Question

The average of 18 observations was calculated and it was 124. Later on it was discovered that two observations 46 and 82 were incorrect. The correct values are 64 and 28. The correct average of 18 observations is?

Answer 1

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Let the sum of 18 observations be ‘x’

Then average of 18 observations =

5995317b0a975a128777672b

5995317b0a975a128777672c

⇒ x = 124 × 18

We get the sum as 124 × 18

It is given that the values 64 and 28 were wrongly entered as 46 and 82

Let the new sum be ‘y’

Then,

y = 124 × 18 – 46 – 82 + 64 + 28 (subtracting the wrong values and adding the correct values)

⇒ y = 124 × 18 – 36

∴ Correct average = 

5995317b0a975a128777672d

⇒ Correct average = 124 – 2

⇒ Correct average = 122