Question

if x is the mean of x1 x2 x3 ... xn then the mean of (x1+k) ,(x2+k), .....(xn+k) will be

Answer 1

Hi...☺

Here is your answer...✌

Answer : (x+k)

For solution see above image ☝
Hope it helps you ⭐

Answer 2

Answer:

$New \: mean = \overline{x} + k$

Step-by-step explanation:

If mean of

$x_1 ,\: x_2,\: x_3, \: x_4,...x_n \: is \: \: \bar {x}$

Now if each observation is increased by k, then new mean will be

$\overline{x} + k$

To prove this,apply the basic formula of finding mean

$\overline{x} = \frac{x_1 + x_2 + x_3 + x_4 + ... + x_n}{n} \: \: \: \: eq1$

Now each observation is increased by k

$New \: mean = \frac{x_1 + k + x_2 + k + x_3 + k + x_4 + k + ... + x_n + k}{n} \\ \\ New \: mean= \frac{x_1 + x_2 + x_3 + x_4 + ... + x_n + k + k + k + k +... + k}{n} \\ \\New \: mean= \frac{x_1 + x_2 + x_3 + x_4 + ... + x_n}{n} + \frac {k + k + k + k +... + k}{n} \\ \\ from \: eq1 \\ New \: mean = \overline{x} + \frac{nk}{n} \\ \\ New \: mean= \overline{x} + k$

Hope it helps you.