The marks obtained by 100 students of a class in an examination are given below:
MarksNumber of students0−525−10510−15615−20820−251025−302530−352035−401840−45445−502
Draw cumulative frequency curves by using (i) 'less than's series and (ii) 'more than' series.
Hence,find the median.
The marks obtained by 100 students of a class in an examination are given below:
MarksNumber of students0−525−10510−15615−20820−251025−302530−352035−401840−45445−502
Draw cumulative frequency curves by using (i) 'less than's series and (ii) 'more than' series.
Hence,find the median.
(i) From the given table, we may prepare the less than frequency table as shown below:
Marks No. of students Less than 5 2 Less than 10 7 Less than 15 13 Less than 20 21 Less than 25 31 Less than 30 56 Less than 35 76 Less than 40 94 Less than 45 98 Less than 50 100
We plot the points A(5,2), B(10,7), C(15,13), D(20,21), E(25,31), F(30,56), G(35,76), H(40,94), I(45,98), and J(50,100).
Join AB,BC,CD,DE,EF,FG,GH,HI,IJ and JA with a free hand to get the curve representing the less than types series.
(ii) More than series:
Marks No. of students More than 0 100 More than 5 98 More than 10 93 More than 15 87 More than 20 79 More than 25 69 More than 30 44 More than 35 24 More than 40 6 More than 45 2
Now on the same graph paper, we plot the points (0,100), (5,98), (10,94), (15,76), (20,56), (25,31), (30,21), (35,13), (40,6) and (45,2).
Join, with a free hand to get the more than type series.
Scale: Along x-axis: 1 big division = 5 marks
Along y-axis: 2 big division = 10 student
The two curves intersect at point L. Draw LM⊥OX cutting the x-axis at M. Clearly, M= 29.5.
Hence, Median = 29.5
(i) From the given table, we may prepare the less than frequency table as shown below:
| Marks | No. of students |
| Less than 5 | 2 |
| Less than 10 | 7 |
| Less than 15 | 13 |
| Less than 20 | 21 |
| Less than 25 | 31 |
| Less than 30 | 56 |
| Less than 35 | 76 |
| Less than 40 | 94 |
| Less than 45 | 98 |
| Less than 50 | 100 |
We plot the points A(5,2), B(10,7), C(15,13), D(20,21), E(25,31), F(30,56), G(35,76), H(40,94), I(45,98), and J(50,100).
Join AB,BC,CD,DE,EF,FG,GH,HI,IJ and JA with a free hand to get the curve representing the less than types series.
(ii) More than series:
| Marks | No. of students |
| More than 0 | 100 |
| More than 5 | 98 |
| More than 10 | 93 |
| More than 15 | 87 |
| More than 20 | 79 |
| More than 25 | 69 |
| More than 30 | 44 |
| More than 35 | 24 |
| More than 40 | 6 |
| More than 45 | 2 |
Now on the same graph paper, we plot the points (0,100), (5,98), (10,94), (15,76), (20,56), (25,31), (30,21), (35,13), (40,6) and (45,2).
Join, with a free hand to get the more than type series.
Scale: Along x-axis: 1 big division = 5 marks
Along y-axis: 2 big division = 10 student
The two curves intersect at point L. Draw LM⊥OX cutting the x-axis at M. Clearly, M= 29.5.
Hence, Median = 29.5
