If the median of the data 15 and 16 and 17 and 2 X + 4 and 3 x minus 2 and 20 and 21 and 22 written in ascending order is 18.5 then X is equals to
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Answer:
Step-by-step explanation:
The given observations are,
6,7,x−2,x,18,21
Number of observations (n)=6 [ even ]
⇒ Median=
2
3
rd
obs+4
th
obs
⇒ 16=
2
x−2+x
⇒ 32=x−2+x
⇒ 32=2x−2
⇒ 34=2x
∴ x=17
∴ The observations becomes,
6,7,15,17,18,21
x
=
6
6+7+15+17+18+21
=
6
84
=14
Variance(σ
2
)=
6
(6−14)
2
+(7−14)
2
+(15−14)
2
+(17−14)
2
+(18−14)
2
+(21−14)
2
=
6
(−8)
2
+(−7)
2
+(1)
2
+(3)
2
+(4)
2
+(7)
2
=
6
64+49+1+9+16+49
=
6
188
=
3
94
=31
3
1
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