Answer
409.8k+ views
Hint: Average can be defined as the ratio of the sum of the observations in the given set of data to the total number of the observations. For example: The given data is \[11,{\text{ }}12,{\text{ }}13,{\text{ }}14\].
Average \[ = {\text{ }}\dfrac{{\left( {11 + 12 + 13 + 14} \right)}}{4}{\text{ }} = {\text{ }}12.5\]
In this particular problem, the average is associated with the percentages. So, we need to assume that the total number of students in the class is 100 just to make the calculation easier.
Complete step-by-step answer:
Let the total number of students in the class be \[100\].
Average marks of all the students in English is given to be \[52.25\]
According to the problem,
Number of the students in the C category = \[25\% \] of the total students \[ = {\text{ }}25\]
Average marks of the students in C category in English \[ = {\text{ }}31\]
Number of the students in the A category = \[20\% \] of the total students = \[20\]
Average marks of the students in A category in English = 80
Hence, the number of the remaining students \[ = {\text{ }}100{\text{ }}-{\text{ }}\left( {25{\text{ }} + {\text{ }}20} \right){\text{ }} = {\text{ }}100{\text{ }}-{\text{ }}45{\text{ }} = {\text{ }}55\]
Let Average marks of the remaining students in English = x
On solving,
\[ \Rightarrow \] \[52.25 \times 100{\text{ }} = {\text{ }}\left( {31 \times 25} \right){\text{ }} + {\text{ }}\left( {80 \times 20} \right){\text{ }} + {\text{ }}\left( {55 \times x} \right)\]
\[ \Rightarrow \] \[5225{\text{ }} = {\text{ }}775{\text{ }} + {\text{ }}160{\text{ }} + {\text{ }}55x\]
\[ \Rightarrow \] \[55x{\text{ }} = {\text{ }}5225{\text{ }}-{\text{ }}775{\text{ }}-{\text{ }}160\]
\[ \Rightarrow \] 55x = 2850
\[ \Rightarrow \] \[x{\text{ }} = {\text{ }}\dfrac{{2850}}{{55}}{\text{ }} = {\text{ }}51.8\]
Hence, the average marks of the remaining students in English is \[51.8\].
Note: The average is commonly known as the Mean or the Expected value.
To find the averages associated with the percentages, we always consider the total number of the observations to be 100 so that the calculations become easier.
So, on solving this problem by using the same method, 25% of the total students i.e. \[100\] becomes \[25\] in the C category and similarly, 20% of the total students i.e. \[100\] becomes \[20\] in A category and hence, we get the average marks of the remaining students in English, \[51.8\].
Average \[ = {\text{ }}\dfrac{{\left( {11 + 12 + 13 + 14} \right)}}{4}{\text{ }} = {\text{ }}12.5\]
In this particular problem, the average is associated with the percentages. So, we need to assume that the total number of students in the class is 100 just to make the calculation easier.
Complete step-by-step answer:
Let the total number of students in the class be \[100\].
Average marks of all the students in English is given to be \[52.25\]
According to the problem,
Number of the students in the C category = \[25\% \] of the total students \[ = {\text{ }}25\]
Average marks of the students in C category in English \[ = {\text{ }}31\]
Number of the students in the A category = \[20\% \] of the total students = \[20\]
Average marks of the students in A category in English = 80
Hence, the number of the remaining students \[ = {\text{ }}100{\text{ }}-{\text{ }}\left( {25{\text{ }} + {\text{ }}20} \right){\text{ }} = {\text{ }}100{\text{ }}-{\text{ }}45{\text{ }} = {\text{ }}55\]
Let Average marks of the remaining students in English = x
On solving,
\[ \Rightarrow \] \[52.25 \times 100{\text{ }} = {\text{ }}\left( {31 \times 25} \right){\text{ }} + {\text{ }}\left( {80 \times 20} \right){\text{ }} + {\text{ }}\left( {55 \times x} \right)\]
\[ \Rightarrow \] \[5225{\text{ }} = {\text{ }}775{\text{ }} + {\text{ }}160{\text{ }} + {\text{ }}55x\]
\[ \Rightarrow \] \[55x{\text{ }} = {\text{ }}5225{\text{ }}-{\text{ }}775{\text{ }}-{\text{ }}160\]
\[ \Rightarrow \] 55x = 2850
\[ \Rightarrow \] \[x{\text{ }} = {\text{ }}\dfrac{{2850}}{{55}}{\text{ }} = {\text{ }}51.8\]
Hence, the average marks of the remaining students in English is \[51.8\].
Note: The average is commonly known as the Mean or the Expected value.
To find the averages associated with the percentages, we always consider the total number of the observations to be 100 so that the calculations become easier.
So, on solving this problem by using the same method, 25% of the total students i.e. \[100\] becomes \[25\] in the C category and similarly, 20% of the total students i.e. \[100\] becomes \[20\] in A category and hence, we get the average marks of the remaining students in English, \[51.8\].
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)