Histogram

 

What is Histogram?

The distribution of numerical data is represented graphically by a histogram. It arranges data into bins, also known as intervals, and shows the frequency of data points in each interval using adjacent bars. This definition of a histogram emphasises its main function, which is to condense big datasets into an understandable visual format.

Continuous data is displayed in a histogram graph, where each bar denotes a range of values as opposed to a single category. The histogram highlights the distribution and form of data, as opposed to a bar chart that contrasts distinct categories.

Table of Contents

• Definition of Histogram
• How to Make Histogram
• When to Use Histogram
• Difference Between Histogram and Bar Graph
• Types of Histogram
• Histogram Applications
• Solved Examples of Histogram
• Conclusion
• Frequently Asked Questions on Histogram

 

Definition

A histogram is a plot that uses bars to show how often different values occur in a set of continuous data. It turns raw data into an easy-to-read histogram graph. To really understand what a histogram is, you need to grasp the idea of grouping data into bins and how it shows frequency visually.

 

How to Make Histogram

Use these steps to create a histogram:

• Gather and prepare the data 
  Compile numerical observations, either continuous or discrete.  

• Define the range and the number of bins. 
  Depending on the data spread, choose variable-width or uniform bin widths.  

• Count frequencies 
  Tally the number of observations that fit into each bin.  

• Draw bars 
  Mark bins on the horizontal axis of the histogram graph. 
  Plot frequency counts on the vertical axis.  

• Title and label axes 
  Give your chart a title, clearly label the axes with the appropriate units, and, if you want, annotate the bars with frequencies.  

Understanding what a histogram is and how to define it leads to a clear process that produces an easy-to-understand histogram graph.

 

When to Use Histogram

A histogram can be used for these purposes:  

• Visualizing the distribution of numerical data  

• Recognizing shape, spread, and central tendency  

• Identifying outliers, skewness, or multiple modes  

• Comparing the underlying distributions in different datasets  

• Modeling continuous probability distributions  

Large datasets benefit significantly from a histogram graph. It offers insight that raw data alone cannot provide.

 

Difference Between Histogram and Bar Graph

It is important to understand the difference between a bar diagram and a histogram. A histogram shows a continuous data distribution using adjacent bars with no gaps. In contrast, bar graphs use separate bars to represent different categories. 

A bar chart displays distinct categories, while a histogram shows bin ranges on the x-axis. The heights of a histogram represent frequency density, not just counts. Histogram bins have a logical numerical order, but the bars in a bar graph can be arranged in any way. 

Therefore, the main differences between a bar diagram and a histogram lie in continuity and data type: bar diagrams are for categorical comparisons, and histograms are for continuous distributions.

 

Types of Histogram

Histograms come in different forms that help us understand how data is spread out. Each type of histogram shows unique features of the dataset, such as symmetry, skewness, or the number of peaks. Let’s take a closer look at these types:

 

Uniform Histogram  

In a uniform histogram, the bars are about the same height in each bin. This means the frequency of occurrence for each range of values is almost equal. There is no obvious peak in the data; it is evenly spread out.  

Example: If we recorded the results of a completely random process, like rolling a die thousands of times, the resulting histogram would look uniform, with each number from 1 to 6 appearing with the same frequency.  

Use Case: In a dataset, uniform histograms can represent either random or consistent behavior.

 

Bimodal Histogram

Two separate peaks, or modes, create a bimodal histogram. This suggests that two distinct groups or processes might be the source of the data. 

Example: If we measure the heights of adult men and women together, the histogram may show two peaks: one for men and one around the average height for women. 

Use Case: Bimodal histograms can help identify data that combines two different populations or behaviors.

 

Symmetric Histogram

In a symmetric histogram, the left and right sides of the graph look like mirror images. This type of histogram usually shows that the data follows a normal distribution, which has a bell-shaped curve. In this case, values are spread out evenly around the mean. 

Example: Test scores for a large class where most students scored near the average, while fewer scored much higher or lower. 

Use Case: Symmetric histograms help us understand balanced data and work well for calculating measures like mean and standard deviation.

 

Skewed Right (Positively Skewed) Histogram

A right-skewed histogram has a longer tail on the right side. Most of the data values focus on the lower end of the scale, with only a few higher values extending toward the right.  

Example: Income levels in a country, most people earn lower or middle incomes, while only a few earn very high incomes.  

Use Case: Right-skewed histograms help identify outliers or high-value exceptions in data.  

 

Skewed Left (Negatively Skewed) Histogram

A left-skewed histogram has a longer tail on the left side. Here, most data points are located at the higher end, while fewer values lie on the lower end.

Example: Age at retirement-most people retire at an older age (around 60), but a few may retire much earlier due to early pensions or other reasons.

Use Case: Useful in analyzing data with a few significantly lower values.

 

Probability Histogram  

A probability histogram is a type of histogram where the vertical axis shows probability instead of frequency. The total area under the bars equals 1 (or 100%). This feature makes it helpful for understanding probability distributions.  

Example: Theoretical outcomes of a dice roll or a probability distribution of exam grades.  

Use Case: Probability histograms are often used in statistics and probability theory to show random variables and their distributions.

These types of histogram are vital for interpreting data distributions and tailoring analysis appropriately.

 

Histogram Applications

Applications for histograms appear in many fields. 

• They summarize large datasets visually using descriptive statistics. 

• In Six Sigma and quality control, they help track process variance. 

• In signal processing, they examine intensity distributions. 

• In finance, they visualize risk profiles and return distributions. 

• In medical research, they measure factors like blood pressure. 

• In machine learning, they help understand feature distributions. 

• In education, they show grade distributions in the classroom. 

These examples demonstrate how a histogram can turn unstructured data into valuable information.

 

Solved Examples of Histogram 

These solved examples of histogram will help you understand what is histogram, how to construct one, and how to interpret a histogram graph.

Example 1: Students' Test Scores

Problem: The math test scores of 20 students are:
45, 48, 50, 53, 56, 59, 60, 61, 63, 65, 66, 69, 70, 72, 74, 75, 77, 80, 83, 85

Step 1: Understand what is histogram
A histogram graph displays the frequency of grouped continuous data using bars.

Step 2: Organize the data
Data is already arranged in increasing order.

Step 3: Define class intervals (bins)
Choose class intervals of width 10:
40-49
50-59
60-69
70-79
80-89

Step 4: Tally frequencies

 

Step 5: Draw the histogram graph
X-axis: Class intervals (bins)
Y-axis: Frequencies
Each bar touches the next (no gaps, unlike a bar graph)

The scores are evenly distributed between 60 and 79, showing a slight concentration in the middle ranges.

 

Example 2: Daily Rainfall in mm (7 days)

Problem: Rainfall data in mm:
2, 5, 3, 7, 12, 9, 11

Step 1: Define class intervals (bins)
0-4 mm
5-9 mm
10-14 mm

Step 2: Count frequencies

 

Step 3: Draw the histogram graph
X-axis: Rainfall range
Y-axis: Frequency
Bars touch each other to represent continuous data

The most common rainfall range was 0-4 mm. This histogram helps to visualize the frequency of rainfall patterns.

 

Example 3: Heights of Students (in cm)

Data:
140, 145, 148, 150, 152, 153, 155, 158, 160, 162, 165, 167, 168, 170, 172

Step 1: Create class intervals
140-144
145-149
150-154
155-159
160-164
165-169
170-174

Step 2: Frequency tally

 

Step 3: Draw histogram
X-axis: Height intervals
Y-axis: Frequency
Bars should be adjacent to show continuity

Interpretation: The distribution is fairly symmetric, peaking around the 150-154 and 165-169 ranges. This is a great example of histogram for school-level analysis.

 

Example 4: Electricity Bills (in ₹)

Data (in ₹):
230, 250, 275, 280, 290, 310, 320, 330, 350, 375

Step 1: Define class intervals
200-249
250-299
300-349
350-399

Step 2: Frequency count

 

Step 3: Plot histogram graph
X-axis: Bill amount (₹)
Y-axis: Number of houses
Draw bars without gaps between them

The most frequent bill range was ₹250-299. This histogram graph quickly highlights the range most households fall into.

 

Conclusion  

A histogram is a useful statistical tool that helps us understand how numerical data is distributed. Unlike bar graphs, which compare categories, a histogram is meant to show how continuous data is spread over defined intervals. By grouping raw numbers into bins and displaying them visually, histograms help us identify patterns, spot outliers, and see the overall shape of the data, including symmetry and skewness.

There are different types of histograms, such as uniform, bimodal, and probability histograms. Their applications are seen in various fields like education, business, and science. By following steps to create and interpret a histogram, you can turn large, complex data sets into clear, actionable insights. 

Whether you are a student learning the basics or a professional examining trends, knowing what a histogram is, when to use it, and how it differs from a bar graph is crucial in data analysis.

Frequently Asked Questions on Histogram

1. What defines a histogram?

The main difference between a histogram and a bar graph is in the type of data and how they are presented:  

A histogram displays continuous numerical data, with touching bars that represent intervals or bins.  

A bar graph shows categorical data, with separate bars for different categories or groups.  

In short, histograms are used to show data distribution, while bar graphs compare distinct categories.

 

2. What is a histogram vs bar graph?

The main difference between a histogram and a bar graph is in the type of data and how they are presented:  

A histogram displays continuous numerical data, with touching bars that represent intervals or bins.  

A bar graph shows categorical data, with separated bars for different categories or groups.

In short, histograms are used to show data distribution, while bar graphs compare distinct categories.

 

3. What is a histogram and an example?

A histogram is a graphical representation of grouped numerical data using bars to show the frequency of values within specific ranges or bins.  

Example:  

If 10 students scored between 70 and 80 marks, and 5 students scored between 80 and 90 marks, a histogram would show two bars: one for 70-80 with a height of 10 and one for 80-90 with a height of 5. This visual helps illustrate what a histogram is in a practical context.

This visual helps understand what is histogram in a practical context.

 

4. Which graph is a histogram?

A histogram graph is one where: 
The X-axis contains numerical intervals or bins. 
The Y-axis represents the frequency of observations within those intervals. 
The bars touch each other, indicating continuity in the data.  

Any graph that displays data this way, with touching bars over numerical ranges, is identified as a histogram.

 

5. How to calculate a histogram?

To calculate a histogram, follow these steps:  

1. Collect the data, which consists of continuous numerical values.  

2. Decide the number of bins or intervals.  

3. Determine the range of data by subtracting the minimum value from the maximum value.  

4. Calculate the bin width by dividing the range by the number of bins.  

5. Tally the frequencies for each bin by counting how many values fall into each range.  

6. Draw the histogram graph with bins on the X-axis and frequencies on the Y-axis.  

This is how you calculate and visually create a histogram.

 

Master data visualization with histograms and strengthen your maths concepts with Orchids The International School!