Calculate standard deviation of the following data:
Marks (more than) 0 10 20 30 40 50 60 70
Frequency 100 90 75 50 25 15 5 0
Answers
Explanation:
Mid Point (X) Frequency (F) i=class interval width A=45 Assumed mean u=ix−A fu 0-105 3 10 45 -4 -12 10-20 15 5 10 45 -3 -1520-30 25 6 10 45 -2 -12 30-40 35 7 10 45 -1 -7 40-50 45=A8 10 45 0 0 50-60 55 9 10 45 1 9 60-70 65 10 10 45 2 20 70-80 75 12 10 45 3 36 80-90 85 6 10 45 4 24 90-100 954 10 45 5 20 Σf=70 Σfu=63
The formula used for arithmetic mean of grouped data by step deviation method is, X=A+∑f∑fu×i
A= Assumed mean of the given data
∑ = Summation of the frequencies given in the grouped data
∑fu = Summation of the frequencies and deviation of a given mean data
u=i(x−A)
i= Class interval width
X = arithmetic mean
X=45+7063×10
=45+9
=54
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Related Questions to study
The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method
Weekly wages (Rupees)
1000−20002000−30003000−40004000−5000No. of workers2545
Answer:
Explanation:
First 10 multiples of 3 are 3,6,9...30.
This is an A.P.
sum=
2
n
(a+l)=
2
10
×(3+30)
∴sum=165.
Mean, u=
n
sum
=
10
165
.
Variance, σ
2
=
n
∑(x
i
2
)
−u
2
.
∴σ
2
=
10
3
2
+6
2
+...30
2
−16.5
2
.
∴σ
2
=
10
3×(1
2
+2
2
+...10
2
)
−16.5
2
.
∴σ
2
=
6×10
9×10×(10+1)×(2×10+1)
−16.5
2
.
∴σ
2
=346.5−272.25
∴σ
2
=74.25