Question

The mean of 16 observations for 30 and Henry checking it was found that the two terms were wrongly taken that was 28 and 18 instead of 32 and 28 respectively . find the correct mean

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Answer 1

The correct mean is 30.875

Explanation:

Mean Value

Given n observations of a specific magnitude, the mean value of the random experiment is:

`\displaystyle \bar x=(\sum x_i)/(n)`

Where xi is each individual value.

Henry made 16 observations and found the mean was 30. Replacing that into the formula, we have

`\displaystyle 30=(\sum x_i)/(16)`

Operating:

`\sum x_i=480`

We know the sum of all the individual values is 480. Knowing that Henry made a mistake and used 28 and 18 instead of 32 and 28, the correct mean should include the correct sum. Since 32 is 4 more than 28, and 28 is 10 more than 18, the correct sum is 480 + 4 + 10 = 494. This gives us the corrected mean:

`\displaystyle \bar x'=(494)/(16)= 30.875`

The correct mean is 30.875