1. M. MASTAK AL AMIN The summary Table A summary table indicates the frequency, amount or percentage of items in a set of categories so that you can see differences between the categories. A summary table lists the categories in one column and the frequency, amount or percentage in a different column. Table 1: Table of percentage distribution of banking preference of the customer of BANK XYZ Table 2: Frequency and Percentage Summary Table Pertaining to Risk Level for 868 Mutual Funds Banking PreferencePercentage (%) ATM16 Automated or live telephone2 Drive-through service at branch 17 In person at branch41 Internet24 Fund Risk Level Number of funds Percentage of funds (%) Low20223.37 Average31135.83 High35540.89 Total864100.00

2. Graphical presentation of statistical data: Graphical presentation gives a birds eye view of the entire data and therefore the information presented is easily understood. A graph or chart is used to present facts in visual form. The most common forms of graphs and diagrams are- bar diagram, column chart, pie chart, histogram, line diagram, scatter diagram, frequency polygon and percentage polygon. Bar diagram, column chart and pie chart are usually constructed for categorical data and the remaining graphs & diagrams are constructed for the data that measured in interval scale. M. MASTAK AL AMIN

3. Bar Chart: A bar chart is a form of presentation in which the frequencies are represented by rectangles seperated along the horizontal axis and drawn as bars of convenience widths. The widths of these bars have no significance but are taken to make the chart look attractive. Figure: Bar Chart for banking preference of the customer. M. MASTAK AL AMIN Banking PreferencePercentage (%) ATM16 Automated or live telephone2 Drive-through service at branch 17 In person at branch41 Internet24

4. M. MASTAK AL AMIN Pie Chart Pie chart is also known as pie diagram, is an effective way of presenting percentage parts when the whole quantity is taken as 100. This is a useful device device for presenting categorical data. It consists of a circle sub-divided into sectors, whose areas are proportional to the various parts into which the whole quantity is divided. Limitations: It is less effective than bar diagram for accurate reading and interpretation, particularly when series are divided into a large number of components or the differences among the components are very small. It is generally inadvisable to attempt to portray a series having more than five or six categories.

5. M. MASTAK AL AMIN Problem: Health care centre visit data of Dinajpur district of Bangladesh in 1996. ResponseFrequency Percent relative frequency Angles of the sector Frequent4932.7117.6 Occasional7147.3170.4 Rare2416.057.6 Never64.014.4 Total150100.0360

6. Histogram: The most common form of graphical presentation of a frequency distribution is the histogram. It is constructed by placing the class boundaries on the horizontal axis and the frequencies or percentages of each group of numerical data on the vertical axis. Each class is shown on the graph by drawing a rectangle whose base is the class boundary and height is the corresponding frequency or percentages of each group of numerical data. M. MASTAK AL AMIN

7. Example: Weekly expenditure in taka for 80 students of an elementary school of Dhaka. M. MASTAK AL AMIN Expenditure Class Frequency 4.5-9.58 9.5-14.529 14.5-19.527 19.5-24.512 24.5-29.54 Total80

8. Q. How does a histogram differ from a bar diagram?  A histogram is basically a set of adjacent rectangles whose areas represent the frequencies, while in a bar diagram the spacing of bars are quite arbitrary and the heights of the rectangles represent the frequencies.  A bar diagram is an one-dimensional figure while a histogram is a two dimensional figure.  Histogram is constructed for numerical data of continuous frequency distribution while the bar diagram is usually constructed for categorical data. M. MASTAK AL AMIN

9. Frequency polygon: A frequency polygon provides an alternative to a Histogram as a way of graphically presenting a distribution of a continuous variable. Here we use the mid-values instead of using rectangle on the horizontal axis and frequencies on the vertical axis and then plot points directly. Classes of Zero frequency are added at each end so that the frequency polygon touches the horizontal axis at both ends. M. MASTAK AL AMIN

10. The Percentage Polygon Constructing multiple histograms on the same graph to compare two or more data sets often gets confusing. Superimposing the vertical bars of one histogram on another histogram makes interpretation difficult. When there are two or more groups, one should use a percentage polygon. A percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoint at their respective class percentages. The following table and figure 1.5 illustrates the construction of the percentage polygon. Table: Frequency distribution of Marks obtained by students Mark Group Mid value Frequency of students Percentage of Students Section 2 Section 3 Section 5 Section 2 Section 3 Section 5 40-50452139.14.08.8 50-605568527.332.014.7 60-706586536.424.014.7 70-8075351113.620.032.4 80-90852369.112.017.6 90-100951244.58.011.8 Total222534100

11. Stem and leaf plot Stem and leaf plot is a graphical technique of representing quantitative data that can be used to examine the shape of a frequency distribution. Here ”stem” represent the tens (leading digits) and the ”leaf” represent the units (trailing digits). Compared to other techniques it is an easy and quick way of displaying data. Example: The following data represent the marks obtained by 20 students in a statistics test- 84173845475376547522 66655554513339195472 Use a stem and leaf plot to display the data. Solution: Here the highest score is 84 and lowest score is 17. The stem and leaf diagram is given below- StemLeaf 17 9 22 38 3 9 45 7 53 4 5 4 1 4 66 5 76 5 2 84 M. MASTAK AL AMIN

12. Cross Tabulations The study of patterns that may exist between two or more categorical variables is common in practice. Often by cross-tabulating the data, these patterns can be explained. One can present cross tabulations in tabular form (contingency tables) or graphical from (side by side charts). The Contingency table A contingency table presents the results of two categorical variables. The joint responses are classified so that the categories of one variable are located in the rows and the categories of the other variable are located in the columns. The values located at the intersections of the rows and columns are called cells. Depending on the type of contingency table constructed, the cells for each row-column combination contain the frequency, the percentage of the overall total, the percentage of the row total, or the percentage of the column total. Table 1.6: Frequency distribution of students by religion and sex Religion Sex Total MaleFemale Muslim252045 Hindu12 24 Christian8614 Buddha538 Others224 Total524395

13. M. MASTAK AL AMIN

14. Scatter diagram It is used to display two quantitative variables which are believed to be inter- related. For example height and weight, age and height, income and expenditure. M. MASTAK AL AMIN Height and weight of 10 students at their 20th birthday Height (in cm)Weight (in kg) 17680 17278 15560 16064 14548 15855 18088 16668 17572 14045