Bar Graphs and Histogram

A bar chart is basically made up of columns that are plotted on a graph. Here is how you can read a bar chart.

The columns that are positioned over a label are used to represent a categorical variable.

The height of the column in the bar graph indicates the size of the group defined by the label of the column.

The bar chart below shows the average household income for the four "New" states that are- New Jersey, New Hampshire, New York, and New Mexico. 

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The chart shows that per capita income is highest in New Jersey; lowest, in New Mexico.

NOTE: Bar graphs are usually used to display "categorical data", which is known as the data that fits into categories.

Bar Graph Definition

The pictorial representation of grouped data, in the form of horizontal or vertical rectangular bars, where the lengths of the bars are equal to the measure of data, are known as bar graphs or bar charts.

The bars that we draw are of uniform width and the variable quantity can be represented on one of the axes. Also, the measure of the variable can be depicted on the other axes. 

The lengths or heights of the bars generally denote the value of the variable and these graphs can also be used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.

Types of Bar Charts

The bar graphs can be vertical or horizontal. The primary feature of a bar graph is its height. If the length of the bar graph is more, then the values are greater than any given data.

Bar graphs normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labeled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.

The Types of Bar Charts are as follows

Horizontal Bar Chart

Horizontal bar graphs represent the data horizontally by using rectangular bars that show the measure of data. The data variables or categories are written and then the rectangular bars are horizontally drawn on the y-axis. The x-axis shows the values of different data variables in the form of bars equal in length to the values.

Vertical Bar Chart

Vertical bar graphs represent the data vertically in a graph by using rectangular bars that show the measure of data. The rectangular bars are drawn vertically on the x-axis, and the value of the height of the rectangular bars is shown on the y-axis. The values on the y-axis represent the quantity of the variables mentioned on the x-axis. 

Stacked Bar Chart

The stacked bar graph, also known as the composite bar graph, divides the whole bar into different parts, with specific labeling to indicate its different parts. Each part of a bar is represented using different colors so that the different categories can be easily identified. 

So in this kind of graph, every rectangular bar represents the whole, and each segment within the bar represents different parts of that whole. 

This kind of graph can be vertical or horizontal.

Grouped Bar Chart

The grouped bar graph also referred to as a clustered bar graph, is used to present the discrete value of two or more data categories. The rectangular bars are grouped by a position for the various levels of one category of a variable. The same colors are used to present the secondary category level in each of the groups. It can be vertical or horizontal.

Uses of Bar Graphs

1. Bar graphs can be used to match things between different groups or to trace changes over time. 

2. Bar graphs are most suitable when the changes are bigger in the case of time estimation.

What is a Histogram and Why Use a Histogram Instead of a Bar Graph?

Why use a histogram instead of a bar graph:- A histogram is made up of columns that can be plotted on a graph. There is no space between the adjacent columns. Here is how you can read a histogram.

The columns are positioned over a label that is used to represent a continuous, quantitative variable.

The column label can be a range of values or a single value.

The height of the column of the histogram indicates the size of the group which is defined by the column label.

The above three points show us “why use a histogram instead of a bar graph”.

What is Histogram?

A histogram is an area diagram. It can be defined as a set of rectangles with bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes. In such representations, all the rectangles are adjacent since the base covers the intervals between class boundaries. The heights of rectangles are proportional to corresponding frequencies of similar classes and for different classes, the heights will be proportional to corresponding frequency densities.

In other words, a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval.

The histogram is given below shows per capita income for mainly five age groups.

We can see from the chart that per capita income is the greatest in the 45 to 54 age group.

A Histogram is Used for Which Type of Data?

Histograms can be used to present "continuous data '', which is basically data that represents measured quantity where the numbers can take on any value in a certain range. A good example can be weight. 

Histogram Types

Let us discuss the different types of histograms here. The following are the different types:

Uniform Histogram

A uniform distribution reveals that the number of classes is too small, and each class has the same number of elements. It may involve distribution that has several peaks. A uniform-shaped histogram shows data that is consistent. 

The two main indications of a uniform distribution are: 

1. The data may not be split into separate intervals or classes. 

2. Its scale may need adjustment for it to offer meaningful observations.

Unimodal and Bimodal Histogram

A unimodal histogram has only one data peak or hump, while a bimodal histogram has two data peaks. These types of histograms are generally quite easy to read.

Symmetric Histogram

When you draw the vertical line down the center of a histogram, and the two sides are identical in size and shape, the histogram is said to be symmetric, also referred to as bell-shaped.

This histogram has a prominent mound in the center and very similar tapering to its left and right. This also means that the data is unimodal (a single-mode identified by the peak). In this case, the mean, median, and mode are all the same values. 

Probability Histogram

A Probability Histogram shows a pictorial representation of a discrete probability distribution.  It consists of a rectangle centered on every value of x, and the area of each rectangle is proportional to the probability of the corresponding value. 

Right-skewed and left-skewed histograms

A right-skewed histogram has a peak that is left of center and a gradual tapering to the right side of the graph. A left-skewed histogram has a peak to the right of the center, gradually tapering to the left side. 

Both these histograms have a unimodal data set.

The right-skewed one has the mode closer to the left of the graph and smaller than either the mean or the median. The mean of right-skewed data will be on the right side and will be a greater value than either the median or the mode. 

In the left-skewed histogram, the mean is closer to the left and is lesser in value than either median or mode. 

Key Difference Between Bar Graphs and Histogram 

(Bar graph vs histogram)

Bar graph vs histogram can be drawn clearly on the following grounds given below:

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Histogram basically refers to a graphical representation; that displays data by way of bars to show the frequency of numerical data. A bar graph is known to be a pictorial representation of data that uses bars to compare different categories of data.

A histogram represents the frequency distribution of continuous variables. Whereas a  bar graph is a diagrammatic comparison of discrete variables.

Histograms present numerical data but bar graphs show categorical data.

The histogram is drawn in a way such that there is no gap between the bars. There needs to be proper spacing between bars in a bar graph which indicates discontinuity.

The items of the histogram are numbers, which can be categorized together, to represent any range of data. In the bar graph, items are considered as individual entities.

In the case of a bar graph, it is quite common to rearrange the blocks, from highest to lowest. But with histogram, this cannot be done, as they are shown in the sequences of classes.

The width of rectangular blocks in a histogram may or may not be the same while the width of the bars in a  bar graph is always the same.

All the points above demonstrate the bar graph vs histogram in a clear manner.

Questions to be Solved

1) Consider the Histograms below.

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Which of the following statements is True?

I. Both data sets are symmetric.

II. Labels on the X-axis are quantitative.

(A) I only

(B) II only

(C) I and II

(D) Neither is true.

(E) There is insufficient information.

Solution

The correct answer is (C). Both the histograms that are given have mirror images around their center, and both are symmetric in nature. With bar charts, the labels on the X-axis are categorical in nature; with histograms, the labels are quantitative in nature. Both of the given charts are histograms. Therefore, the labels are quantitative.