Question

the mean of 5 number is 18. if one number is excluded then the mean is 16 ​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Given :

• Mean of 5 numbers is 18.
• If one number is excluded then the mean is 16.

To Find :

The excluded number.

Solution :

Analysis :

Here we have to take the excluded number as x. Then using the formula of mean we can get the excluded number.

Required Formula :

Mean = Sum of Observations/No of observations

Explanation :

We know that when we are given the mean and the number of observations and is asked to find the sum of the observations then our required formula is,

Mean = Sum of Observations/No of observations

where,

• Mean = 18
• No of observations = 5

Using the required formula and substituting the values,

⇒ Mean = Sum of Observations/No of observations

⇒ 18 = Sum of Observations/5

⇒ 18 × 5 = Sum of Observations

⇒ 90 = Sum of Observations

∴ Sum of Observations = 90.

Now,

Let the excluded number be “x”.

We know that the sum of 5 numbers is 90. So, after excluding one number from it we will get 90 - a.

☯ According to the question,

Mean = Sum of Observations/No of observations

where,

• Mean = 16
• Sum of Observations = 90 - a
• No of observations = 4

Using the required formula and substituting the values,

⇒ Mean = Sum of Observations/No of observations

⇒ 16 = (90 - a)/4

⇒ 16 × 4 = 90 - a

⇒ 64 = 90 - a

⇒ a = 90 - 64

⇒ a = 26

∴ a = 26.

The excluded number is 26.