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Question

Calculate the arithmetic mean by assumed mean method for the data given below.
Marks$$0-10$$$$10-20$$$$20-30$$$$30-40$$$$40-50$$$$50-60$$
No. of students   $$5$$   $$10$$   $$25$$   $$30$$   $$20$$   $$10$$


Solution

Let the assumed mean be $$A = 35$$
MarksMid-value
    $$\left( x \right) $$
No. of students
       $$\left( f \right) $$
$$d=x-35$$$$fd$$
$$0-10$$
$$10-20$$
$$20-30$$
$$30-40$$
$$40-50$$
$$50-60$$
 $$5$$
$$15$$
$$25$$
$$35$$
$$45$$
$$55$$
 $$5$$
$$10$$
$$25$$
$$30$$
$$20$$
$$10$$
$$-30$$
$$-20$$
$$-10$$
  $$0$$
 $$10$$
 $$20$$
$$-150$$
$$-200$$
$$-250$$
   $$0$$
 $$200$$
 $$200$$
$$\sum { f } =100$$$$\sum { fd } =-200$$
$$\overline { x } =A+\dfrac { \sum { fd }  }{ \sum { f }  } $$
     $$=35+\left( \dfrac { -200 }{ 100 }  \right) =35-2=33$$

Mathematics

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