Unformatted text preview: sum of the frequency of
the class and the frequencies of the pervious classes, ie adding the
frequencies successively, so that the last cumulative frequency
gives the total number of items.
108 Discrete Series:
Step1: Find cumulative frequencies. N +1
Step2: Find 2
Step3: See in the cumulative frequencies the value just greater than N +1 2
Step4: Then the corresponding value of x is median.
Example 14:
The following data pertaining to the number of members in
a family. Find median size of the family.
Number of
members x
Frequency
F 1 2 3 4 5 6 7 8 9 10 11 12 1 3 5 6 10 13 9 5 3 2 2 1 Solution:
X
1
2
3
4
5
6
7
8
9
10
11
12 f
1
3
5
6
10
13
9
5
3
2
2
1
60 Median = size
109 cf
1
4
9
15
25
38
47
52
55
57
59
60 N +1
of 2 th item 60 + 1 th
= size of item
2
= 30.5th item
The cumulative frequencies just greater than 30.5 is 38.and the
value of x corresponding to 38 is 6.Hence the median size is 6
members per family.
Note:
It is an appropriate method because a fractional value given
by mean does not indicate the average number of members in a
family.
Continuous Series:
The steps given below are followed for the calculation of
median in continuous series.
Step1: Find cumulative frequencies.
N
Step2: Find 2
Step3: See in the cumulative frequency the value first greater than
N 2 , Then the corresponding class interval is called the Median class. Then apply the formula
N
−m
Median = l + 2
×c
f
Where
l = Lower limit of the median class
m = cumulative frequency preceding the median
c = width of the median class
f =frequency in the median class.
N=Total frequency.
Note :
If the class intervals are given in inclusive type convert
them into exclusive type and call it as true class interval and
consider lower limit in this.
Example 15: 110 The following table gives the frequency distribution of 325
workers of a factory, according to their average monthly income in
a certain year.
Income group (in Rs)
Number of workers
1
Below 100
20
100150
42
150200
55
200250
62
250300
45
300350
30
350400
25
400450
15
450500
18
500550
10
550600
2
600 and above
325
Ca...
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 Winter '08
 Moshiri
 Business, Statistics

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