The mean of 25 observations is 27. If one observation is included, the mean still remains 27. Find the included observation.

Given,

The mean of 25 observations is 27.

By formula,

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

$\therefore 27 = \dfrac{\text{Total sum of observations}}{25} \\[1em] \text{Total sum of observations} = 27 \times 25 = 675.$

Given, mean after including new number remains 27.

No. of observations = 25 + 1 = 26.

$\therefore 27 = \dfrac{\text{New sum of observations}}{26} \\[1em] \text{New sum of observations} = 27 \times 26 = 702.$

New number included = New sum of observations - Total sum of observations = 702 - 675 = 27.

Hence, the new included observation = 27.