Data Management - Graphing

1. Unit Review Data Management - Graphing

2. Definitions – Page 1 • Graph – A way of showing information so it is more easily understood; a graph can be concrete (e.g. boys in one line and girls in another), pictorial (e.g. pictures of boys in one row and pictures of girls in another), or abstract (e.g. two bars on a bar graph to show how many students and how many are girls) • Data – Information gathered in a survey, in an experiment, or by observing (e.g. data can be in words, such as a list of students’ names; in numbers, such as quiz marks; or in pictures, such as drawings of favourite pets)

3. Definitions – Page 2 • Scale – numbers and marks arranged at regular intervals that are used for measurement or to establish position (e.g. The markings on the axis of a graph) • Interval – The distance between two endpoints on a graph scale; intervals in a graph should be equal, but not overlapping (e.g. If the scale axis is numbered 0, 5, 10, 15, then the intervals are 5. If you are asked to decide on intervals for graphing information, make sure you choose intervals that will include all of your data, i.e. 0-4, 5-9, 10-14, 15-19...the value of these intervals is 5.)

4. Definitions – Page 3 • Range – describes the span of the data, you calculate the range by subtracting the lowest number in the data from the highest number of data (e.g. If the data set is 4, 6, 2, 8, 16, 12, we calculate 16-2=14, therefore the range is 14.) • Biased results – Survey results for part of a group that are not likely to apply to the rest of the group • Trend – the general direction of data presented in a graph; the data can increase, decrease, or stay the same over time

5. Definitions – Page 4 • Types of graphs: • Pictograph (a graph that uses pictures to represent quantities) • Bar graph (a graph that compares data using vertical or horizontal bars) • Broken-line graph (a graph where data points are joined by line segments) • Circle or pie graph (a graph that shows data using parts of a circle)

6. Pictographs • As you may guess from its name, pictographs use pictures to help provide visuals when presenting information on a graph • It is important to decide how much each picture will represent (based on your data) before you start drawing a pictograph

7. Pictographs • A pictograph looks like this (picture taken from http://ronblond.com/MathGlossary/Division03/Pictograph/index.html):

8. Pictographs • The pictograph in the previous slide represents this information (“Frequency” means how many students)(picture taken from http://ronblond.com/MathGlossary/Division03/Pictograph/index.html):

9. Bar Graphs • As you may guess from its name, bar graphs use either vertical (up and down) or horizontal (side to side) bars to help provide visuals when presenting information on a graph • It is important to decide on what intervals will be represented by each bar (based on your data) before you start drawing a bar graph

10. Bar Graphs • A bar graph looks like this (picture taken from http://jptuke.wordpress.com/units/unit-1/data-analysis-graphing/):

11. Bar Graphs • The bar graph in the previous slide represents this information (“Frequency” means how many students):

12. Broken-line Graphs • Broken-line graphs use data points connected by line segments to provide visuals when presenting information on a graph (the line often looks jagged or like a zig-zag, which is why we call it “broken”) • It is important to decide what your scale will be on each axis (based on your data) before you start drawing a broken-line graph • DON’T FORGET that the first data point on your broken-line graph appears on the y-axis or at a point within the graph (like the picture in the next slide), not at your O point in the corner of the axis

13. Broken-line Graphs • A broken-line graph looks like this (picture taken from: http://www.studyzone.org/testprep/math4/d/linegraph4l.cfm):

14. Broken-line Graphs • The broken-line graph in the previous slide represents this information (“Frequency” means how many):

15. Circle Graphs • As you may guess from its name, circle graphs use sections of a circle to help provide visuals when presenting information on a graph • This can also be called a “pie graph”

16. Circle Graphs • A circle graph looks like this (picture taken from: http://kinz-land.com/2007/08/31/breaking-news-18-of-kids-own-20-webkinz/):

17. Mean and Mode • Mean – A type of average; the sum of a set of numbers divided by the number of numbers in the set (e.g. If the set is 3, 4, 5, 2, 2, 3, and 2, all 7 of these numbers add up to 21. You figure out the mean by calculating 21÷7=3. Therefore your mean is 3.) • Mode – A type of average; the number that occurs the most often in a set of numbers. The easiest way to figure this out is to put the numbers in order from smallest to largest. (e.g. If the set is 3, 4, 5, 2, 2, 3, and 2, in order from smallest to largest it would look like 2, 2, 2, 3, 3, 4, and 5. From here you can easily see that 2 occurs the most often and is therefore your mode.)

18. Stem-and-Leaf Plots • A stem-and-leaf plot is like a chart that we can use to organize data in groups • The stem (left side of the chart) shows the beginning of the number • The leaf (right side of the chart) shows the rest of the number • To read a stem-and-leaf plot, we take the stem number and combine it with one leaf number at a time

19. What does information on a Stem-and-Leaf Plot look like? • Stem-and-leaf plots look like these (pictures taken from http://worksheets.tutorvista.com/math/87614/graphic-statistics.html ):

20. Steps to putting information into a Stem-and-Leaf Plot • First we want to group the numbers from smallest to largest values • Then we want to group the numbers by their beginning digits • To complete the stem and leaf plot, simply draw a t-chart, write the first number(s) of each number in the stem section of the plot, then list the last number(s) of each number in the leaf section of the plot