MDM4U - 5.1 Displaying Data Visually

Learning goal: Classify data by typeCreate appropriate graphs

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

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

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

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

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

Day Number of absences

Monday 5

Tuesday 4

Wednesday 2

Thursday 0

Friday 8

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)

10 1 3 7

11 2 4 5 5

12 1 3 5 7 7

13 3 4 4 6 7 8

14 1 4 6 6 6

15 2 2 4 9

16 5 7 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

Stem Leaf

10 1 3 7

11 2 4 5 5

12 1 3 5 7 7

13 3 4 4 6 7 8

14 1 4 6 6 6

15 2 2 4 9

16 5 7 8

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

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%

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

Displaying Data –Pie / Circle Graphs A circle divided up

to represent the data

Shows each category as a % of the whole

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)

Line Graph

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

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

Pictograph Use images (size or quantity) to represent

frequency

Heat Map

Use colours to represent different data ranges

Does not have to be a geographical map

e.g., Gas Price Temperature

Homework

pg. 203 #1, 4, 5