Parameter, sample statistic, and frequency distribution

Example 1: Constructing a frequency distribution

The returns earned by 15 mutual funds in the last year are 12 percent, 8 percent, -10 percent, 4 percent, 11 percent, -4 percent, 9 percent, 0 percent, -2 percent, -5 percent, 6 percent, 7 percent, 14 percent, 18 percent, and -12 percent. Construct a frequency distribution for this data.

Solution:

First arranging the returns in ascending order (all returns are in percentage): -12, -10, -5, -4, -2, 0, 4, 6, 7, 8, 9, 11, 12, 14, 18

Then calculating the range of data, Range = Maximum value - Minimum value = 18 - (-12) = 30.

Now, decide the total number of intervals in the frequency distribution. Let's choose it as 6.

So, the interval width will be equal to the range divided by the total number of intervals. Interval width = 30/6 = 5.

The intervals will be such so that it starts with the minimum value and then adding the interval width to each interval and finally ending with the maximum value.

Then we need to count the number of observations that fall in each interval, and that will be the frequency of that interval.

Note that the intervals are defined in such a manner so that any observation doesn't fall in more than one interval.