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Unformatted text preview: 38
40
46
30
6
5060
53
24
7
6070
61
17
8
7080
66
9
5
8090
70
4
4
90100
70 70 N = = 35
2
2
114 N 2 −m xc Median = l + f 35 − 32 = 40 + × 10
8
= 40 +3.75
= 43.75
Example 19:
Compute median for the following data.
MidValue
5
15 25
35 45 55 65 75
Frequency
7
10 15
17 8
4
6
7
Solution :
Here values in multiples of 10, so width of the class interval is 10.
Mid x
5
15
25
35
45
55
65
75 C.I
010
1020
2030
3040
4050
5060
6070
7080 f
7
10
15
17
8
4
6
7
74 74 N = = 37
2
2
N − m
2 ×c
Median = l + f 115 c.f
7
17
32
49
57
61
67
74 37 − 32 = 30 + × 10 17 = 30 + 2.94
= 32.94
Graphic method for Location of median:
Median can be located with the help of the cumulative
frequency curve or ‘ ogive’ . The procedure for locating median in a
grouped data is as follows:
Step1: The class boundaries, where there are no gaps between
consecutive classes, are represented on the horizontal axis
(xaxis).
Step2: The cumulative frequency corresponding to different
classes is plotted on the vertical axis (yaxis) against the
upper limit of the class interval (or against the variate value
in the case of a discrete series.)
Step3: The curve obtained on joining the points by means of
freehand drawing is called the ‘ ogive’ . The ogive so drawn
may be either a (i) less than ogive or a (ii) more than ogive.
N
N +1
Step4: The value of
or
is marked on the yaxis, where
2
2
N is the total frequency.
N
Step5: A horizontal straight line is drawn from the point
or
2
N +1
on the yaxis parallel to xaxis to meet the ogive.
2
Step6: A vertical straight line is drawn from the point of
intersection perpendicular to the horizontal axis.
Step7: The point of intersection of the perpendicular to the xaxis
gives the value of the median.
Remarks :
1. From the point of intersection of ‘ less than’ and ‘ more than’
ogives, if a perpendicular is drawn on the xaxis, the point so
obtained on the horizontal axis gives the value of the median.
2. If ogive is drawn using cumulated percentage frequencies,
then we dr...
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 Winter '08
 Moshiri
 Business

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