Question

The average of a set of 15 observations is recorded, but later it is found that for one observation, the digit in the tens place was wrongly recorded as 8 instead of 3. After correcting the observation, the average is
1. reduced by \(\dfrac{1}{3}\)
2. increased by \(\dfrac{10}{3}\)
3. reduced by \(\dfrac{10}{3}\)
4. reduced by 50

Answer 1

Correct Answer - Option 3 : reduced by \(\dfrac{10}{3}\)

Formula Used:

Average = \(\frac{X_i}{n}\)

Here, X_i is the sum of observation and n is the number of reading

Calculation:

Let the average initially be x

Then the sum of the observations = 15x

As the tens digit is recorded 5 more, therefore the sum is 50 more than the correct sum. 

Correct sum of the observations = 15x - 50

The correct average = \(\rm 15x-50\over15\) = x - \(10\over3\)

∴ The average is reduced by \(10\over3\)