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# Frequency Histogram|Definition & Meaning

**Definition**

A **graphical representation** of a **numeric data set’s frequency distribution** is called a **frequency histogram**. There are **multiple observations** in **each category** or **range of values** shown in this type of bar graph. **Data** that are **continuous** can **be summarized** **with** a **histogram**. Thus, **learning about** the **same is essential** for the students since it **helps** them **understand** and **interpret** the **different kinds of data.**

**Illustration of Frequency Histogram Concept**

Figure 1 – Illustration of frequency histogram Concept

Frequency **histograms** are** graphs** **showing** the** frequency** of data.** Data sets** are **visualized** with a **bar graph** showing the **frequency** of a **particular value** occurring in them.

In order** to make a frequency histogram** for a **data set** that includes **1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4 numbers**, you would **first** need to **create bars** for **each unique value** in the data set. You would need to **create four bars** in this case **because** there are **four unique values (1, 2, 3, and 4)**.

In order **to calculate** the **frequency** of each **value**, which is the **number of times** it **appears** in the **dataset**, you must **first determine** its **occurrence frequency**. There is **one occurrence** of the **value 1**, **two occurrences** of the **value 2**, **three occurrences** of the **value 3**, and **four occurrences** of the **value 7**. The** frequencies** should be** plotted** **on** the **y-axis**, while the **unique values** should be **plotted** on the **x-axis**.

**Components of Frequency Histogram**

Figure 2 – Components of Frequency Histogram

A frequency histogram has **several components**, including the following:

**X-axis**

The **x-axis represents** the **values of the data set**. In the **example above**, the **x-axis contains** the values **1, 2, 3, and 4**.

**Y-axis**

The **y-axis** **represents** the **frequencies** **of** the **data set**. In the **example above,** the y-axis contains the **frequencies 1, 2, 3, and 4**.

**Bars**

The **bars** of the histogram **represent** the **frequencies** of the data set. In the** example above**, the **height of each bar** **represents** the **frequency** of **each value**.

**Labels**

The histogram should include **tags** for the **x-axis and y-axis**, as well as a **title** that **describes** the **data set**.

**Scale**

The histogram should have a **scale** that **shows** the **range of values on the x-axis and the y-axis**. This **allows** the **reader to quickly interpret** the **height of the bars** and the **values on the x-axis**.

**Steps to Create Frequency Histogram**

To create a frequency histogram, follow these steps:

**Identify**the**data set**that you want to create a histogram.**Determine**the**unique values**in the data set.**Count**the**number of times**each**unique value occurs**in the data set. This is**known**as the**frequency of each value**.**Create a bar**for**each unique value**in the data set.**Plot**the**frequencies on the y-axis**, with the**unique values on**the**x-axis.****Add labels**to the**x-axis, y-axis**, and**bars of the histogram**.**Add a title**to the histogram that describes the data set.**Add a scale**to the histogram that**shows the range**of values on the x-axis and the y-axis.**Review**the**histogram**to see**if**it**accurately represents the data set**and if it**reveals any patterns**or**trends**in the data.**Make**any**necessary adjustments**to the**histogram**to**improve its clarity and accuracy**.

**Frequency Histogram and Bar Graph: A Comparison**

Figure 3 – Frequency Histogram vs Bar Graph

A **bar graph** and a **frequency histogram** are **similar** in that they **both use bars** to **represent data**. However, they are **quite different** things. We highlight the **key differences** below.

**Frequency Histogram**

- A
**frequency histogram**is**used to show the frequency**of a data set.**For example**, a frequency histogram might be used to**show**the**number of times**each**temperature occurred**in a**data set**. - The
**bars**in a**frequency histogram**must**have the same width**. This is because the**width of the bars**in a**frequency histogram****represents**the**range of values**in the**data se**t, and**all values**in the**data set**must be**represented**with the**same width**.

**Bar Graph**

- One difference is that a
**bar graph****compares**the**values**of**different categories**. For example, a bar graph might be used to**compare**the**average temperatures**in**different cities.** - Another difference is that the
**bars in**a**bar graph**can**have different widths.**

**Types of Frequency Histograms**

There are several types of frequency histograms, including the following:

**Simple Frequency Histogram**

A simple frequency histogram is a** basic type of histogram** that** shows** the **frequency of a data set**. It is created **by plotting the frequencies** of the data set **on** the** y-axis**, with the **unique values on** the **x-axis**.

**Cumulative Frequency Histogram**

A **cumulative frequency histogram** is a type of histogram that **shows** the** total number of observations** **at or below each value** in the data set. It is created **by plotting** the **cumulative frequencies** of the data set on the **y-axis**, with the **unique values on** the** x-axis**.

**Relative Frequency Histogram**

A type of histogram that **shows** the **proportion of observations** falling into each** category **is called a **relative frequency histogram**. It is created **by plotting** the **relative frequencies** of the data set **on** the** y-axis**, with the **unique values on** the **x-axis**.

**Practical Example of a Frequency Histogram**

**Suppose** you have **a data set** that **contains** the **test scores** of a **group of students**. The data set looks like this **85, 95, 75, 80, 85, 90, 85, 75, 80, 90.** **Create** a **frequency histogram** for this dataset, additionally **comment** on the **visualization**.

**Solution**

Figure 4 – Practical Example of Frequency Histogram

**Step 1**

To create a simple frequency histogram for this data set, we **firs**t need to **determine the unique values** in the data set. **In this case**, the unique values are **75, 80, 85, 90, and 95**.

**Step 2**

Then, we have to **determine the frequency of each value**, which is the **number of times** it **occurs** **in** the **data se**t. In this case, the value 7**5 occurs twice**, the value** 80 occurs twice**, the **value 85 occurs three times**, the value **90 occurs twice**, and the value **95 occurs once**.

**Step 3**

Finally, **plot these frequencies** on the y-axis of the histogram, with the unique values on the x-axis. The r**esulting histogram** would look as **shown above**.

**Conclusion**

**Histograms display** the **frequencies of values** in the data set **as** the **height of each bar**. The **height of the first bar**, for example, **represents** the **frequency of** the value **75**, **which is 2**. The** height of the second bar** represents the** frequency** of the value **80**, which **is 2**. And so on.

From this histogram, **we can see** that the **most common test score** in the **data set is 85**, which **occurred three times**. We can also see that the **value 75** and the **value 80** each **occurred twice**, while the **values 90** and **95** each **occurred once**. **Identifying patterns or trends** in the data set **can be achieved by** using **this information** to clarify the distribution of test scores.

*All mathematical drawings and images were created with GeoGebra.*