Question

The mean of 10 observations was calculated as 45 . It was detected on rechecking that the value of 40 was wrongly copied as 10 .Find the correct mean .

Answer 1

Answer:

48

Step-by-step explanation:

Mean = (sum of 10 observations)/10

45 = (sum of 10 observations)/10

450 = sum of 10 observations

On rechecking, it was detected on rechecking that the value of 40 was wrongly copied as 10.

∴ sum of correct obs = (450 - 10) + 40

                                   = 480

  no. of obs = 10

Hence,

  Mean = 480/10 = 48

Answer 2

Answer:

Given :-

• The mean of 10 observations was calculated as 45.
• It was detected on rechecking that the value of 40 was wrongly copied as 10.

To Find :-

• What is the correct mean.

Formula Used :-

$\clubsuit$ Mean Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}}}}$

Solution :-

First, we have to find the sum of observations :

Given :

• Mean = 45
• Total Number of observations = 10

According to the question by using the formula we get,

$\implies \sf 45 =\: \dfrac{Sum\: of\: Observations}{10}$

By doing cross multiplication we get,

$\implies \sf Sum\: of\: Observations =\: 45(10)$

$\implies \sf Sum\: of\: Observations =\: 45 \times 10$

$\implies \sf\bold{\purple{Sum\: of\: Observations =\: 450}}$

Now,

$\bigstar$ It was detected on rechecking that the value of 40 was wrongly copied as 10.

Hence, the sum of observations will be :

$\implies \sf Sum\: of\: Observations =\: 450 - 10 + 40$

$\implies \sf Sum\: of\: Observations =\: 450 + 30$

$\implies \sf \bold{\green{Sum\: of\: observations =\: 480}}$

Now, we have to find the correct mean :

Given :

• Sum of Observations = 480
• Total Number of Observations = 10

According to the question by using the formula we get,

$\small\leadsto \bf{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}}$

Similarly,

$\longrightarrow \sf Correct\: Mean =\: \dfrac{48\cancel{0}}{1\cancel{0}}$

$\longrightarrow \sf Correct\: Mean =\: \dfrac{48}{1}$

$\longrightarrow \sf\bold{\red{Correct\: Mean =\: 48}}$

${\small{\bold{\underline{\therefore\: The\: correct\: mean\: is\: 48\: .}}}}$