HOW TO FIND THE CORRECT MEAN FROM INCORRECT MEAN

Example 1 :

The average height of 10 students in a class was calculated as 166 cm. On verification it was found that one reading was wrongly recorded as 160 cm instead of 150 cm. Find the correct mean height.

Solution :

Average height  of 10 students x̄ = 166 cm

Here 166 is the incorrect mean and n = 10

We have x̄ = ∑x / n  =  ∑x / 10 

∑x / 10   =  166

Multiply 10 by both sides

The incorrect ∑x  =  1660

The incorrect ∑x = 1660

The correct  ∑x  

  =  incorrect  ∑x  – the wrong value + correct value

  =  1660 – 160 + 150 = 1650

Hence, the correct A.M. = 1650 / 10

  =  165 cm

Hence the correct mean height is 165 cm.

Example 2 :

The average height of 20 students in a class was calculated as 160 cm. On verification it was found that one reading was wrongly recorded as 132 cm instead of 152 cm. Find the correct mean height.

Solution :

Average height  of 10 students x̄ = 160 cm

Here 166 is the incorrect mean and n = 20

We have x̄ = ∑x / n  =  ∑x / 20 

∑x / 20   =  160

Multiply 20 by both sides

The incorrect ∑x  =  160 (20)  =  3200

The incorrect ∑x  =  3200

The correct  ∑x  

  =  incorrect  ∑x  – the wrong value + correct value

  =  3200 – 132 + 152  =  3220

Hence, the correct A.M.  =  3220 / 20

  =  161 cm

Hence the correct mean height is 161 cm.

Example 3 :

If in a class of 20 students, 5 students have scored 76 marks, 7 students have scored 77 marks and 8 students have scored 78 marks, then compute the mean of the class.

Solution :

Mean  =  Sum of marks of 20 students / 20

5 students have scored 76 marks

7 students have scored 77 marks

8 students have scored 78 marks

  =  [ 5 (76) + 7 (77) + 8 (78) ] / 20

  =  (380 + 539 + 624) / 20

  =  1543 / 20

  =  77.15

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