EXAMPLE 3 If the median of the following frequency distribution is 46, find the missing frequencies. Variable: 10 - 20 20-30 30-40 40-50 50-60 60-70 70-80 Total 65 Frequency: 12 30 ? 25 18 229 SOLUTION Let the frequency of the class 30 - 40 be f, and that of the class 50- 60 be f2. The

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The cumulative frequency just greater than N/2 = 30 is 50 and the corresponding class is
STATISTICS
15.29
Marks
Calculation of Median
No. of students
Cumulative frequency
0- 10
10-30
(Frequency)
30-60
15
20
60-80
80-90
30
50
8
58
60
Here, N = 60 . N/2 = 30
N= Σ, =60
30 - 60. Hence, 30 - 60 is the median class.
1= 30, f = 30, F = 20, h = 30
- F
Median = 1 + 2
Now,
x h
f
Median = 30 +
30 – 20
x 30 = 40
30
EXAMPLE 3 If the median of the follozping frequency distribution is 46, find the tsono
frequencies.
Variable:
10 - 20 20-30 30-40 40 - 50 50- 60 60-70 70-80 Total
229
Frequency:
12
30
65
25
18
SOLUTION Let the frequency of the class 30 - 40 be f, and that of the class 50 - 60 be f2. The
total frequency is 229.
12 + 30 + f + 65 + f, + 25 + 18 = 229 = f, + f2 = 79
It is given that the median is 46.
Clearly, 46 lies in the class 40 - 50. So, 40 - 50 is the median class.
1 = 40, h = 10, f = 65 and F = 12 + 30 + fi = 42 + f, N = 229
Now,
N
- F
Median = 1 + xh
229
(42+ fi)
x 10
46 = 40 +
46
> 2f = 67 = f = 33.5 or 34 (say)
%3D
Therefore, f2 = 45.
nd f = 45.
Sir
Transcribed Image Text:The cumulative frequency just greater than N/2 = 30 is 50 and the corresponding class is STATISTICS 15.29 Marks Calculation of Median No. of students Cumulative frequency 0- 10 10-30 (Frequency) 30-60 15 20 60-80 80-90 30 50 8 58 60 Here, N = 60 . N/2 = 30 N= Σ, =60 30 - 60. Hence, 30 - 60 is the median class. 1= 30, f = 30, F = 20, h = 30 - F Median = 1 + 2 Now, x h f Median = 30 + 30 – 20 x 30 = 40 30 EXAMPLE 3 If the median of the follozping frequency distribution is 46, find the tsono frequencies. Variable: 10 - 20 20-30 30-40 40 - 50 50- 60 60-70 70-80 Total 229 Frequency: 12 30 65 25 18 SOLUTION Let the frequency of the class 30 - 40 be f, and that of the class 50 - 60 be f2. The total frequency is 229. 12 + 30 + f + 65 + f, + 25 + 18 = 229 = f, + f2 = 79 It is given that the median is 46. Clearly, 46 lies in the class 40 - 50. So, 40 - 50 is the median class. 1 = 40, h = 10, f = 65 and F = 12 + 30 + fi = 42 + f, N = 229 Now, N - F Median = 1 + xh 229 (42+ fi) x 10 46 = 40 + 46 > 2f = 67 = f = 33.5 or 34 (say) %3D Therefore, f2 = 45. nd f = 45. Sir
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