Answer
410.1k+ views
Hint: In this question, we have the number of observations and its mean given to us. So by using the formula of mean we will get the total sum of observations. And then we will calculate the correct mean by substituting the values in the formula.
Formula used:
Mean,
$\bar x = \dfrac{{\sum x }}{N}$
Here,
$\bar x$ , will be the mean
$N$ , will be the number of observations.
$\sum x $ , will be the sum of the observation.
Also, the correct mean will be calculated by using the formula as
$Correct{\text{ }}\bar x = \dfrac{{\sum x \left( {Wrong} \right) + \left( {Correct{\text{ value}}} \right) - \left( {Incorrect{\text{ value}}} \right)}}{N}$
Complete step-by-step answer:
First of all we will see the values given to us. So we have the values
$N = 100$
$\bar x = 40$
So by using the formula of mean, we have the equation as $\bar x = \dfrac{{\sum x }}{N}$
On substituting the values, we will get the equation as
$ \Rightarrow 40 = \dfrac{{\sum x }}{{100}}$
And on solving the above equation by doing the cross multiplication, we will get
$ \Rightarrow \sum {x\left( {Wrong} \right)} = 40 \times 100$
And on solving the multiplication, we get
$ \Rightarrow \sum {x\left( {Wrong} \right)} = 4,000$
So we have the correct values which are equal to
$ \Rightarrow 3 + 72$
And on solving it, we get
$ \Rightarrow 75$
And also we have the incorrect values which are equal to
$ \Rightarrow 30 + 27$
And on solving it, we get
$ \Rightarrow 57$
So by using the formula for the correct mean, we have the formula as $Correct{\text{ }}\bar x = \dfrac{{\sum x \left( {Wrong} \right) + \left( {Correct{\text{ value}}} \right) - \left( {Incorrect{\text{ value}}} \right)}}{N}$
So on substituting the values in the above position, and equating it we will get
$ \Rightarrow Correct{\text{ }}\bar x = \dfrac{{4,000 + 75 + 57}}{{100}}$
And on adding the numerator of the above part, we get
$ \Rightarrow Correct{\text{ }}\bar x = \dfrac{{4,018}}{{100}}$
And on solving it again, we get
$ \Rightarrow Correct{\text{ }}\bar x = 40.18$
Therefore, the correct value of the mean will be equal to $40.18$ .
Note: So here we have calculated the correct mean and we can see that not too high-level solutions are needed for such types of questions. So this method is suggested doing this type of question .
Formula used:
Mean,
$\bar x = \dfrac{{\sum x }}{N}$
Here,
$\bar x$ , will be the mean
$N$ , will be the number of observations.
$\sum x $ , will be the sum of the observation.
Also, the correct mean will be calculated by using the formula as
$Correct{\text{ }}\bar x = \dfrac{{\sum x \left( {Wrong} \right) + \left( {Correct{\text{ value}}} \right) - \left( {Incorrect{\text{ value}}} \right)}}{N}$
Complete step-by-step answer:
First of all we will see the values given to us. So we have the values
$N = 100$
$\bar x = 40$
So by using the formula of mean, we have the equation as $\bar x = \dfrac{{\sum x }}{N}$
On substituting the values, we will get the equation as
$ \Rightarrow 40 = \dfrac{{\sum x }}{{100}}$
And on solving the above equation by doing the cross multiplication, we will get
$ \Rightarrow \sum {x\left( {Wrong} \right)} = 40 \times 100$
And on solving the multiplication, we get
$ \Rightarrow \sum {x\left( {Wrong} \right)} = 4,000$
So we have the correct values which are equal to
$ \Rightarrow 3 + 72$
And on solving it, we get
$ \Rightarrow 75$
And also we have the incorrect values which are equal to
$ \Rightarrow 30 + 27$
And on solving it, we get
$ \Rightarrow 57$
So by using the formula for the correct mean, we have the formula as $Correct{\text{ }}\bar x = \dfrac{{\sum x \left( {Wrong} \right) + \left( {Correct{\text{ value}}} \right) - \left( {Incorrect{\text{ value}}} \right)}}{N}$
So on substituting the values in the above position, and equating it we will get
$ \Rightarrow Correct{\text{ }}\bar x = \dfrac{{4,000 + 75 + 57}}{{100}}$
And on adding the numerator of the above part, we get
$ \Rightarrow Correct{\text{ }}\bar x = \dfrac{{4,018}}{{100}}$
And on solving it again, we get
$ \Rightarrow Correct{\text{ }}\bar x = 40.18$
Therefore, the correct value of the mean will be equal to $40.18$ .
Note: So here we have calculated the correct mean and we can see that not too high-level solutions are needed for such types of questions. So this method is suggested doing this type of question .
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)