the mean of 5 number is 18. if one number is excluded then the mean is 16
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the mean of 5 number is 18. if one number is excluded then the mean is 16
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Given :
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,
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,
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.