Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is

Question

Philoid · Accepted Answer

Let a, b, c,d,e be the observation and mean is m

Let suppose new mean be m₁

M₁ =m+k

Now, The standard deviation

So, The standard deviation for new observation

Now, we can compare both observation

a+k-n=a+k-(m+k)

a+k–n = a+k–m- k

a+k-n=a-m

Similary

b+k-n=b-m

c+k-n=c-m

d+k-n=d-m

e+k-n=e-m

when we substitute the values, we get,

S₁ = S

Hence, The Sd is S