Question

The frequency distribution of scores obtained by 230 candidates in a medical entrance test is as follows.

Scores:	400-450	450-500	500-550	550-600	600-650	650-700	700-750	750-800
Number of Candidates:	20	35	40	32	24	27	18	24

Draw cumulative frequency curve by less than and more than method on the same axes. Also, draw the two types of cumulative frequency polygons.

Answer 1

Less than method: we first prepare the cumulative frequency table by less than method as given below:

Scores	Number of Candidates	Scores less than	Cumulative Frequency
400-450	20	450	20
450-500	35	500	55
500-550	40	550	95
550-600	32	600	127
600-650	24	650	151
650-700	27	700	178
700-750	18	750	196
750-800	34	800	230

Other than the given class intervals, we assume a class interval $350-400$ prior the first class interval $400-500$ with zero frequency.
Now, we mark the upper class limits on x-axis and the cumulative frequencies along Y-axis on suitable scales.
Thus, we plot the points $(400,0),(450-20),(500,55),(550,95),(600,127),(650,151),(700,178),(750,196),and(800,230)$
On joining points by a free hand smooth curve to obtain an ogive by less than method as shown in Fig. 7.3.
In order to obtain the cumulative frequency polygon by less than join these points. by line segment as given in Fig. 7.4.
Other than the given class intervals, we assume class interval $800-850$ after the last class interval $750-800$ with zero frequency.
Now, we mark the lower class limits on X-axis and the cumulative frequencies along Y-axis on suitable scales.
Thus, we plot the points $(400,230),(450,210),(500,175),(550,175),(600,103),(650,79),(700,61),(750,27),and(800,0).$
By joining these points by a free hand smooth curve, we obtain an ogive by more than method as shown in Fig. 7.3.
The cumulative frequency polygon by more than method is obtained by joining these points by line segment as shown in Fig. 7.4.
More than method: let us first prepare the cumulative frequency table by more than method as given below:

Scores	Number of candidates	Score more than	Cumulative Frequency
400-450	20	400	230
450-500	35	450	210
500-550	40	500	175
550-600	32	550	135
600-650	24	600	103
650-700	27	650	79
700-750	18	700	61
750-800	34	750	27