Per se **Frequency Distribution** is a very simple concept - Categorizing data and displaying the same in a summarized form into a relatively small number of intervals. Some properties -

- Way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
- Two major means of summarizing a set of numbers: pictures and summary numbers
- Frequency distributions can be used for both qualitative and quantitative data
- Each entry in the table contains the frequency or count of the occurrences of values within that particular group or interval

Thomas obtained the following marks in his 10 Statistics tests during the semester:

24, 26, 18, 21, 27, 27, 30, 44, 32, 38

How can you draw any inference from here?

First step is to summarize and see what the data has to say.

So how would you organize, classify this data, form the table and present it in the form of a picture? Simplest is to put it in a tabular form (Frequency Distribution):

Class | Frequency |

15 - 25 | 3 |

25 - 35 | 5 |

35 - 45 | 2 |

Here the total number of classes is 3. And we can clearly see that most of the marks secured in the mid range. Small number of times very low and very high marks are secured.

**Find the range of the data:****Decide the approximate number of classes:****Determine the approximate class interval size:****Decide the starting point:****Determine the remaining class limits (boundary):****Distribute the data into respective classes:****Tally Bars (Tally Marks)**

*There is not right or wrong way for creating the distribution table - the only point that should be noted is that the class size should be consistent.**Relatively uniform in terms of frequency distribution. it should not happen that all the 10 data point get in one interval and the frequency for the rest of the classes is 0.*

**A histogram -**graphical equivalent of a frequency distribution; it is a bar chart where continuous data on a random variable's observations have been grouped into intervals**A frequency polygon-**is the line graph equivalent of a frequency distribution; it is a line graph that joins the frequency for each interval, plotted at the midpoint of that interval.

In our case study,

- If a histogram is drawn then it would be 3, 5 and 2.
- Count frequencies of a particular class and if the mid points are joined this will be called a frequency polygon for frequency distribution.

Data of Thomas can be shown in the form of a histogram:

Midpoints of the interval of corresponding rectangle in a histogram are joined together by straight lines. It gives a polygon i.e. a figure with many angles. Unlike histograms, frequency polygons can be superimposed so as to compare several frequency distributions. For the marks obtained by Thomas we can have the frequency polygon as shown below:

Managing and operating on frequency tabulated data is much simpler than operation on raw data. There are simple algorithms to calculate median, mean, standard deviation etc. from these tables as well.

CFA Program is the gold standard in education and lays a strong foundation on Quantitative Analysis and understanding the principles of data distribution. If you are interested in gaining a fundamental stronghold on your finances, you can consider enrolling for the CFA examination. More details about the examination can be obtained by sending an email to info@edupristine.com or calling +91 989 298 0608.

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