Question

The average weight of 45 students in a class was calculated as 36 kg. It was later found that, the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was 32 kg but it was calculated as 34 kg and the weight of another boy in the class was 45 kg, whereas it was calculated as 40 kg. What is the actual average weight of the 45 students in the class?

Answer 1

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Answer 2

Given :

The average weight of 45 students in a class was calculated as 36 kg.

The actual weight of one of the boys in the class was 32 kg but it was calculated as 34 kg and the weight of another boy in the class was 45 kg, whereas it was calculated as 40 kg.

To Find :

Find the actual mean

Solution:

$Average = \frac{\text{Sum of observations}}{\text{No. of observations}}$

The average weight of 45 students in a class was calculated as 36 kg.

So, $36 = \frac{\text{Sum of weights}}{45}\\36 \times 45 =\text{Sum of weights}\\1620=\text{Sum of weights}$

We are given that  the weight of two students in the class was wrongly calculated.

The actual weight of one of the boys in the class was 32 kg but it was calculated as 34 kg and the weight of another boy in the class was 45 kg, whereas it was calculated as 40 kg.

So, new sum = 1620+32+45-34-40=1623

New mean =$\frac{1623}{45}$

New mean =30.06

Hence The actual mean is 30.06