Histogram

A histogram is a graphic representation of data in a grouped frequency distribution with continuous classes. They resemble bar graphs, but there are no gaps between the consecutive rectangles. Histograms are widely used for ranging data into groups. It is a highly practical graph due to its clarity and simplicity.

The use of graphs and charts facilitates the analysis of data. Data represented visually is easier to understand and is thus clearer to the human mind. A histogram is an extremely helpful type of graph due to its simplicity and clarity of comprehension. It is the most commonly used graph type for any frequency distribution.

A histogram in statistics is a graphical depiction of data distribution. It is a collection of rectangles next to one another, where each bar represents a different type of data. In this context, frequency refers to the number of times a number appears in statistical data. It is known as a frequency distribution when shown in a table. Therefore, a histogram is one of the different graphs that can represent a frequency distribution visually. The ability to quickly display vast data sets is one advantage of it. Therefore, when a data set has 100 or more values, it is better to use a histogram.

In the graph, the X-axis displays the data's possible results in a range, while the Y-axis displays the number of data points in each range. One can check the number of data points in each data range as a result of data grouping. The pictorial representation, therefore, is simpler to comprehend and evaluate. The visual representation of it is similar to that of a bar graph. However, both are different in many aspects.

Let us check out the main differences between a histogram vs. a bar graph. Even though they are similar and identical, there are key differences. First, histograms display variable distributions, while bar charts compare different variables. Bar charts plot categorical data while histograms plot quantitative data in separate bins or buckets. These bins refer to the slots of data that are segregated. In bar charts, one can rearrange bars while histograms they cannot. However, there are certain exemptions for the same. In addition, a histogram's bars are all the same length as there are no gaps between the bins. Another typical difference is that histograms display rectangles without touching each other. On the other hand, bar graphs display rectangles separate from each of them with equal spaces between them.

Below are the common types of histogram models:

#1 Symmetric- Uni model:

A Symmetric or uni model graph represents s normal distribution. The shape formed here will be a bell shape. The graph is symmetrical with a vertical line in the middle, and both sides are the same size and shape.

#2 The Bi model:

The Bi model has two peaks when a data collection contains observations on two distinct types or merged groups. Therefore, the data here need separate analysis as normal distributions.

#3 Skewed Left model:

The distribution here is skewed to the left. Therefore, it is also referred to as a negatively skewed histogram graph.

#4 Skewed right model:

The distribution here is skewed to the right. It is also referred to as a positively skewed histogram graph.

#5 Random model:

In this model, there are no apparent patterns like that of uniform distribution. This model has several peaks. One can have mixed several data elements in a random distribution. Consequently, the data should be divided and examined individually.

Creating a graphical representation can sometimes be confusing, but it is doable. Plotting a histogram in excel is one way to do it, but given below are a few instructions that can help create one.

• One should mark the class intervals(groups) on the X-axis and the frequencies on the Y-axis for the histogram graph first.
• They should draw both the axes with the same scales.
• Class intervals must be exclusive while entering the data.
• The rectangles shall be created using the class intervals as the bases (width) and the appropriate frequencies as the heights (length).
• A rectangle is constructed on each class interval. The frequency listings are on the vertical axis, and the class limitations are on the horizontal axis of the graph.
• If the intervals are equal or identical, each rectangle's height will be proportional to its associated class frequency.
• Whenever the intervals are not equal, the area of each rectangle will be proportional to the respective class frequency.

For example,

The following table gives the study hours of 400 students.

Study hours: 100-200,200-300,300-400,400-500,500-600,600-700,700-800

The number of students: 15,55,60,85,75,62,48

Here Y-axis marks the number of students. The class intervals are on the X-axis. In both cases, there is uniformity existing between the values. The class intervals of all students have a range of 100 as per the above instructions. Alternatively, a histogram in excel can be created with ease.

The asymmetry of the skewed distribution results from a natural limit that forbids results on one side. The peak point of the distribution is off-centered and extends toward the limit, and a tail extends away from it.

A right-skewed distribution is also referred to as a positively skewed distribution. A right-skewed distribution has a greater concentration of data values on the left side and a smaller concentration on the right side. Typically, the distribution is right-skewed when data has a range limit on the left side of the graph. When the data is skewed to the right, the mean value will be higher than the data set's median.

The negatively skewed distribution is another name for a distribution that is left-skewed. When a distribution is left-skewed, a greater proportion of data values are found on the right side and a smaller proportion on the left. Therefore, when the data has a range limit on the right side of the histogram, the distribution is typically said to be left-skewed. The median of the data set will be greater than the mean value in a left-skewed graph.

The histogram is the most commonly used graphical form for any frequency distribution. Diagrammatic representation has its perks. Data as histogram examples can be visually represented in a variety of fields, such as:

• It can be used to identify the most efficient pricing plans in the context of sales and marketing. The most practical pricing plans are then used to streamline the marketing campaigns.
• In the operations field, these graphs are used in Six Sigma. Six Sigma is a technique used in operations research to identify process variations. The frequency of delays in each step can help determine the issues with a certain process. The project managers use error data on graphs to identify issues and develop solutions.
• They can be used in the restaurant business to determine when peak customer traffic occurs. The restaurant can then manage the workforce based on peak customer demand. Alternatively, during the lean season, they can maintain a lower staff.
• In hospitals, Staff members can track patient entries to determine the peak resource demand. The process can be better managed as a result of this.
• It can be used to identify the trading potential at different places or groups of investors.
• In medical research, it can provide information on identifying whether or not the patient suffers from others