Question

The average of 100 observations was calculated as 35. It was found later that one of the observations was misread as 83 instead of 53. The correct average is?

Answer 1

Answer:

Let no. of observations be x. Then,

$\frac{x}{100} = 35 \\ x = 35 \times 100 \\ x = 3500 \\ hence \: sum \: of \: all \: observtions \: is \: 3500 \\diff \: between \: both \: nos = 83 - 53 = 30 \\now \: new \: average \\ = \frac{x - 30}{100} \\ = \frac{3500 - 30}{100} \\ = \frac{3470}{100} \\ = 34.7$