Question

The mean of 20 observations is 63.If an observation 50 is replaced by 90. Find the new mean.​

Answer 1

Answer:

• The new mean is 65.

Step-by-step explanation:

Given that:

• The mean of 20 observations is 63.
• An observation 50 is replaced by 90.

To Find:

• The new mean.

We know that:

• Mean = (Sum of observations)/(Number of observations)

We have:

• Number of observations = 20
• Mean = 63

⟶ 63 = (Sum of observations)/20

⟶ Sum of observations = 63 × 20

⟶ Sum of observations = 1260

Now finding the new mean:

We have.

• Number of observations = 20

As an observation 50 is replaced by 90.

• Sum of observations = 1260 - 50 + 90 = 1300

⇒ Mean = 1300/20

⇒ Mean = 65

Hence,

• The new mean = 65

Answer 2

Given:-

• Mean of 20 observation = 63

• An observation 50 is replaced by 90.

To Find:-

• New Mean

Formula used:-

• $Mean\: =\: \dfrac{Sum\:of\: Observation}{No\:of\: Observation}$

Solution:-

$Mean\: =\: \dfrac{Sum\:of\: Observation}{No\:of\: Observation}$

$⟹\:63\: =\: \dfrac{Sum\:of\: Observation}{20}$

$⟹\:Sum\:of\: Observation = 63×20$

$⟹\:Sum\:of\: Observation = 1260$

As observation 50 is replaced by 90. So,

New Sum of Observation = 1260 - 50 + 90 = 1300

$⟹\:New\:Mean\: =\: \dfrac{1300}{20}$

$⟹\:New\:Mean\: =\: 65$

Hence, The New Mean is 65.