Statistics Fundamentals: Summarizing Data Using Frequency

One of the simplest ways to summarize data is a frequency distribution, which is a tabular display of data summarized into relatively small numbers of intervals. Rates of returns are fundamental units for investment decisions. Frequency distributions help summarize returns.
 
The following are the steps to constructing a frequency distribution:

1. Sort data in ascending order;
2. Calculate the range of the data;
3. Decide on the number of intervals in the frequency distribution (“k”);
4. Determine interval width (=range/k);
5. Determine the intervals (set of values within which an observation falls) and ending points by (a) successively adding the interval width to the minimum value and (b) stopping after reaching an interval that includes the maximum value;
6. Count the observations falling in each interval;
7. Construct a table of intervals, from min to max, to show the absolute frequency (the number of observations within a given interval)

 
Once establishing a frequency distribution, you can compute three other useful ways to compute the data, which are
Relative Frequency is the absolute frequency of an interval/total number of observations;
Cumulative Frequency consequently adds the number of observations from the first to the last interval;
Cumulative Relative Frequency consequently adds the relative frequency to show the percentage of observations at a certain point