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**Frequency Distribution Formula**

**Introduction to Frequency Distribution Formula**

The frequency distribution formula is the distribution of frequency in either tabular format or graphically. The frequency of a given data refers to the number of times the data points occur and the frequency distribution refers to a tabular representation that shows each data point and its frequency. The frequency distribution formula is one of the many ways to organize the given data. Let us study the frequency distribution formula using solved examples.

**What is Frequency Distribution?**

Frequency distribution is used to organize the collected data in table form. The data could be marks scored by students, temperatures of different towns, points scored in a volleyball match, etc. After data collection, we have to show data in a meaningful manner for better understanding. Organize the data in such a way that all its features are summarized in a table. This is known as frequency distribution.

Let’s consider an example to understand this better. The following are the scores of 10 students in the G.K. quiz released by Mr. Chris 15, 17, 20, 15, 20, 17, 17, 14, 14, 20. Let’s represent this data in frequency distribution and find out the number of students who got the same marks.

Quiz Marks |
No. of Students |

15 | 2 |

17 | 3 |

20 | 3 |

14 | 2 |

We can see that all the collected data is organized under the column quiz marks and the number of students. This makes it easier to understand the given information and we can see that the number of students who obtained the same marks. Thus, frequency distribution in statistics helps us to organize the data in an easy way to understand its features at a glance.

**Frequency Distribution Graphs**

There is another way to show data that is in the form of graphs and it can be done by using a frequency distribution graph. The graphs help us to understand the collected data in an easy way. The graphical representation of a frequency distribution can be shown using the following:

- Bar Graphs: Bar graphs represent data using rectangular bars of uniform width along with equal spacing between the rectangular bars.

- Histograms: A histogram is a graphical presentation of data using rectangular bars of different heights. In a histogram, there is no space between the rectangular bars.
- Pie Chart: A pie chart is a type of graph that visually displays data in a circular chart. It records data in a circular manner and then it is further divided into sectors that show a particular part of data out of the whole part.
- Frequency Polygon: A frequency polygon is drawn by joining the mid-points of the bars in a histogram.

**Types of Frequency Distribution**

There are four types of frequency distribution under statistics which are explained below:

**Ungrouped frequency distribution:**It shows the frequency of an item in each separate data value rather than groups of data values.**Grouped frequency distribution:**In this type, the data is arranged and separated into groups called class intervals. The frequency of data belonging to each class interval is noted in a frequency distribution table. The grouped frequency table shows the distribution of frequencies in class intervals.**Relative frequency****d****istribution:**It tells the proportion of the total number of observations associated with each category.**Cumulative frequency****distribution:**It is the sum of the first frequency and all frequencies below it in a frequency distribution. You have to add a value with the next value then add the sum with the next value again and so on till the last. The last cumulative frequency will be the total sum of all frequencies.

**Frequency Distribution Table**

A frequency distribution table is a chart that shows the frequency of each of the items in a data set. Let’s consider an example to understand how to make a frequency distribution table using tally marks. A jar containing beads of different colors- red, green, blue, black, red, green, blue, yellow, red, red, green, green, green, yellow, red, green, yellow. To know the exact number of beads of each particular color, we need to classify the beads into categories. An easy way to find the number of beads of each color is to use tally marks. Pick the beads one by one and enter the tally marks in the respective row and column. Then, indicate the frequency for each item in the table.

**What is Frequency Distribution Formula?**

To know the frequency of data, we have to divide the number of categories/values into intervals, then count the number of results in each interval, then the number of times of occurrences represents frequency. The frequency distribution formula is given as:

Frequency distribution refers to a table that shows each item and its frequency.

**Solved Examples on Frequency Distribution Formula**

**Example 1: **Alison noted her results after her 12 throws of a fair dice as follows: 4, 6, 1, 2, 2, 5, 6, 6, 5, 4, 2, 3. Create the frequency distribution of the given data using the frequency distribution formula.

Solution:

To find: Frequency distribution.

Using the frequency distribution formula,

Outcomes |
Frequency |

1 | 1 |

2 | 3 |

3 | 1 |

4 | 2 |

5 | 2 |

6 | 3 |

Total | 12 |

**Example 2: **Favourite subject of 20 students is given below. Find the frequency distribution of the subjects given below.

Mathematics | English | Science |

Science | Mathematics | Science |

English | Art | Mathematics |

Mathematics | Science | Art |

Art | Science | Mathematics |

Art | Mathematics | English |

English | Mathematics |

Solution:

To find: Frequency distribution

Subject |
Frequency |

English | 4 |

Art | 4 |

Science | 5 |

Mathematics | 7 |

Total | 20 |

**Frequently Asked Questions on Frequency Distribution Formula**

1: What is a Frequency Distribution in Math?

Answer: In statistics, the frequency distribution is a graph or data set organized to represent the frequency of occurrence of each possible outcome of an event that is observed a specific number of times. Frequency distribution is a tabular or graphical representation of the data that shows the frequency of all the observations.

2: What are the 2 Types of Frequency Distribution Table?

Answer: The 2 types of frequency distributions are:

- Ungrouped frequency distribution
- Grouped frequency distribution

3: Why are Frequency Distributions Important?

Answer: Frequency charts are the best way to organize data. Doctors use it to understand the frequency of diseases. Sports analysts use it to understand the performance of a sportsperson. Wherever you have a large amount of data, frequency distribution makes it easy to analyze the data.

4: How do you find Frequency Distribution?

Answer: Follow the steps to find frequency distribution:

- Step 1: To make a frequency chart, first, write the categories in the first column.
- Step 2: In the next step, tally the score in the second column.
- Step 3: And finally, count the tally to write the frequency of each category in the third column.

Thus, in this way, we can find the frequency distribution of an event.

5: What is the Difference Between Frequency Table and Frequency Distribution?

Answer: The frequency table is a tabular method where the frequency is assigned to its respective category. Whereas, a frequency distribution is known as the graphical representation of the frequency table.

6: What is Grouped Frequency Distribution?

Answer: A grouped frequency distribution shows the scores by grouping the observations into intervals and then lists these intervals in the frequency distribution table. The intervals in grouped frequency distribution are called class limits.

7: What is Ungrouped Frequency Distribution?

Answer: The ungrouped frequency distribution is a type of frequency distribution that displays the frequency of each individual data value instead of groups of data values. In this type of frequency distribution, we can directly see how often different values occurred in the table.

8: What are the Components of Frequency Distribution?

Answer: The components of the frequency distribution are as follows:

- Class interval
- Types of class interval
- Class boundaries

- Midpoint or classmark
- Width or size of class interval
- Class frequency
- Frequency class width