The mean of 30 observations recorded in an experiment is 5. If the observed largest value of 34 is deleted, find the mean of the remaining distributions.

The formula for the mean is $\text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}}$.
Given:
Initial number of observations ($N_1$) = 30
Initial mean ($\bar{x}_1$) = 5
Let the initial sum of observations be $\sum x_1$.

$$\bar{x}_1 = \frac{\sum x_1}{N_1}$$ $$5 = \frac{\sum x_1}{30}$$ $$\sum x_1 = 5 \times 30$$ $$\sum x_1 = 150$$

The largest value deleted is 34.
New sum of observations ($\sum x_2$) = Initial sum - Deleted value

$$\sum x_2 = 150 - 34$$ $$\sum x_2 = 116$$

New number of observations ($N_2$) = Initial number - 1 (since one observation is deleted)

$$N_2 = 30 - 1$$ $$N_2 = 29$$

New mean ($\bar{x}_2$) = $\frac{\text{New sum of observations}}{\text{New number of observations}}$

$$\bar{x}_2 = \frac{\sum x_2}{N_2}$$ $$\bar{x}_2 = \frac{116}{29}$$ $$\bar{x}_2 = 4$$

The mean of the remaining distributions is $\textbf{4}$.