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Types of Data Displays Based on the 2008 AZ State Mathematics Standard Pictograph (Grades 1 and 2) Pictograph (Grades 1 and 2) For Grade 1: the pictures/icons in the pictograph represent a quantity of 1. For Grade 2: The pictures/icons in the pictograph represent more than 1 and a key is required to interpret the graph. Pictograph Example Pictographs Summary Pictograph Advantages Disadvantages A pictograph uses an icon to •Easy to read •Hard to quantify partial represent a quantity of data icons values in order to decrease •Visually appealing the size of the graph. A key •Icons must be of consistent must be used to explain the size icon •Handles large data sets easily using keyed icons •Best for only 2 – 6 categories •Very simplistic Tally Chart “Favorite Pets” (Grade 1) Frequency Table “Favorite Pets” (Grades 2 and 3) Note: A frequency table may or may not have a column for the tally marks. Pictograph made from the previous tally chart and frequency table Bar Graphs (Grades 2, 3, 4, 5) Bar graph Advantages Disadvantages A bar graph displays •Visually strong •Graph categories can be discrete data in separate reordered to emphasize columns. A double bar •Can easily compare two or certain effects. graph can be used to three data sets. compare two data sets. •Use only with discrete data Categories are considered unordered and can be rearranged alphabetically, by size, etc. Bar Graphs (Grades 2, 3, 4, 5) Grade 2: Single Bar Graph Grade 3: Single Bar Graph Grade 4: Double Bar Graph Grade 5: Multi-Bar Graph Bar Graph made from previous tally chart and pictograph Bar Graphs Example Horizontal Bar Graph Example Vertical Bar Graph Example Which Direction? Vertical Bar Graph Displays data better than horizontal bar graphs, and is preferred when possible. Horizontal Bar Graph Useful when category names are too long to fit at the foot of a column. Vertical vs. Horizontal Double Bar Graph (Grade 4) Multi-Bar Graph (Grade 5) Line Graph (Grades 3, 4, 5) Line graph Advantages Disadvantages A line graph plots •Can compare multiple •Use only with continuous data as continuous data sets continuous data points and then joins easily them with a line. Multiple data sets can be graphed together, but a •Interim data can be key must be used. inferred from graph line. Line Graph (Grades 3, 4, 5) • Grade 3: Single Line Graph • Grade 4: Single Line Graph • Grade 5: Double Line Graph Single Line Graph (Grades 3 and 4) Double Line Graph (Grade 5) Pie Chart – Circle Graph (Grade 4) Pie chart Advantages Disadvantages A pie chart displays data as •Visually appealing •No exact numerical data a percentage of the whole. Each pie section should •Shows percent of total for •Hard to compare 2 data have a label and each category. sets percentage. A total data number should be included. •“Other” category can be a problem •Total unknown unless specified •Best for 3 – 7 categories •Use only with discrete data Pie Chart – Circle Graph Example Pie (circle) charts - more info • A way of summarizing a set of categorical data or displaying the different values of a given variable (e.g. percentage distribution). • A circle is divided into a series of segments. Each segment represents a particular category. • The area of each segment is the same proportion of a circle’s area as the category is of the total data set. • Quite popular. Circle provides a visual concept of the whole (100%). • Best used for displaying statistical information when there are no more than six components – otherwise, the resulting picture will be too complex to understand. • Pie charts are not useful when the values of each component are similar because it is difficult to see the differences between slice sizes. Stem and Leaf Plot (Grade 6) Stem and Leaf Plot Advantages Disadvantages Stem and leaf plots record •Concise representation of •Not visually appealing data values in rows, and can data easily be made into a •Does not easily indicate histogram. Large data sets •Shows range, minimum & measures of centrality for can be accommodated by maximum, gaps & clusters, large data sets. splitting stems. and outliers easily •Can handle extremely large data sets Stem and Leaf Plot Stem and Leaf Plot Histograms (Grade 6) Histogram Advantages Disadvantages A histogram is a type of bar •Visually strong •Cannot read exact values graph that displays because data is grouped continuous data in ordered •Can compare to normal into categories. columns. Categories are of curve continuous measure such •More difficult to compare as time, inches, two data sets. temperature, etc. •Usually vertical axis is a frequency count of items falling into each category. •Use only with continuous data. Histogram Histogram Line Plot (Grade 4 and 5) Line plot Advantages Disadvantages A line plot can be used as an •Quick analysis of data •Not as visually appealing initial record of discrete data values. The range •Shows range, minimum & •Best for under 50 data determines a number line maximum, gaps & clusters, values which is then plotted with X’s and outliers easily (or something similar) for each data value. •Needs small range of data •Exact values retained. Line Plots (dot plot) Example Line Plot for the Number of M&M's™ in a Package X X X X X X X X X X X X X X X X X X X X X X X X X 12 13 14 15 16 17 18 19 20 21 22 23 Graph paper is a good idea for it is crucial that each recorded X be uniform in size and placed exactly across from each other (one-to-one correspondence). Notice the cluster at 17 & 18 as well as the gap at 13 and 22. The mode is 18, the median is the second X from the bottom for number 18, and the mean is 17.68 or 18. Line plot made from a Tally Chart There are many more types of Data Displays Here are a few - - - Stacked Vertical Bar Graph Example Histogram Example (a type of bar graph) Frequency Polygon Salaries of Acme Box and Whisker Plot Box plot Advantages Disadvantages A box plot is a concise •Shows 5-point summary •Not as visually appealing graph showing the five point and outliers as other graphs summary. Multiple box plots can be drawn side by •Easily compares two or •Exact values are not side to compare more than more data sets retained. one data set. •Handles extremely large data sets easily. Box & Whisker Graph Example Scatter Plot Scatter plot Advantages Disadvantages A scatter plot displays the •Shows a trend in the data •Hard to visualize results in relationship between two relationship large data sets factors of the experiment. A trend line is used to •Retains exact data values •Flat trend line gives determine positive, negative and sample size. inconclusive results. or no correlation. •Shows minimum/maximum •Data on both axes should and outliers be continuous. Scatter Plot Scatter Plot Example No Correlation If there is absolutely no correlation present, the value given is 0. Perfect linear correlation: A perfect positive correlation is given the value of 1. A perfect negative correlation is given the value of -1. Strong linear correlation: The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables. Weak linear correlation: The closer the number is to 0, the weaker the correlation. Map Graph Cosmograph Map chart Advantages Disadvantages A map chart displays data •Good visual appeal •Needs limited categories by shading sections of a map, and must include a •Overall trends show well. •No exact numerical values key. A total data number should be included. •Color key can skew visual interpretation. Map Chart Cosmograph Map Graph • Parts of whole so similar to a pie graph • Less numerical and more graphic Venn Diagram Venn Diagram Venn Diagram

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MODULE RECORD, Engineering Statistics, Module Code, UNIVERSITY OF PLYMOUTH, probability and statistics, engineering design, probability density functions, Module Title, sensible interpretation, statistical methodology

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posted: | 7/8/2011 |

language: | English |

pages: | 59 |

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