AP EAMCET Engineering 22 Sep 2020 Shift 1 Paper

Let the five observations are x1,x2,x3,x4,x5.
so, mean =‌

x1+x2+x3+x3+x2

5

=9 (given)
⇒‌‌x1+x2+x3+x4+x5=45.....(i)
and standard deviation =

5

∑

i=1

√‌

(9−xi)2

5

=0( given )
⇒‌‌

3

∑

i=1

(9−xi)2=0⇒xi=9‌∀i
Now, let observation x5 is changed with y, so
mean =‌

x1+x2+x3+x4+y

5

=10 \;emsp;(given)
⇒‌‌x1+x2+x3+x4+y=50
⇒‌‌45−x5+y=50‌‌ (from Eq. (i))
⇒‌‌x5+5=y⇒y=14‌‌{∵x5=9}
Now, the changed standard deviation is
{∵x1=x2=x3=x4=9}