30-39	3	0.075	3			0.0750
40-49	3	0.075	6			0.1500
50-59	7	0.175	13			0.3250
60-69	9	0.225	22			0.5500
70-79	9	0.225	31			0.7750
80-89	6	0.150	37			0.9250
90-99	3	0.0750	40			1.0000

c)

d)

e)

proportion of the marks is less than or equal to 60 = 14/40 = 0.35

f) proportion of the marks is more than 70 = 17/40=0.425