Question

the following table shows marks scored by students in an examination of a certain paper
mark 0-10 10-20 20-30 30-40 40-50
number of 20 24 40 36 20
students
calculate the average mark by using deviation method​

Answer 1

Answer:

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Answer 2

(refer to the attachment)

Correct Question :

To calculate the average marks by using step deviation method. (with reference to the picture)

Explanation :

We have to construct a table (attachment), taking :

• Assumed mean (a) = 25
• Width of the class (c) = 10

Now, using the formula to find mean using step deviation method,

$\boxed{\bf Mean=a+c\times\dfrac{\sum f_iu_i}{\sum f_i}}$

where,

• a = 25
• c = 10
• fᵢuᵢ = 12
• fᵢ = 140

Substituting the values,

$\\ :\implies\sf Mean=25+10\times\dfrac{12}{140}$

$\\ :\implies\sf Mean=25+1\!\!\!\not{0}\times\dfrac{12}{14\!\!\!\not{0}}$

$\\ :\implies\sf Mean=25+1\times\dfrac{12}{14}$

$\\ :\implies\sf Mean=25+\dfrac{\cancel{12}\ \ ^6}{\cancel{14}\ \ ^7}$

$\\ :\implies\sf Mean=25+1\times\dfrac{6}{7}$

$\\ :\implies\sf Mean=25+\dfrac{6}{7}$

Taking LCM of 7 and 1 = 7,

$\\ :\implies\sf Mean=\dfrac{175+6}{7}$

$\\ :\implies\sf Mean=\dfrac{181}{7}$

$\\ :\implies\sf Mean=25.85(\approx25.9)$

$\\ \therefore\boxed{\bf Mean=25.9}$

The average marks is 25.9

Explore More :

• Mean using direct method :

$\bf Mean=\dfrac{\sum f_iy_i}{\sum f_i}$

• Mean using short - cut method :

$\bf Mean=a+\dfrac{\sum f_id_i}{\sum f_i}$

where,

• a = Assumed mean
• yᵢ = Class Mark
• fᵢ = Frequency
• dᵢ = Class Mark - Assumed mean