Answer :

Given that number of observations (n) = 18

Incorrect Mean (x̅ ) = 7

and Incorrect Standard deviation, (σ) = 4

We know that,

…(i)

∴ Incorrect sum of observations = 126

Finding correct sum of observations, 12 was misread as 21

So, Correct sum of observations = Incorrect Sum – 21 + 12

= 126 – 21 + 12

= 117

Hence,

= 6.5

Now, Incorrect Standard Deviation (σ)

Squaring both the sides, we get

Since, 12 was misread as 21

So,

= 1170 – 441 + 144

= 873

Now,

Correct Standard Deviation

= 2.5

Hence, Correct Mean = 6.5

and Correct Standard Deviation = 2.5

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