Frequency & Relative Frequency Tables, Explain with example and figure.

In order to know about frequency and relative frequency table, one must know what is meant by frequency. Frequency refers to the number of times any particular data is occurring. Therefore in simpler terms it can be stated that frequency refers to the number of occurrence of a particular score in a given data set. For example if five different persons are there having a weight of 68 Kilograms, then the weight of 68 Kilograms is said to have a frequency of 5. The frequency of any data is represented by the symbol ‘ f ’.

Frequency table as the name suggests refer to the table that organizes raw data compactly and display a series of data along with their frequencies. The data in this table is arranged in either ascending or descending order. These tables are useful when there are huge data having several occurrences. The frequency table usually consists of three columns. The first column shows the several outcomes that occur in the given data set, the second column shows the frequency of each and outcome and the third column shows the tally marks. Tally marks are also termed as the hash marks that acts as a numeral form and helps in counting. These tally marks are usually clustered in a group of five hashes. This kind of table is very helpful in making large data simpler to be understood and analyzed.

A frequency table can be used for computation of both discrete and continuous variables. It can take the format of both grouped data and ungrouped data. The following paragraph states how a frequency table can be put into use. Two examples are shown – one without class intervals and other with class intervals. 

Without Class Intervals

Question: The marks that have been awarded to class 8 students containing 30 students are as follows:

Solution: In order to construct the frequency table we proceed as follows:

Step: 1 – We construct a three column table and arrange the given set of data in ascending order as shown

Step: 2 – As we go through the list of the number we put a tally mark in the respective column. For example the first number we see in the question is 6. So we put a tally mark against 6.

The process continues unless all the data are marked in the table.

Step: 3 – As soon as we complete marking, we count the marks against each data and put the value in the frequency column.

With Class Intervals

Question: Marks out of 40 are given as follows for a group of 30 students in a class -

Solution: In order to construct the frequency table we proceed as follows:

Step: 1 – We construct a three column table and then prepare a class interval.

Step: 2 – As we go through the list of the number we put a tally mark in the respective column. For example the first number we see in the question is 0. So we put a tally mark against 0-10. Similarly for 10 we put tally marks in 10-20 class interval.

The process continues unless all the data are marked in the table and after that we put the respective frequencies, which is as below:

Relative Frequency Table:

This is one type of frequency distribution where instead of knowing about the exact counts we prefer to know the percentage. In simple words it is a frequency distribution table showing the relative frequencies, which refers to the representation of the categorical variables in terms of proportions or percentages. The examples used above are again utilized in order to show the use of a relative frequency distribution table.

General steps include organizing the data in ascending order or arranging into respective class intervals. Frequencies are then put after each of the respective data. The total of the frequency is done and then we find the relative frequency by dividing the respective frequency with the total frequency and then multiplying with 100. It is showed as below:

Without Class Interval

With Class Interval

In the above example it has been seen that the three columns represent marks, frequencies and the relative frequencies. The relative frequencies have been calculated by dividing the count with the summation of the frequency and then it is multiplied by 100 in order to get the value in percentage. The value that we get before multiplying it with 100 is called as proportion. Proportion values will look as follows:

Classical Approaches to Probability:

Probability can be measured in three ways – Classical Approach, Relative Frequency Approach and Subjective Approach. This paragraph discusses in details about the classical approach. Probability refers to the concept of measuring the likelihood of something that can happen or is happening. The classical approach of probability states that it is simple probabilistic form that has the chances of equal odds to happen. It is basically a statistical concept that measures the likelihood of something that is happening or is about to happen but in a sense that it contains the elements, which are equally likely to happen.  

We denote P (A) as the probability of an event A. We use a very simple formula in order to calculate the classical probability. The formula is –

Probability = [Number of Favorable Outcomes (N) / Number of Possible Outcomes (f)]

Some of the examples are given as below:

1. Finding out even numbers in a through of a die.

A die have six numbers printed over it and they are 1, 2, 3, 4, 5 and 6. So the number of possible outcome is 6. There are three even numbers in a die which are 2, 4, 6. The number of favorable outcome is therefore 3. So the probability is 3/6 which is equal to ½.

1. The formula can be only used when all the events are equally likely. So if we choose any card from a general deck of card it gives a probability of 1/52 of getting a particular type of card. So if it is asked to find out the probability of selecting an ace from a deck of card, then the probability would be –

Total card – 52

Total type – 4 (Spade, Heart, Club and Diamond)

Number of cards in each type – 13

Each type has an ace. So number of Aces will be 4. Total count is 52. Therefore Probability = N/f = 4/52 = 1/13.

Difference between Frequency Table and Relative Frequency Table

1. Frequency refers to the number of times a particular event is occurring whereas relative frequency refers to the number of time the event happens divided by the total number of repetition.
2. Frequency table uses tally marks whereas relative frequency does not use tally marks.
3. Frequency table represents the data in numerical form whereas relative frequency represents the data in percentage or proportionate form.   
4. Frequency can be easily found through simple observation and notation whereas relative frequency is obtained by using simple division. Construction of frequency table involves arranging the collected data in ascending orders along with their respective frequencies, whereas relative frequency table represents a chart showing the mode of the collected data, which is based upon the population sampled.