Statistics Part 1

	Size	Mean	Variance
Observation I	10	2	2
Observation II	n	3	1

Variance of combined set is 17∕9.
Let the observations for group I be set A:{x1,x2,x3,...,x10}
⇒‌‌‌

∑ xi

10

=2
⇒‌‌‌‌∑xi=20
and ∑(‌

xi2

10

)−(‌

∑xi

10

)2=2
⇒‌‌‌

∑xi2

10

−‌

400

100

=2
⇒‌‌‌

∑xi2

10

=6
⇒‌‌‌‌∑xi2=60
Let the observation for group II be set B:{y1,y2,y3,...,y10}
‌

∑yi

n

=3⇒

∑

yi

=3n
and ‌

∑yi2

n

−(‌

∑yi

n

)2=1
‌

∑yi2

n

−9=1⇒∑yi2=10n
Combined variance =17∕9
σ2=‌

∑(xi2+yi2)

n+10

−[∑(‌

xi+yi

n+10

)]2
⇒‌‌‌

17

9

=‌

60+10n

n+10

−[‌

20+3n

n+10

]2
⇒‌‌‌

17

9

=‌

(10n+60)(n+10)−(3n+20)2

(n+10)2

⇒‌‌‌

17

9

=‌

(10n2+160n+600)−(9n2+120n+400)

(n+10)2

⇒‌‌‌

17

9

=‌

n2+40n+200

n2+20n+100

⇒‌‌17n2+340n+1700=9n2+360n+1800
⇒‌‌8n2−20n−100=0
⇒‌‌2n2−5n−25=0
⇒‌‌2n2−10n+5n−25=0
⇒‌‌2n(n−5)+5(n−5)=0
⇒‌‌(2n+5)(n−5)=0
∴‌‌n=5