Question

The Following is the result of the examination of 55 students in statistics

Classes                        FREQUENCY

33-40                                       4

41-48                                       8

49-56                                       10

57-64                                       11

65-72                                       9

73-80                                       6

81-88                                       2

89-96                                       5

Compute the Following:

1. MODE
2. SIXTY-TWO PERCENTILE

Answer 1

Following table shows the cumulative frequency:

Classes	FREQUENCY, f	Relative Frequency, f/55	Cumulative relative frequency, CF
33-40	4	0.07	0.07
41-48	8	0.15	0.22
49-56	10	0.18	0.4
57-64	11	0.2	0.6
65-72	9	0.16	0.76
73-80	6	0.11	0.87
81-88	2	0.04	0.91
89-96	5	0.09	1
Total	55	1

Mode is the data value with highest frequency. Since class 57-64 has highest frequency so modal class is 57-64.

For 62 percentile we need to find the data value that has 0.62 data values less than equal to it. Using cumulative relative frequency that data value should lie in class 65-72. That is class having sixty two percentie is 65-72. Approximate value of 62nd percentile is (65+72) /2 = 68.5.