Basic understanding of Plots and diagrams used in data interpretation
- 1. Plots And Diagrams Presented by: Megha Bhilawade Jinto Johnson John Suraj Subedi
- 2. Contents • Introduction • Graph • Pie Chart • Bar graph • Dot Plot • Box Plots • Stem Plot • Histogram • Scatter Plot • Time series Plot 2 28-11-2019
- 3. Introduction • There are many ways of collecting data. • Data analysis consists of one or more or 3 activities Graph of data Table of data Compute something from data • Simplification makes it easier to understand and to extract information in the new form. • Data simplification cannot cover the original information. • There is always a loss of some kind of information when we analyse the data. Iversen and Gergen,1997,p.75-7628-11-2019 3
- 4. Graph • Graphs are made of 2 main purpose Extract information from data Communicate the information to others • Therefore it is one of the statistical methods of analysing data Iversen and Gergen,1997,p.75-7628-11-2019 4
- 5. Pie Chart • A pie chart is a type of graph in which a circle is divided into sectors that each represents a proportion of the whole. Pie charts are a useful way to visualize information that might be presented in a small table. 12% 34% 35% 19% Juices Mango Strawberry Cherries Banana Source:Briliant.org28-11-2019 5
- 6. Advantages • Good for showing the relative sizes of graph • Several groups can be represented and compared • Good for categorical variable • One piece of pie can move to another location without changing the meaning of the chart Iversen and Gergen,1997,p.75-7628-11-2019 6
- 8. Disadvantages • Not compatible for showing many observation • Are not useful for representing large number of groups. Source:Briliant.org28-11-2019 8
- 9. 8% 8% 10% 6% 5% 7% 3% 9% 7%2% 9% 3% 7% 4% 3% 3% 1% 3% 2% Juices Mango Strawberry Cherries Banana Blueberries Carrot Guava Tomato Apple Avacado Mixed Fruit Grape Orange Beetroot Kiwifruit Lemon Melon Papaya Pineapple Source:Briliant.org28-11-2019 9
- 10. Bar graph • A bar chart is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. Bar charts can be used to show comparisons among categories. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Mango Mango(1) Mango(2) Mango(3) Different brand Mango Juices Source:Briliant.org28-11-2019 10
- 11. Advantages • Show each data category in a frequency distribution • Display relative numbers/proportions of multiple categories • Summarize a large amount of data in a visual, easily interpretable form • Make trends easier to highlight than tables do • Estimates can be made quickly and accurately • Accessible to a wide audience Africa Geography Blog,26th August 201528-11-2019 11
- 12. Disadvantages • Can be easily manipulated to give false impressions Africa Geography Blog,26th August 201528-11-2019 12
- 15. Dot Plot • A dot plot is a graphic display using dots and a scale to compare the frequency within categories or groups. • Dot plots clearly display clusters, scatters and outliers. 28-11-2019 15Source : Cpalms.org
- 16. Example : 28-11-2019 16Iversen and Gergen,1997,p.80.
- 17. 28-11-2019 17Iversen and Gergen,1997,p.80. It clearly shows that most of the women were in their middle to late twenties and early thirties, with a scattering between 35 and 60. Dot Plot
- 18. Dot Plots : Advantages : • Distribution of the variables shown clearly. • Original value has shown without losing any values Disadvantages : • Not suitable for large data set. 28-11-2019 18Source : Cpalms.org
- 19. Box plot • The box plot is a standardized way of displaying the distribution of data based on the minimum, first quartile, median, third quartile, and maximum of the data set. Max Q1Min Q2 Q3 25% 25% 25% 25% 28-11-2019 19
- 20. • A box plot summarizes data using the median, upper and lower quartiles, and the extreme (least and greatest) values. It allows you to see important characteristics of the data at a glance. • The data values found inside the box represent the middle half ( 50%) of the data. • The line segment inside the box represents the median 28-11-2019 20Iversen and Gergen,1997,p.80. 19 24 27 6032
- 21. Skewness in boxplot • Normal distribution : Q3-Q2 = Q2-Q1 • Positive skew : Q3-Q2 > Q2-Q1 • Negative skew : Q3-Q2 < Q2-Q1 28-11-2019 21Source : Cpalms.org Mode<median<mean Mode=median=mean Mode>median>mean
- 22. Box Plots : Advantages : • Shows 5 number summary • Makes comparison easy • Identify outliers • Handles extremely large data set Disadvantages : • Individual data is lost • Can be confusing to read 28-11-2019 22Source : Cpalms.org
- 23. Stem Plot • Has a vertical stem with branches grow out on both sides • Branches at left – first digit • Branches at right – remaining digits 28-11-2019 23 Iversen and Gergen,1997,p.80.
- 24. Histogram • A histogram is a type of graph that shows the frequency distribution of data within equal intervals (thus, there are no spaces between the bars). • Most commonly used graph 28-11-2019 24 Iversen and Gergen,1997,p.80.
- 25. 28-11-2019 25
- 26. The number of intervals used to divide the variable into intervals affects the shape of the histogram. 28-11-2019 26Iversen and Gergen,1997,p.80.
- 27. Histogram: Advantages : • Suitable for large data set • Distribution of the variables shown Disadvantages : • Individual data is lost 28-11-2019 27Source : Cpalms.org
- 28. Graphing two metric variables • Used to display data on two metric variables • Examples….. • ages of brides and the ages of grooms.. • height and weight of individuals • age and income • SAT scores and grade point • average, national literacy and gross domestic product 28-11-2019 28 (Iversen and Gergen,1997,p.91)
- 29. Graphing two metric variables contd.. • common way to display data on two variables. • consists of two axes, a horizontal axis and a vertical axis. • pair of observations of two variables is shown as a point in the graph. • Dots representing data points are scattered on the diagram. • Critical-To-Quality (CTQ) characteristic and a factor affecting it, two factors affecting a CTQ or two related quality characteristics. • dots cluster together in a line across the diagram shows the strength with which the two factors are related. Scatterplot 28-11-2019 29 (Moore et al, 2013.p. 99)
- 30. Graphing two metric variables contd.. WHAT DATA IS NECESSARY TO MAKE A SCATTER PLOT? • Multiple (two) sets of numerical data An independent variable A dependent variable In some cases, an independent variable and dependent variable can be interchanged When Would You Use a Scatter Plot? to investigate a relationship between two quantities identify the trend in the data set. (negative correlation, positive correlation, o no correlation) 28-11-2019 30 (Arteaga et al, 2012.p. 266)
- 31. What can it do for us ? • To control variation in any process,. • cause-and-effect diagram can help you identify probable causes. • Related and how they are related, you will know what to control or what to vary to affect a quality characteristic. • Uses for measure & analyze phases of Lean Six Sigma. Graphing two metric variables contd.. 28-11-2019 31 (Moore et al, 2013.p. 103)
- 32. Graphing two metric variables contd.. 28-11-2019 32(Arteaga et al, 2012.p. 268)
- 33. • Here is a scatter plot showing the relationship between students who took a History Test and a Math Test. • Is there a relationship between the scores? • Describe the relationship. History Vs. Math Graphing two metric variables contd.. 28-11-2019 33
- 34. • Since there is a positive correlation with the data, predict what a student who earned a 75% on their history test earned on their math test. • What can I draw that will help me make that prediction? History Vs. Math Graphing two metric variables contd.. 28-11-2019 34
- 35. • The line of best fit will help you make a prediction as to what score the student would get on their math test if they earned a 75% on their history test. • What score would he get on the math test? About 77% 75% on History Test Graphing two metric variables contd.. 28-11-2019 35
- 36. Advantage of scatter plot • Clearly reflects the relation between two variables. • No numerical information is lost and simplification of the data is gained. • Easy to create and to interpret. • Show Minimum, Maximum and outliers of the data set. Disadvantage of the scatter Plot • N0 graphs lines to see exactly where the point is • Helps to see the relationship but its difficult to tell if the relation is positive, Negative or if there isn’t one. Graphing two metric variables contd.. Scatterplot 28-11-2019 36 (Iversen and Gergen,1997,p.94)
- 37. Graphing two metric variables contd.. Introduction • A time series or time sequence is a data set in which the observations are recorded in the order in which they occur. • A time series plot is a graph in which the vertical axis denotes the observed value of the variable (say x) and the horizontal axis denotes the time (which could be minutes, days, years, etc.). • When measurements are plotted as a time series, we often see • trends, • series, or • other broad features of the data Time series plot 28-11-2019 37 (Box et al ,1997,p.34)
- 38. Graphing two metric variables contd.. 28-11-2019 38 (Iversen and Gergen,1997,p.92)
- 39. Graphing two metric variables contd.. 28-11-2019 39 (Iversen and Gergen,1997,p.94)
- 40. Graphing two metric variables contd.. possible to change the shape of a time series plot and give entirely different impressions of the data. Time series graph has the major advantages and disadvantages of scatterplots: numerical information is retained and data are simplified, but the shape of the graph can be misleading. 28-11-2019 40 (Iversen and Gergen,1997,p.94)
- 41. Conclusion • Formulate questions • Collect and organize data systematically to identify patterns and discover relationships • Represent data in different types of plots to yield different results • Develop conclusions and make recommendations based on data analysis 28-11-2019 41
- 42. Reference • Brilliant.org • African geography blog • Iversen and Gergen.(1997).Statistics: A conceptual approach. Description of date: Graphs and tables,75-76 • Arteaga, Pedro & Batanero, Carmen & Contreras, José & Cañadas, Gustavo. (2012). “Understanding Statistical Graphs: A research survey”. Boletín de Estadística e Investigación Operativa. 28. 262- 277. • Moore, D. S., Notz, W. I, & Flinger, M. A. (2013). The basic practice of statistics (6th ed.). New York, NY: W. H. Freeman and Company. • G.E.P. Box, G. Jenkins, “Time Series Analysis, Forecasting and Control”, Holden-Day, San Francisco, CA, 1970. 28-11-2019 42