7) Calculate Sk, for the following set of
observations of yield of wheat in kg from 13
plots
4.6, 3.5.4.8, 5.1, 4.7, 5.5, 4.7, 3.6, 3.5, 4.2,
3.5, 3.6, 5.2
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Answer:
First the set of observations is arranged in ascending order.
3.5,3.5,3.5,3.6,3.6,4.2,4.6,4.7,4.7,4.8,5.1,5.2,5.5
∵n=13i.e.,n is odd.
∴ Median (Q
2
)=(
2
n+1
)
th
term
⇒Q
2
=(
2
13+1
)
th
term
⇒Q
2
=7
th
term
⇒Q
2
=4.6
Lower Quartile (Q
1
)=(
4
n+1
)
th
term
⇒Q
1
=(
4
13+1
)
th
term
∵(
4
n+1
)=3.5
⇒Q
1
=
2
3
rd
term+4
th
term
⇒Q
1
=
2
3.5+3.6
⇒Q
1
=3.55
Upper Quartile (Q
3
)=[
4
3(n+1)
]
th
term
⇒Q
3
=[
4
3(11+1)
]
th
term
∵(
4
n+1
)=9.5
⇒Q
3
=
2
9
th
term+10
th
term
⇒Q
3
=
2
4.8+5.1
⇒Q
3
=4.95
So, we have Q
1
=3.55,Q
2
=4.6&Q
3
=4.95
Now,
Sk
b
=
Q
3
−Q
1
Q
3
+Q
1
−2Q
2
⇒Sk
b
=
4.95−3.55
4.95+3.55−(2×4.6)
⇒Sk
b
=
1.4
−0.7
⇒Sk
b
=−0.5
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