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