# Difference Between Bar Diagram And Histogram Pdf

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- 8 key differences between Bar graph and Histogram chart
- Bar Chart vs Histogram
- Histogram vs Bar Graph: Must Know Differences
- 8 Difference Between Bar Graph And Histogram

There are two differences, one is in the type of data that is presented and the other in the way they are drawn. In bar graphs are usually used to display "categorical data", that is data that fits into categories. For example suppose that I offered to buy donuts for six people and three said they wanted chocolate covered, 2 said plain and one said with icing sugar. I would present this in a bar garph as:. Histograms on the other hand are usually used to present "continuous data", that is data that represents measured quantity where, at least in theory, the numbers can take on any value in a certain range.

## 8 key differences between Bar graph and Histogram chart

A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson. The bins are usually specified as consecutive, non-overlapping intervals of a variable.

The bins intervals must be adjacent and are often but not required to be of equal size. If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency —the number of cases in each bin.

A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categories , with the sum of the heights equaling 1. However, bins need not be of equal width; in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin.

Examples of variable bin width are displayed on Census bureau data below. As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous. Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation : estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1.

If the length of the intervals on the x -axis are all 1, then a histogram is identical to a relative frequency plot. A histogram can be thought of as a simplistic kernel density estimation , which uses a kernel to smooth frequencies over the bins.

This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes.

Histograms are nevertheless preferred in applications, when their statistical properties need to be modeled. The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently.

An alternative to kernel density estimation is the average shifted histogram, [5] which is fast to compute and gives a smooth curve estimate of the density without using kernels.

The histogram is one of the seven basic tools of quality control. Histograms are sometimes confused with bar charts. A histogram is used for continuous data , where the bins represent ranges of data, while a bar chart is a plot of categorical variables. Some authors recommend that bar charts have gaps between the rectangles to clarify the distinction. The words used to describe the patterns in a histogram are: "symmetric", "skewed left" or "right", "unimodal", "bimodal" or "multimodal".

It is a good idea to plot the data using several different bin widths to learn more about it. Here is an example on tips given in a restaurant. The U. Census Bureau found that there were million people who work outside of their homes. This is likely due to people rounding their reported journey time. This histogram shows the number of cases per unit interval as the height of each block, so that the area of each block is equal to the number of people in the survey who fall into its category.

The area under the curve represents the total number of cases million. This type of histogram shows absolute numbers, with Q in thousands.

This histogram differs from the first only in the vertical scale. The area of each block is the fraction of the total that each category represents, and the total area of all the bars is equal to 1 the fraction meaning "all". The curve displayed is a simple density estimate. This version shows proportions, and is also known as a unit area histogram. In other words, a histogram represents a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies: the height of each is the average frequency density for the interval.

The intervals are placed together in order to show that the data represented by the histogram, while exclusive, is also contiguous. Empty intervals are represented as empty and not skipped. In a more general mathematical sense, a histogram is a function m i that counts the number of observations that fall into each of the disjoint categories known as bins , whereas the graph of a histogram is merely one way to represent a histogram.

Thus, if we let n be the total number of observations and k be the total number of bins, the histogram m i meets the following conditions:. A cumulative histogram is a mapping that counts the cumulative number of observations in all of the bins up to the specified bin. That is, the cumulative histogram M i of a histogram m j is defined as:. There is no "best" number of bins, and different bin sizes can reveal different features of the data. Grouping data is at least as old as Graunt 's work in the 17th century, but no systematic guidelines were given [11] until Sturges ' work in Using wider bins where the density of the underlying data points is low reduces noise due to sampling randomness; using narrower bins where the density is high so the signal drowns the noise gives greater precision to the density estimation.

Thus varying the bin-width within a histogram can be beneficial. Nonetheless, equal-width bins are widely used. Some theoreticians have attempted to determine an optimal number of bins, but these methods generally make strong assumptions about the shape of the distribution.

Depending on the actual data distribution and the goals of the analysis, different bin widths may be appropriate, so experimentation is usually needed to determine an appropriate width.

There are, however, various useful guidelines and rules of thumb. The braces indicate the ceiling function. Sturges' formula [12] is derived from a binomial distribution and implicitly assumes an approximately normal distribution. It may also perform poorly if the data are not normally distributed.

The Rice Rule [15] is presented as a simple alternative to Sturges' rule. Doane's formula [16] is a modification of Sturges' formula which attempts to improve its performance with non-normal data. Scott's normal reference rule [17] is optimal for random samples of normally distributed data, in the sense that it minimizes the integrated mean squared error of the density estimate.

The Freedman—Diaconis rule is: [18] [11]. It replaces 3. This approach of minimizing integrated mean squared error from Scott's rule can be generalized beyond normal distributions, by using leave-one out cross validation: [19] [20].

The choice is based on minimization of an estimated L 2 risk function [21]. Rather than choosing evenly spaced bins, for some applications it is preferable to vary the bin width.

This avoids bins with low counts. A common case is to choose equiprobable bins , where the number of samples in each bin is expected to be approximately equal. When plotting the histogram, the frequency density is used for the dependent axis.

While all bins have approximately equal area, the heights of the histogram approximate the density distribution. For equiprobable bins, the following rule for the number of bins is suggested: [22].

This choice of bins is motivated by maximizing the power of a Pearson chi-squared test testing whether the bins do contain equal numbers of samples. This simple cubic root choice can also be applied to bins with non-constant width. From Wikipedia, the free encyclopedia. For the histogram used in digital image processing, see Image histogram and Color histogram.

Skewed right. Skewed left. Mathematics portal. Skew Variation in Homogeneous Material". Prentice Hall. Wadsworth, Cengage Learning. Scott December Wiley Interdisciplinary Reviews: Computational Statistics. Tague The Quality Toolbox. Milwaukee, Wisconsin : American Society Quality. Retrieved Retrieved 31 July Eileen Magnello December Descriptive Statistics: Histogram. New York: John Wiley.

Journal of the American Statistical Association. Venables and B. Project Leader: David M. All of Statistics. New York: Springer. Neural Computation. Retrieved 29 March Goodness-of-Fit Techniques. Seven basic tools of quality. Outline Index. Descriptive statistics. Mean arithmetic geometric harmonic Median Mode.

## Bar Chart vs Histogram

Histogram is a type of bar chart that is used to represent statistical information by way of bars to display the frequency distribution of continuous data. It indicates the number of observations that lie in-between the range of values, which is known as class or bin. A histogram chart helps you to display the distribution of numerical data by rendering vertical bars. You can compare non-discrete values with the help of a histogram chart. For example, the count of students who got English subject marks on an exam in various ranges that can be visualized using a histogram chart. What is Bar Chart? Bar Chart is used to compare the frequency, total count, sum, or an average of data in different categories by using horizontal or vertical bars.

Despite their similarities in displaying and comparing statistical data, a bar chart and a histogram are two different types of graphical presentations. This article shows the differences between the two. A bar chart , also known as a bar graph, is a presentation that breaks down categorical data by groups, which are represented by rectangular bars of different lengths. Most useful in displaying differences in value amongst a set of variables, a bar graph compares data by the use of either vertical or horizontal bars. A bar chart is made up of a horizontal and a vertical axis. While one axis displays specific categories, the other presents discrete values. The length of the bar is proportionate to the value it represents.

## Histogram vs Bar Graph: Must Know Differences

Like dotplots , bar charts and histograms are used to compare the sizes of different groups. If you view this web page on a different browser e. A bar chart is made up of columns plotted on a graph. Here is how to read a bar chart. Like a bar chart, a histogram is made up of columns plotted on a graph.

A bar chart is made up of bars plotted on a graph. It displays data values in thin, vertical rectangles. The height of each rectangular column is indicative of the value of its category. Bar charts can be used to show positive or negative values. The histogram is a chart representing a frequency distribution; heights of the bars represent observed frequencies.

A bar graph also referred to as Bar Chart or Bar Diagram is a pictorial representation of data that uses bars to compare different categories of data. It displays grouped data by way of parallel rectangular bars of equal length but varying width. The bars can be plotted vertically or horizontally.

### 8 Difference Between Bar Graph And Histogram

A histogram is an approximate representation of the distribution of numerical data. It was first introduced by Karl Pearson. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins intervals must be adjacent and are often but not required to be of equal size. If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency —the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categories , with the sum of the heights equaling 1.

Have you ever noticed that the histogram and bar chart look quite similar, and wondered why we need two different types of chart? Well, if you closely look at them, you can understand that there are many differences between a bar graph and a histogram chart. A bar chart , which is also widely known as a column chart, is used to compare the frequency, count, total, or average of data in different categories by using vertical or horizontal bars. Discrete categories comparison is graphically visualized using a bar chart. Bars require two values, x and y, to render. The x value might be string, numeric, date-time, log, etc. The y value should always be numeric.

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### 2 Comments

The fundamental difference between histogram and bar graph will help you to identify the two easily is that there are gaps between bars in a bar graph but in the histogram, the bars are adjacent to each other.