1. MDM4U - 5.1 Displaying Data Visually Learning goal:Classify data by type Create appropriate graphs

2. Why do we collect data? We learn by observing Collecting data is a systematic method of making observations  Allows others to repeat our observations Good definitions for this chapter at:  http://www.stats.gla.ac.uk/steps/glossary/alphabet.html

3. Types of Data 1) Quantitative – can be represented by a number  Discrete Data Data where a fraction/decimal is not possible e.g., age, number of siblings  Continuous Data Data where fractions/decimals are possible E.g., height, weight, academic average

4. Types of Data 2) Qualitative – cannot be measured numerically  e.g., eye colour, surname, favourite band  Ordinal Data Data that can be ranked e.g. poor, fair, very good  Nominal Data data and cannot be ranked e.g. blue eyes, green eyes, brown eyes

5. Who do we collect data from? Population - the entire group from which we can collect data / draw conclusions  Data does NOT have to be collected from every member Census – data collected from every member of the pop’n  Data is representative of the population  Can be time-consuming and/or expensive Sample - data collected from a subset of the pop’n  A well-chosen sample will be representative of the pop’n

6. Organizing Data A frequency table is often used to display data, listing the variable and the frequency. What type of data does this table contain? Intervals can’t overlap Use from 3-12 intervals / categories DayNumber of absences Monday 5 Tuesday 4 Wednesday 2 Thursday 0 Friday 8

7. Organizing Data (cont’d) Another useful organizer is a stem and leaf plot. This table represents the following data: 101 103 107 112 114 115 115 121 123 125 127 127 133 134 134 136 137 138 141 144 146 146 146 152 152 154 159 165 167 168 Stem (first 2 digits) Leaf (last digit) 101 3 7 112 4 5 5 121 3 5 7 7 133 4 4 6 7 8 141 4 6 6 6 152 2 4 9 165 7 8

8. Organizing Data (cont’d) What type of data is this? The class interval is the size of the grouping  100-109, 110-119, 120-129, etc.  No decimals req’d for discrete data Stem can have as many numbers as needed A leaf must be recorded each time the number occurs StemLeaf 101 3 7 112 4 5 5 121 3 5 7 7 133 4 4 6 7 8 141 4 6 6 6 152 2 4 9 165 7 8

9. Displaying Data – Bar Graphs Typically used for qualitative/discrete data Shows how certain categories compare Why are the bars separated? Would it be incorrect if you didn’t separate them? Number of police officers in Crimeville, 1993 to 2001

10. Bar graphs (cont’d) Double bar graph  Compares 2 sets of data Internet use at Redwood Secondary School, by sex, 1995 to 2002 Stacked bar graph  Compares 2 variables  Can be scaled to 100%

11. Displaying Data - Histograms Typically used for Continuous data The bars are attached because the x-axis represents intervals Choice of class interval size (bin width) is important. Why? Want 5-6 intervals

12. Displaying Data –Pie / Circle Graphs A circle divided up to represent the data Shows each category as a % of the whole

13. Scatter Plot Shows the relationship (correlation) between two numeric variables May show a positive, negative or no correlation Can be modeled by a line or curve of best fit (regression)

14. Line Graph Shows long-term trends over time  e.g. stock price, price of goods, currency

15. Box and Whisker Plot Shows the spread of data Divides the data into 4 quartiles  Each shows 25% of the data  Do not have to be the same size Based on medians

16. Pictograph Use images (size or quantity) to represent frequency

17. Heat Map Use colours to represent different data ranges Does not have to be a geographical map e.g., Gas Price Temperature

18. Homework pg. 203 #1, 4, 5