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The literal meaning of the word frequency is the rate at which something occurs over a specified period. The frequency of an observation signifies that the observation occurs in the data happens a certain number of times. Take a look at the following data set –

a, b, d, f, e, b, b, c, g, d, c, c, b, b, a, d, b

In the series mentioned above, the frequency of the letter b is 6.

Now that you know how the frequency of observations is measured, let's discuss what frequency distribution is.

Frequency distribution is the representation of data (either in graphical or tabular format) to show the number of observations with a given interval. The length (or size) of the interval depends on the data that is being analyzed or the objectives of the analyst.

A frequency distribution is used as a statistical tool to provide a visual representation for the distribution of observations made within a particular examination. Analysts use this process to visualize or illustrate the data collected in a sample.

For example, if you measure the weight of 50 people in an office, some may be underweight, some may be overweight. But there's a high probability of higher frequency in the normal weight range.

The essential factors for gathering data are that the intervals used must not overlap and it must also include all the possible observations. Frequency distributions can be presented in the form of a table, a histogram or a bar chart.

Preparing the frequency distribution table is not as difficult as you may think it is. You just need to learn the major steps to create one. Let's use the example of the data set we used earlier.

a, b, d, f, e, b, b, c, g, d, c, c, b, b, a, d, b

Here's what you need to do to create a frequency distribution table with this data set:

**Step 1: Write the categories:**

For the first column in the table, you need to mention the categories. In the given data set, you should be categorizing the data as per their values. So, the categories will be in ascending order.

**Step 2: Tally the entries:**

In the second column of the table, you need to tally the number of entries in each category. As you may have noticed in the given data set, the letter be is mentioned 6 times. So, in tally, it will be ~~IIII~~ I.

**Step3: Mention the frequency:**

In the third column, write the frequency of the category in the given dataset. As mentioned, the frequency of the entry "b" is 6. You need to write the frequency of each category.

Here’s how the table is going to look:

Category | Tally | Frequency |

a | II | 2 |

b | IIII I | 6 |

c | III | 3 |

d | III | 3 |

e | I | 1 |

f | I | 1 |

g | I | 1 |

Even though the tally has been used with the tables conventionally, it is no longer mandatory to use it in every frequency distribution table.

Frequency distribution can be presented in a number of ways, depending on the usage and application of the data. Furthermore, the frequency distribution is also classified into several types based on the nature of raw data.

In this blog, we will discuss 5 major types of frequency distributions that you may need in the study of statistics.

**Grouped frequency distribution:**

To make correct and relevant observations from data sets, you may need to group data into class intervals. With this approach, you can ensure that the frequency distribution represents your data properly. Let’s show you an example:

Class Interval | Frequency |

50-65 Kg | 3 |

65-80 Kg | 7 |

80-95 Kg | 5 |

If there’s any data entry of 65Kg, it should be placed in the class interval of 65-80Kg and not 50-65Kg. This is the convention you need to follow.

**2. Ungrouped frequency distribution:**

Ungrouped data is referred to as the data that you first gather from a text or study. It is basically raw data that is not sorted into categories, grouped or classified. The ungrouped data is just a list of numbers. To create an ungrouped frequency distribution table, you need to find out several things, including:

- The values of the data you are dealing with, in an ascending or descending order
- The frequency of each data occurrence

- Relative frequency of each data, which is the ratio of the frequency of the particular data to the total number of data in the set

- The percentage of the relative frequency
- Cumulative frequency of each data
- Cumulative proportion, which is the ratio of the cumulative frequency of the data to the total number

- Cumulative percent, which is the cumulative proportion presented as percentages

Let’s say that we have an ungrouped data set like the following one:

3, 0, 1, 5, 4, 3, 3, 6, 6, 5, 4, 4, 5, 8, 9, 0, 3, 7

Now, if you want to create an ungrouped data frequency table on this data set, it would look like this:

X | f | f_{r} | % | Cf | Cp | C% |

0 | 2 | 0,11 | 11 | 2 | 0,11 | 11 |

1 | 1 | 0,06 | 6 | 3 | 0,17 | 17 |

2 | 0 | 0 | 0 | 3 | 0,17 | 17 |

3 | 4 | 0,22 | 22 | 7 | 0,39 | 39 |

4 | 3 | 0,17 | 17 | 10 | 0,56 | 56 |

5 | 3 | 0,16 | 16 | 13 | 0,72 | 72 |

6 | 2 | 0,11 | 11 | 15 | 0,83 | 83 |

7 | 1 | 0,05 | 5 | 16 | 0,88 | 88 |

8 | 1 | 0,06 | 6 | 17 | 0,94 | 94 |

9 | 1 | 0,06 | 6 | 18 | 1 | 100 |

N=18 | Σ=1 | Σ%=100 |

Cumulative frequency distribution showcases the sum of all the previous or succeeding frequencies up to a certain class. A proper example can help you understand it better.

Let's say that there are people with weights ranging from 55kg to 96 kg. The cumulative frequency of the data (individual weight) can be represented as the following:

Weights (kg) | Cumulative Frequency |

Less than 60 | 3 |

Less than 70 | 3+5 =8 |

Less than 80 | 8+3 =11 |

Less than 90 | 11+2 =13 |

Less than 100 | 13+1 =14 |

**4. Relative frequency distribution:**

The frequency of a data set divided by the total frequency is called the relative frequency of the particular data set. Relative frequencies are typically represented as a percentage. The total of the relative frequencies of all values in the data set is 1 or 100%.

Weights (kg) | Relative Frequency |

50-59 | 3/14 = 0.2143 or 21.43% |

60-69 | 5/14 = 0.3571 or 35.71% |

70-79 | 3/14 = 02143 or 21.43% |

80-89 | 2/14 = 0.1428 or 14.28% |

90-99 | 1/14 = 0.0715 or 7.15% |

Here's an example for you.

**5. Relative cumulative frequency distribution:**

The cumulative frequency of a data set divided by the total frequency is referred to as relative cumulative frequency. It is also termed as percentage cumulative frequency since the representation is made in percentage. Let's see an example of a relative cumulative frequency distribution table.

Weights (kg) | Cumulative Frequency |

Less than 60 | 3/14 = 0.2143 or 21.43% |

Less than 70 | 8/14 = 0.5714 or 57.14% |

Less than 80 | 11/14 = 0.7857 or 78.57% |

Less than 90 | 13/14 = 0.9286 or 92.86% |

Less than 100 | 14/14 = 1 or 100% |

There are several other types of frequency distribution besides the ones mentioned above. However, these types are the most common ones that you will need to conduct statistical work.

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