Histogram

A histogram is a type of tool for visually representing a given data set in statistics to understand the frequency distribution of the data. The histogram is a group of various lengths of rectangles each rectangle represents a certain data point. The word “histogram” is derived from the Greek word “histos”, which means “web” or “framework”, and “gramma” meaning “drawing” or “writing”. 

1.0Histogram Definition

A histogram shows the distribution of a dataset, it is used for displaying the continuous (or quantitative) form of data frequency distribution. On a histogram, data is shown in intervals, but the height in each bar relates to the frequencies or counts where data points were found in one specific interval. Let us understand this with an Example of Histogram: 

In a class, the marks scored by students in mathematics are as follows: 

The Histogram for the following data can be shown as follows: 

2.0Drawing a Histogram

Histograms are drawn with the help of the following steps:

1. Sort the data into particular data intervals.
2. Count the number of data points falling in each interval.
3. Calculate the Midpoint of the interval, also known as a class mark, by the formula:
4. Class Mark = Upper Limit+Lower Limit2
5. Plot a bar for every interval where the height of the bar equals the frequency of that particular interval.

• For drawing a histogram, take a graph paper draw and mark the x and y axis on it.  
• Give labelling to the x-axis with the intervals and the y-axis with the frequency. 

6. Ensure the bars are touching each other to represent continuous data.

3.0Bar Chart and Histogram

You may have noticed that bar charts and histograms look very similar to one another, but both are differentiated on various levels: 

4.0Types of Histogram

Histograms can vary based on the shape and distribution of the data set. The different types of histograms include: 

1. Uniform Distribution: In a histogram in which all the bars have almost the same height, indicating the points are distributed evenly across the distribution. 
2. Normal Distribution (Bell Curve): The bars in this distribution are distributed in symmetric and bell-shaped curves, indicating that most of the data points are concentrated around the central value.
3. Skewed Distribution: The bars on one side of the histogram are longer than the other in a skewed distribution, showing asymmetry across the data set. This is further divided into: 

• Positive Skew: The maximum of data points remains on the left side of the graph, hence, also known as Left Skewed Histogram. 
• Negative skew: The maximum of data points remains on the right side of the graph, also known as the Right skewed histogram. 

4. Bimodal Distribution: it is the visual representation of the type of data set which has two modes or the values that appear most of the time in the data set.

5.0Use of Histogram 

• Statistics: A histogram in statistics is used for the visualisation of a given data set, including the central tendency (mean, median, mode) of the data and outliers. It helps in understanding how a value is distributed across the data. 
• Quality Control: Histograms track production data, which ensures that products meet specifications. They highlight process variability, defects, and inefficiencies, thereby maintaining consistent product quality in manufacturing.
• Business: In business, histograms analyse sales, customer behaviour, and product performance, which offers insights for marketing strategies, inventory management, and identifying trends for better decision-making.
• Education: In education, histograms display test score distributions, identifying performance trends and areas which need improvement and evaluating teaching effectiveness for targeted interventions and better learning outcomes.

6.0Solved Examples

Example: A factory monitors the diameter of products in a batch. The following table shows the number of products falling within certain diameter ranges:

Draw a Histogram for the given data. 

Solution: