Question

The marks of 200 students in a test is given below : 

Marks%	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89
No. of Students	7	11	20	46	57	37	15	7

Draw an ogive and find

(i) the median 

(ii) the number of students who scored more than 35% marks

Answer 1

We construct cumulative frequency table of the given distribution : 

Marks	No.of students (f)	Cumulative Frequency
9.5-19.5	7	7
19.5-29.5	11	18
29.5-39.5	20	38
39.5-49.5	46	84
49.5-59.5	57	141
59.5-69.5	37	178
69.5-79.5	15	193
79.5-89.5	7	200

Take a graph paper and draw both the axes. 

On the x -axis , take a scale of 1cm=10 to represent the marks. 

On the y - axis , take a scale of 1 cm =50 to represent the no. of students .

Now, plot the points (19.5,7) ,(29.5,18) ,(39.5,38) ,( 49.5,84) ,(59.5,141) ,(69.5,178) ,(79.5,193) ,(89.5,200). 

Join them by a smooth curve to get the ogive. 

(i) No. of terms = 200 
.·. Median= `(100 + 101)/2` = 100.5^th term

Through mark of 100.5 on y-axis draw a line parallel to x-axis which meets the curve at A. From A, draw a perpendicular to x-axis which meets it at B. 

The value of B is the median which is 52. 

(ii)  From marks % = 35 draw a line parallel to y-axis and meet the curve at R. From R, Draw a perpendicular on y-axis which meets it at S. The difference of the value obtained when subtracted from 200 gives the number of students who scored more than 35%. 

⇒ 200 - 23 = 172 

172 students scored more than 35 %