if the data of heights of 10 students are given in centimeter. what is the unit of its varience
Answers
Answer:
Class interval f
i
x
i
u
i
=
h
x
i
−A
u
i
2
f
i
u
i
f
i
u
i
2
70-75 3 72.5 -4 16 -12 48
75-80 4 77.5 -3 9 -12 36
80-85 7 82.5 -2 4 -14 28
85-90 7 87.5 -1 1 -7 7
90-95 15 92.5 0 0 0 0
95-100 9 97.5 1 1 9 9
100-105 6 102.5 2 4 12 24
105-110 6 107.5 3 9 18 54
110-115 3 112.5 4 16 12 48
Total 60 6 254
We have N=∑f
i
=60
Width of class h=5
Assumed mean A=92.5(say)
Mean,
x
ˉ
=A+
N
∑
i=1
9
f
i
u
i
×h
=92.5+
60
6
×5=92.5+0.5=93
⇒
x
ˉ
=93
Variance σ
2
=h
2
⎣
⎢
⎡
N
∑
i=1
9
f
i
u
i
2
−(
N
∑
i=1
9
f
i
u
i
)
2
⎦
⎥
⎤
σ
2
=5
2
⎣
⎢
⎡
60
254
−(
60
6
)
2
⎦
⎥
⎤
=5
2
(60)
2
[60×254−6
2
]
=
3600
25
[15240−36]
=
3600
25
×15204
σ
2
=105.58
Standard Deviation =
Variance
σ=
105.58
σ=10.27
Answer:
variance will be in metres
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