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Notes
In this concept we will study about Relation of Ogive and Median. These graphical representation of the frequency distribution are called Ogives. Actual limits are on the xaxis and cumulative frequencies on the yaxis.
Ogive is also known as cumulative frequency distribution.
You will be asked to draw either a less than frequency ogive or more than frequency ogive.
Example: The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :
Convert the distribution above to a less than type cumulative frequency distribution and also to a more than type cumulative frequency distribution, and draw its ogive.
1) Less than type cumulative frequency table
Classes 
cf 
Less than 10 
2 
Less than 15 
14 
Less than 20 
16 
Less than 25 
20 
Less than 30 
23 
Less than 35 
27 
Less than 40 
30

2) More than type cumulative frequency table
Classes 
cf 
More than 5 
30 
More than 10 
28 
More than 15 
16 
More than 20 
14 
More than 25 
10 
More than 30 
7 
More than 35 
3 
The graphical representation of both the ogives will be
Here, `N/2= 30/2= 15`
Now, we will take 15 on y axis and draw a perpendicular line that touches the curve, and from the point where the perpendicular touches the curve draw a perpendicular that touches the x axis, the point at which the perpendicular touches the x axis is the median.
Thus, here the Median is 17.5
Related QuestionsVIEW ALL [54]
Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24
Age (in years)  0 – 10  10 – 20  20 – 30  30 – 40  40 – 50 
Number of persons 
5  25  ?  18  7 
For one term, absentee record of students is given below. If mean is 15.5, then the missing frequencies x and y are.
Number of days  0  5  5  10  10  15  15  20  20  25  25  30  30  35  35  40  TOTAL 
Total Number of students  15  16  x  8  y  8  6  4  70 
The given distribution shows the number of wickets taken by the bowlers in oneday international cricket matches:
Number of Wickets  Less than 15  Less than 30  Less than 45  Less than 60  Less than 75  Less than 90  Less than 105  Less than 120 
Number of bowlers  2  5  9  17  39  54  70  80 
Draw a ‘less than type’ ogive from the above data. Find the median.
The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:
Age (in years)  10 – 20  20 – 30  30 – 40  40 – 50  50 – 60  60 – 70 
Number of patients  60  42  55  70  53  20 
Form: Less than type cumulative frequency distribution.
The marks obtained by 100 students of a class in an examination are given below.
Mark  No. of Student 
0  5  2 
5  10  5 
10  15  6 
15  20  8 
20  25  10 
25  30  25 
30  35  20 
35  40  18 
40  45  4 
45  50  2 
Draw 'a less than' type cumulative frequency curves (ogive). Hence find the median.
The following table gives the lifetime (in days) of 100 electric bulbs of a certain brand.
Lifetine (in days)  Less than 50 
Less than 100 
Less than 150 
Less than 200 
Less than 250 
Less than 300 
Number of Bulbs  7  21  52  9  91  100 