Mean of 9 observations was found to be 35. Later on, it was detected that an observation 81 was misread as 18. Find the correct mean of the observations.

By formula,

Mean = $\dfrac{\text{Total sum of observations}}{\text{No. of observations}}$

$\therefore 35 = \dfrac{\text{Total sum of observations}}{9} \\[1em] \text{Total sum of observations} = 35 \times 9 = 315.$

Since, 81 was misread as 18.

So, Actual sum of observation = Total sum of observations - 18 + 81 = 315 - 18 + 81 = 378.

Correct mean = $\dfrac{378}{9}$ = 42.

Hence, the correct mean = 42.