Median

In a frequency table, when we use the assumed mean method, the deviation of each observation from the assumed mean is calculated. The mean of these deviations is denoted by . The actual mean can be expressed as: where:
is the size of the intervals,
is the mean of the deviations,
is the assumed mean.

The correct answer is option (A):

Correct answer:

Explanation:
The formula for the median of a grouped data set is: Where: - is the lower boundary of the median class, - is the total number of frequencies, - is the cumulative frequency of the class before the median class, - is the frequency of the median class, - is the class width.

Hence, the correct formula for median in a grouped data set is .

The given data is 30, 34, 35, 36, 37, 38, 39, 40.

There are 8 data points.

Since there are 8 data points, the middle two values are the 4th and 5th values, which are 36 and 37.

So, the median is $ $

Therefore, the median increases by 0.5.