Question

If the mean of 25 observations is 27 and each observation is decreased
by 7. what will be the new mean?
ANSWER FAST ......​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• The new mean is 20.

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Let $x_1, x_2, x_3,....x_{25}$ be the 25 observations and ${\mu}_1, \:{\mu}_2$ be the old and the new mean. Then,

$\to {\mu}_1 = 27$

$\to \frac{x_1+ x_2+x_3+....+x_{25}}{25} = 27$

$\to x_1+ x_2+..+x_{25} = 27\times 25...(1)$

Now,

$\:\:\:\:\: {\mu}_2$

$= \frac{(x_1-7)+(x_2-7)+(x_3-7)+....+(x_{25}-7)}{25}$

$= \frac{x_1+ x_2+x_3+....+x_{25}-7\times 25}{25}$

$= \frac{27\times 25-7\times 25}{25}$

$= \frac{(27-7) \times 25}{25}$

$= 27-7$

$= 20$