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Question

While calculating the mean of 3 single-digit numbers, Xavier mistakenly replaced the number 6 by 9, and obtained the mean as 5. Find the actual mean of the data set.
  1. 4

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Solution

The correct option is A 4
While calculating the mean of 3 single-digit numbers, Xavier replaced 6 by 9, and obtained the mean as 5.
Consider, the other 2 single-digit numbers are []and[].

As Xavier obtained the mean of data set {[],[],9} as 5, we can write

[]+[]+93=5

[]+[]+93×3=5×3
(multiplying 3 in both sides)

[]+[]+9=15

[]+[]+99=159
(substracting 9 from both sides)

[]+[]=6

Need to find: Actual mean of the data set {[],[],6}, i.e.,

[]+[]+63

=6+63
([]+[]=6)

=123=4

The actual mean of the data set is 4.

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