Data collected from tests, experiments and various surveys have little meaning until they have been arranged or classified in some systematic way. So it is required to organize our material into groups of sources under sub-heads. These are known as class-intervals (C.I.).
Sample Table
|
132 |
126 |
87 |
94 |
97 |
191 |
174 |
105 |
133 |
139 |
|
171 |
93 |
112 |
123 |
106 |
85 |
105 |
80 |
93 |
63 |
|
138 |
179 |
95 |
137 |
88 |
112 |
170 |
87 |
154 |
120 |
|
56 |
82 |
131 |
126 |
141 |
89 |
92 |
109 |
138 |
121 |
|
164 |
156 |
121 |
89 |
146 |
146 |
163 |
131 |
75 |
115 |
|
137 |
146 |
56 |
94 |
102 |
90 |
71 |
110 |
134 |
150 |
|
159 |
192 |
65 |
79 |
126 |
153 |
112 |
159 |
132 |
65 |
|
139 |
120 |
147 |
68 |
102 |
101 |
96 |
148 |
108 |
152 |
|
153 |
138 |
93 |
128 |
92 |
98 |
108 |
112 |
67 |
68 |
|
145 |
86 |
112 |
83 |
103 |
76 |
157 |
96 |
134 |
96 |
Thus classifying scores in a meaningful sequence is called frequency distribution. This is drawn up according to the following steps.
1. First of all the range of the entire group of scores is to be determined. The range is the gap between the highest and the lowest scores. The highest score in the Table 1 is 191 and the lowest 56. So the range is 135 (i.e. 191-56).
2. After the range is found out, the number and the size of classes are to be settled. Commonly, the class-intervals used in drawing up a frequency distribution are 3 at a minimum. The maximum class-intervals can go up to 20. A standard of 5 to 10 class intervals are taken as an ideal one. The size of class- intervals depends on range and the number of class-intervals to be decided. When the range is wider, the class-size should be more in order to condense the number of class-intervals. Here in this case as per Table-3, when the size of class-interval is taken to be 10, the number of class interval becomes 15, but with 20 as class-size, the number of class-interval is reduced to 8.
3. When the sizes of the class-intervals are fixed at 10 or 20, we get in number of class-intervals in column No. 1. Then tallies are put in the second column to accommodate scores in their proper intervals as shown separately in the Table-3. In case of class-intervals of 10 units, the first class-interval starts with 50 at the bottom of scores and in case of 20 units of class- size, the class-intervals start with 40 at the bottom one. The lowest score in the series of 100 scores is 56. Care has been taken to give coverage to this score of 56 at lowest class- interval and no score has got repeated in any of the two consecutive class-intervals.
4. The tallies in the column No. 2 are bundled up in 5 tallies (one crossing over four other tallies). It is so done for convenience of counting and to avoid the confusion in counting a large number of free-tallies. After carefully tallying all 100 scores in their proper class-intervals, the tallies are counted. The total number of tallies in each class-interval gives the frequency of scores in particular class-intervals. The sum of all the “f ” values gives N.
By this method following steps by step a group of unordered data are grouped into a compressed form of frequency distribution. Looking at both the frequency distribution under (A) & (B), it can be said easily and quickly that 46 per cent of this group have scored first class (60% of marks and more), while 37 per cent have fallen down 50 per cent of marks. Only 17 per cent of the groups have got Second class achievement. The more the class- size, the quicker it is to read the frequency table at a glance.