Lesson 4.3 Statistical Graphs and Charts PDF

Review Measures of Mathematics in the Modern World: Central Tendency Data Management Measures of Variation Measures of Lesson 4.3 Statistical Graphs and Charts Position or...

Review Measures of Mathematics in the Modern World: Central Tendency Data Management Measures of Variation Measures of Lesson 4.3 Statistical Graphs and Charts Position or Location Sources: (1) Lachica, G.P.; (2) some data and graphs from psa.gov.ph; (3) for all other images, credits to the rightful owners. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Outline: 1. Commonly used statistical graphs and charts a. Bar graph d. Scatter diagram or plot b. Histogram e. Line graph c. Pie chart 2. Other graphs and charts a. Box and whisker chart b. Bubble chart 3. Sample statistical charts and graphs for PH Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs COMMONLY USED STATISTICAL GRAPHS When do we typically use them? Bar Graph Interest is difference on magnitude Line Graph Multiple Bar Trends across time Graph or period Comparing several items Pie Chart Scatter Diagram Interest is on allocation or portion of a whole Relationship between two variables Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph A bar chart is a graph represented by spaced rectangular bars that describe the data points in a set of data. It is usually used to plot discrete and categorical data. Advantages Do’s: Summarizes a large amount of data Start the y-axis at zero in an understandable form. Label the axes Easily accessible to a wide Put value labels on bars audience. Don’ts: Disadvantages Using too many colors It does not reveal key assumptions Using 3-D imagery or like causes, effects, patterns, etc. distracting May require further explanation. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Vertical bar charts display data Horizontal bar charts display the vertical in a series of bars that run from axis that represents the categories being the bottom to the top of the compared, while the horizontal axis chart. represents a value. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Grouped bar charts are bar charts in which multiple sets of data items are compared, with a single color used to denote a specific series across all sets. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph The stacked bar graphs is a graph that is used to break down and compare parts of a whole. Each bar in the chart represents a whole, and segments in the bar represent different parts or categories of that whole. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Question: What’s wrong with the given bar graph? Error: DISPLACED AXES However, in the corrected graph Here, it seems the differences are above, the differences do not vary a significant. lot. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Note: The price increase was not Note: Because the scale leaves out as big as it appeared to be. 0 to 100, it appears that 6th grade’s sales is thrice as much as that of 7th grade. In fact, grade 6 sold just about 20% more than grade 7. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Note: It seems that the number of people in US receiving federal welfare has doubled from 2009 Q1 to 2011 Q2 but in reality it does not due to manipulated or misplaced y-axis. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph Note: The scale is too compressed that we can hardly see the differences among the brands. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Histogram Histogram chart visualizes the frequency of discrete and continuous data in a dataset using joined rectangular bars. Things to remember Each rectangular bar defines the number of elements that fall into a predefined class interval. It helps in visualizing large amounts of data. It reveals the variation, centering, and distribution of the data. Disadvantages It does not visualize the exact values in a dataset. It only visualizes continuous data. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Histogram A normally distributed histogram is usually bell-shaped. www.usablestats.com In a bimodally distributed histogram chart, two groups of histogram charts that are of normal distribution. www.presentationeze.com Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Histogram This is an asymmetric graph (skewed distribution) with an off-center pick usually tending towards the end of the graph. www.cdc.gov www.presentationeze.com This type of histogram chart does not have a regular pattern. It produces multiple peaks and can also be called a multimodal (random) distribution Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Bar Graph vs Histogram Bar charts measure categorical Histograms measure data: data that can be split into continuous, quantitative data: different categories or types. data that can be counted Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart A pie chart is a circular graph used to illustrate numerical proportions in a dataset. This graph is usually divided into various sectors, where each sector represents the proportion of a particular numerical element in the set. Disadvantages It is inapplicable for large datasets. It cannot visualize groups of data. This is the most basic type of pie chart and can also be simply called a pie chart. www.psa.gov.ph Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart Exploded Pie Chart. One of the sectors of the circle is separated (or exploded) from the chart. It is used to lay emphasis on a particular element in the data set. www.officetooltips.com www.mission.wordpress.com A pie of pie is a chart that generates an entirely new (usually small) pie chart from the existing one. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart www.psa.gov.ph www.psa.gov.ph Doughnut Chart 3D Pie Chart Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart Do’s: Make sure your segments add up to 100 Use when comparing percentages Keep it clean and consistent Don’ts: Compare too many categories Use a pie chart if your segments end up being roughly the same size Compare two pie charts side by side Use 3-D imagery or tilt your pie chart Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart Question: What’s wrong with the given graph? Note: Values do not add up to 100%. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Pie Chart Question: What’s wrong with the given graph? Note: Too many parts or categories to compare. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Scatter Plots Scatter plots are charts used to visualize random variables with dot-like markers that represent each data point. The closer the data points come to making a straight line means the correlation between the two variables is higher, or the relationship is stronger. Advantages It clearly shows data spread It is usually colorful and visually appealing Disadvantages It cannot give the exact extent of correlation. It can only be used to study the relationship between two variables. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Scatter Plot www.blogs.sas.com www.online.visual-paradigm.com Two groups of data visualized on a Two groups of data visualized on a scatter plot are said to be positively scatter plot are said to be negatively correlated if an increase in one correlated if an increase in one implies implies an increase in the other. a decrease in the other. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Scatter Plot Two groups of data visualized on a scatter plot are said to have no correlation if there is no clear correlation between them. www.online.visual-paradigm.com Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Scatter Plot Do’s: Use scatter plots when you have a lot of data. Use regression lines to guess Y if you have X Start the Y-axis at 0 Don’ts: Compare too many regression lines Exclude outliers Note: Data points too compressed that it becomes difficult to see what values are represented. www.huebler.blogspot.com Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Line graphs are represented by a group of data points joined together by a straight line. Each of these data points describes the relationship between the horizontal and the vertical axis on the graph. To remember It helps in studying data trends over a period of time. Disadvantages It is not convenient to plot when dealing with fractions and decimals. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs www.psa.gov.ph www.psa.gov.ph Simple Line Graph Multiple Line Graph Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Do’s: Start the x-axis at zero Clearly label your axes Remove distracting chart from quickly seeing the overall trend. Zoom in on the y-axis if your data set starts above zero Don’ts: Compare more than 5-7 Use too many colors to distinguish the different data sets Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Question: What’s wrong with the given graph? Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Note: 2016 was split into two different data points, hence making the x-axis not equally spaced. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Note: Too many lines to compare. www.thefederalist.com Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Note: Now it seems that US spending on science is correlated to hanging suicides, in which in reality they are not. Such spurious correlation is due to matching the y-axes of two different events. A spurious correlation is when two events or variables are seemingly associated but are not causally related. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Line Graphs Note: The addition of the line graph is incorrect since the x- axis is categorical. A line graph is not appropriate for categorical variables. Source: https://xxlbi.com/ Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Graphs Box and Whisker A statistical graph for displaying sets of numerical data through their quartiles. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Graphs Box and Whisker Using box and whisker to compare variability (or distribution) of data sets or groups. Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Graphs Box and Whisker Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Graphs Bubble Chart Bubble charts are super useful types of graphs for making a comparison of the relationships between data in 3 numeric-data dimensions: the Y-axis data, the X- axis data, and data depicting the bubble size. Simple Bubble Chart The bubble chart shows four data comparisons: total attempts (x-axis), shooting percentage (y-axis), volume (color), and shooting efficiency (bubble size). Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Descriptive Common Types Supplementary Supplementary Statisticsof Statistics ofPH PH of Graphs Graphs Graphs Map Bubble Chart A map bubble chart is usually used to illustrate data on a map. www.mapsvg.com Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs SOME GRAPHICAL PRESENTATIONS OF THE DATA OF THE PHILIPPINES Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Contour to distinguish level of data values or highlight scale Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Descriptive Common Types Supplementary Supplementary Statistics of PH of Graphs Graphs Graphs Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV  Note: You may visit www.psa.gov.ph to see more of our country’s important statistics, statistical presentations, statistical infographics, and data analysis or statistical reports. T h a n k Y o u! Mathematics in the Modern World: Data Management: Data Analysis MTH 101:Unit MTH 101: UnitIV IV