Statistics

The formula for the average of the first natural numbers is: For the first 50 natural numbers: Thus, the correct answer is .

The sum of deviations from the mean is always 0, i.e.: This is because the mean is defined such that the sum of deviations from it is 0. Thus, the correct answer is 0.

To find the median of the given distribution, we need to arrange the data values in ascending order and compute the cumulative frequency. The cumulative frequency is calculated by summing the frequencies sequentially:

The total number of observations is . The median corresponds to the position th observation. The cumulative frequency just exceeding 21.5 is for , meaning the median value is 9. Thus, the correct answer is 9.