Question

In a village the average age of n people is 42 years. But after the
verification it was found that the age of a person had been
considered 20 years less that the actual age, so the new
average, after the increased by 1. The value of n is:


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Answer 1

Answer:

20

Step-by-step explanation:

(x1+x2+...+xn)/n=42

(x1+x2+...+xn)=42*n

correct summation (x1+x2+...+xn+20)=42*n+20

new avg=42+1=43

now (correct summation)/n=43

(42*n+20)/n=43

42n/n+20/n=43

20/n=1

n=20

Answer 2

Given:

In a village the average age of n people is 42 years.  But after the  verification it was found that the age of a person had been  considered 20 years less that the actual age, so the new  average increased by 1

To find:

The value of n i.e. Number of people in the village

Step-by-step explanation:

As given

$\bar {x}=42$

as we know average is given by

$\bar {x}= \dfrac{\sum x_i}{n}$

where $\bar {x}$ is the mean $x_i$ are the observations(ages) and n is the total number of observations(number of people)

Therefore

$42= \dfrac{\sum x_i}{n} \\\\\Rightarrow 42n =\sum x_i$

Now it was found that the age of a person had been  considered 20 years less that the actual age

Therefore

$\sum x_i_{(new)}= 42n+20$

And the new mean becomes

$\bar {x}_{new}= 42+1=43$

Therefore we have

$\bar{x}_{new}=\dfrac{\sum x_{i (new)}}{n} \\\\\Rightarrow 43 = \dfrac{42n+20}{n} \\\\\Rightarrow 43n=42n+20\\\\\Rightarrow n=20$

Hence, there are 20 people in the village