Question

The
mean of 100 observation is 50. If one
of the observation, which was 50 is replaced
by 150.find the resulting mean​

Answer 1

Answer:

51

Step-by-step explanation:

   Mean = sum of observations/no. of observations

In the given question,  initially:

           Mean = 50

           No. of observations = 100

⇒ Mean = (sum of 100 observations)/100

⇒ 50 = (sum of 100 observations)/100

⇒ 5000 = sum of 100 observations

When 50 is replaced by 150,  50 is removed from 5000 and 150 is added.

Sum of observations = 5000 - 50 + 150

                                   = 5100

Hence,

Mean = 5100/100

          = 51

Resulting mean is 51.

Answer 2

Answer:

Given :-

• The mean of 100 observations is 50.
• One of the observation which is 50 is replaced by 150.

To Find :-

• What is the resulting 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 = 50
• Total Number Of Observations = 100

According to the question by using the formula we get,

$\implies \sf 50 =\: \dfrac{Sum\: Of\: Observations}{100}$

By doing cross multiplication we get,

$\implies \sf Sum\: Of\: Observations =\: 100(50)$

$\implies \sf Sum\: Of\: Observations =\: 100 \times 50$

$\implies \sf\bold{\green{Sum\: Of\: Observations =\: 5000}}$

Now,

$\bigstar$ One of the observation which is 50 is replaced by 150.

Then,

$\leadsto \sf Total\: Sum\: Of\: Observations =\: 5000 - 50 + 150$

$\leadsto \sf Total\: Sum\: Of\: Observations =\: 4950 + 150$

$\leadsto \sf\bold{\purple{Total\: Sum\: Of\: Observations =\: 5100}}$

Now, we have to find the resulting mean :

Given :

• Sum Of Observations = 5100
• Total Number Of Observations = 100

According to the question by using the formula we get,

$\footnotesize \bigstar\: \: \sf\bold{\blue{Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}}}\: \: \bigstar$

$\longrightarrow \sf Mean =\: \dfrac{51\cancel{00}}{1\cancel{00}}$

$\longrightarrow \sf Mean =\: \dfrac{51}{1}$

$\longrightarrow \sf\bold{\red{Mean =\: 51}}$

${\small{\bold{\underline{\therefore\: The\: resulting\: mean\: is\: 51\: .}}}}$