Discrete Frequency Distribution

Frequency distribution in statistics is a list, table (i.e., frequency table), or graph (i.e., bar plot or histogram) that shows the frequency of different outcomes in a sample. The frequency or count of occurrences of values within a certain group or interval is contained in each table entry. A frequency distribution illustrates the number of occurrences in each class and a summarised grouping of data sorted into mutually exclusive groupings. It is a method of displaying disorganised data, such as election results, people’s income in a specific location, product sales during a specific time period, graduate student debt amounts, and so on. Histograms, line charts, bar charts, and pie charts are examples of graphs that can be used with frequency distributions. For both qualitative and quantitative data, frequency distributions are used.

Frequency Distribution Types

In statistics, there are four types of frequency distributions, which are described below:

An ungrouped frequency distribution shows the frequency of an item in each individual data value rather than groups of data values.

The data is sorted and segregated into groups called class intervals in a grouped frequency distribution. In a frequency distribution table, the frequency of data corresponding to each class interval is recorded. The grouped frequency table depicts the frequency distribution in class intervals.

The relative frequency distribution determines the proportion of the total number of observations associated with each category.

In a frequency distribution, the cumulative frequency distribution is the sum of the initial frequency and all frequencies below it. You must add one value to the next, then add the sum to the next, and so on until the last value is reached. The end cumulative frequency will be the total of all frequencies.

A discrete distribution is one in which the data can only take one of a few possible values, such as integers. A continuous distribution is one in which data can take on any value within a given range of values (which may be infinite). The values in a discrete distribution can be assigned probabilities – for example, “the probability that the web page will have 12 hits in an hour is 0.15.” A continuous distribution, on the other hand, has an infinite number of possible values, and the probability associated with any one of those values is null. As a result, continuous distributions are frequently characterised in terms of probability density, which may be translated into the likelihood that a value will fall inside a given range.

Definition of Discrete Frequency Distribution

Let the given data consist of n different values x1, x2…, xn, each with a frequency of f1, f2,…, fn. Then, as shown below, this data can be represented in tabular form with variables and related frequencies, resulting in a discrete frequency distribution:

The occurrences of data values such as observation x1 occur f1 times, x2 occur f2 times, and so on are described in the table above.

The values of the variable are thus decided individually in a discrete frequency distribution. The frequency of a value or observation is determined by the number of times it appears. Ungrouped frequency distribution is another name for discrete frequency distribution.

Table of Frequency Distribution

A frequency distribution table is a graph that illustrates how often each item in a data set occurs. To see how to build a frequency distribution table with tally marks, examine the following example. Red, green, blue, black, red, green, blue, yellow, red, red, green, green, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red, green, yellow, red We must first classify the beads into groups in order to determine the exact quantity of beads of each hue. Using tally markings is a simple approach to determine the number of beads of each colour. Pick up the beads one by one and place them in the appropriate row and column. Then, for each item in the table, note the frequency.

Construction of Discrete Frequency Distribution

Tally markings can be used to create a discrete frequency distribution table for easy understanding and precise results. The following example will help you understand what I’m talking about:

Example:

The following are the results of a monthly test in which 25 students received a total of 20 points. Make a discrete frequency distribution of the data.

15, 13, 16, 16, 15, 16, 17, 14, 15, 16, 16, 17, 14, 15, 16, 16, 17, 14, 15, 16, 16, 17, 14, 15, 16, 16, 17, 14, 15, 16, 16, 17, 14, 16, 15, 17, 13

Ans-

Given :

17, 16, 14, 15, 16, 17, 14, 16, 15, 17, 13,15, 13, 16, 16, 15, 16, 17, 14, 15, 16, 16,17, 14, 17

This can be represented as:

When the number of data values is tiny, a discrete frequency distribution table is created. If there are more observations, a grouped frequency table must be prepared for easy calculation. Many statistical issues will benefit from this method of data grouping. In addition, we can create a frequency table without the need of tally marks.

Discrete Frequency Distribution Mean

With the right formulas, we may find the measures of central tendency for any discrete frequency distribution. With the help of the solved example below, let’s learn how to find the mean given a discrete distribution of data:

Q-) Evaluate the mean of the given data:

Answer: 

Mean = ∑f(x)/∑f = 239/40 = 5.975

Conclusion

A discrete frequency distribution is a table that shows each number and the number of times it appears in a list (frequency). The numbers are usually integers, but other step sizes (such as tenths) are acceptable as long as each number is an integral multiple of the step size.A continuous frequency distribution, on the other hand, requires the data to be grouped into set width intervals, with the frequency being the number of numbers in the list that fall within each interval.