Bar_Graphs_Histograms_PieCharts_Box&WhiskerPlots

Bar Graphs, Histograms, Pie Charts and Box Plots

1. DMA_2_Bar Graphs, Histograms, Pie-Charts, Box and Whisker Plots By Prof. Mangal S. Dandekar

2. What are bar graphs? Bar graphs are charts or graphical representations of certain data, quantities, or numbers. It consists of rectangular bars with variable heights. The height of each bar represents the value of the quantity it represents. Bar graphs are ideal for comparing numbers and data. Bar graphs have vertical and horizontal axes known as the x and y-axis, respectively.

3. Difference between Tally Charts and Bar Graphs

4. Some Other Types of Bar Graph Stacked Bar Graph The stacked bar graph is also referred to as the composite bar graph . It divides the whole bar into different parts. In this, each part of a bar is represented using different colours to easily identify the different categories. It requires specific labelling to indicate the different parts of the bar. Thus, in a stacked bar graph every rectangular bar represents the whole, and each segment in the rectangular bar shows the different parts of the whole. It can be shown vertically or horizontally. Grouped Bar Graph The grouped bar graph is also referred the clustered bar graph . It is used to show the discrete value for two or more categorical data. In this, rectangular bars are grouped by position for levels of one categorical variable, with the same colours showing the secondary category level within each group. It can be shown both vertically and horizontally.

5. What is Histogram? A histogram is a graphical representation of a grouped frequency distribution with continuous classes. It is an area diagram and 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 other words, a histogram is a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval. When to Use Histogram? The histogram graph is used under certain conditions. They are: The data should be numerical. A histogram is used to check the shape of the data distribution. Used to check whether the process changes from one period to another. Used to determine whether the output is different when it involves two or more processes. Used to analyse whether the given process meets the customer requirements.

6. How to Plot Histogram? You need to follow the below steps to construct a histogram. Begin by marking the class intervals on the X-axis and frequencies on the Y-axis. The scales for both the axes have to be the same. Class intervals need to be exclusive. Draw rectangles with bases as class intervals and corresponding frequencies as heights. A rectangle is built on each class interval since the class limits are marked on the horizontal axis, and the frequencies are indicated on the vertical axis. The height of each rectangle is proportional to the corresponding class frequency if the intervals are equal. The area of every individual rectangle is proportional to the corresponding class frequency if the intervals are unequal.

7. Difference between Histogram and Bar Graph

8. Types of Histogram The histogram can be classified into different types based on the frequency distribution of the data. There are different types of distributions, such as normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distribution, heart cut distribution, and so on. The histogram can be used to represent these different types of distributions. The different types of a histogram are: Uniform histogram Symmetric histogram Bimodal histogram

9. 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.

10. Bimodal Histogram If a histogram has two peaks, it is said to be bimodal. Bimodality occurs when the data set has observations on two different kinds of individuals or combined groups if the centers of the two separate histograms are far enough to the variability in both the data sets.

11. Symmetric Histogram A symmetric histogram is also called a bell-shaped histogram. When you draw the vertical line down the center of the histogram, and the two sides are identical in size and shape, the histogram is said to be symmetric. The diagram is perfectly symmetric if the right half portion of the image is similar to the left half. The histograms that are not symmetric are known as skewed.

12. Histogram Solved Example Question: The following table gives the lifetime of 400 neon lamps. Draw the histogram for the below data.

13. What is a Pie Chart? The “ pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc. Formula The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°. The total value of the pie is always 100%.

14. What is a Pie Chart? To work out with the percentage for a pie chart, follow the steps given below: Categorize the data Calculate the total Divide the categories Convert into percentages Finally, calculate the degrees Therefore, the pie chart formula is given as (Given Data/Total value of Data) × 360° Note: It is not mandatory to convert the given data into percentages until it is specified. We can directly calculate the degrees for given data values and draw the pie chart accordingly.

15. Box and whisker plot The method to summarize a set of data that is measured using an interval scale is called a box and whisker plot. These are maximum used for data analysis. We use these types of graphs or graphical representation to know: Distribution Shape Central Value of it Variability of it A box plot is a chart that shows data from a five-number summary including one of the measures of central tendency . It does not show the distribution in particular as much as a stem and leaf plot or histogram does. But it is primarily used to indicate a distribution is skewed or not and if there are potential unusual observations (also called outliers) present in the data set. Boxplots are also very beneficial when large numbers of data sets are involved or compared.

16. Parts of Box Plots

17. Parts of Box Plots Minimum : The minimum value in the given dataset First Quartile (Q1) : The first quartile is the median of the lower half of the data set. Median: The median is the middle value of the dataset, which divides the given dataset into two equal parts. The median is considered as the second quartile. Third Quartile (Q3): The third quartile is the median of the upper half of the data. Maximum: The maximum value in the given dataset. Apart from these five terms, the other terms used in the box plot are: Interquartile Range (IQR): The difference between the third quartile and first quartile is known as the interquartile range. (i.e.) IQR = Q3-Q1 Outlier: The data that falls on the far left or right side of the ordered data is tested to be the outliers. Generally, the outliers fall more than the specified distance from the first and third quartile. (i.e.) Outliers are greater than Q3+(1.5 . IQR) or less than Q1-(1.5 . IQR).

18. Boxplot Distribution The box plot distribution will explain how tightly the data is grouped, how the data is skewed, and also about the symmetry of data. Positively Skewed : If the distance from the median to the maximum is greater than the distance from the median to the minimum, then the box plot is positively skewed. Negatively Skewed : If the distance from the median to minimum is greater than the distance from the median to the maximum, then the box plot is negatively skewed. Symmetric : The box plot is said to be symmetric if the median is equidistant from the maximum and minimum values.

19. Box Plot Box Plot Chart In a box and whisker plot: the ends of the box are the upper and lower quartiles so that the box crosses the interquartile range a vertical line inside the box marks the median the two lines outside the box are the whiskers extending to the highest and lowest observations. Applications It is used to know: The outliers and their values Symmetry of Data Tight grouping of data Data skewness – if, in which direction and how