1.1 Displaying Data Visually

Learning goal: Classify data by typeCreate appropriate graphs

MSIP / Home Learning: p. 11 #2, 3ab, 4, 7, 8

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

2) Qualitative – cannot be measured numerically e.g., eye colour, surname, favourite band

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 Sampling methods in Ch 2

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

See p. 8 of the text for an example of creating these by hand

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 See p. 9 for instructions We will revisit in 3.3

Pictograph Use images to represent frequency (scaled by

either quantity or size)

Heat Map

Use colours to represent different data ranges

Does not have to be a geographical map

e.g., Gas Price Temperature

Timeline Shows a series of events over time

MSIP / Home Learning

p. 11 #2, 3ab, 4, 7, 8

Mystery Data

Gas prices in the GTA

3-Jan-0

8

22-Feb-0

8

12-Apr-0

8

1-Jun-0

8

21-Jul-0

8

9-Sep-0

8

29-Oct-

080.0000.2000.4000.6000.8001.0001.2001.4001.600

f(x) = − 1.78984476996036E-05 x² + 1.41853083716074 x − 28104.9051549717R² = 0.818508472651409

Hint: These values should get you pumped!

An example… these are prices for Internet service packages find the mean, median and mode State the type of data create a suitable frequency table, stem and leaf plot

and graph13.60 15.60 17.20 16.00 17.50 18.60 18.7012.20 18.60 15.70 15.30 13.00 16.40 14.3018.10 18.60 17.60 18.40 19.30 15.60 17.1018.30 15.20 15.70 17.20 18.10 18.40 12.0016.40 15.60

Answers…

Mean = 494.30/30 = 16.48 Median = average of 15th and 16th numbers Median = (16.40 + 17.10)/2 = 16.75 Mode = 15.60 and 18.60 Decimals so quantitative and continuous. Given this, a histogram is appropriate

1.2 Conclusions and Issues in Two Variable Data

Learning goal: Draw conclusions from two-variable graphs

Due now: p. 11 #2, 3ab, 4, 7, 8

Infographic due tomorrow

MSIP / Home Learning: Read pp. 16–19

Complete p. 20–24 #1, 4, 9, 11, 14

“Having the data is not enough. [You] have to show it in ways people both enjoy and understand.”- Hans Rosling http://www.youtube.com/watch?v=jbkSRLYSojo

What conclusions are possible? To draw a conclusion…

Data must address the question Data must represent the population

Census, or representative sample (10%)

Types of statistical relationships Correlation

When two variables appear to be related i.e., a change in one variable is associated with a change in

the other e.g., salary increases as age increases

Causation a change in one variable is PROVEN to cause a change in

the other requires an in-depth study e.g., incidence of cancer among smokers WE WILL NOT DO THIS IN THIS COURSE!!! Don’t use the p-word!

Case Study – Opinions of school 1 046 students were surveyed The variables were:

Gender Attitude towards school Performance at school

Example 1)What story does this graph tell?

Example 1 – cont’d

The majority of females responded that they like school “quite a bit” or “very much”

Around half the males responded that they like school “a bit” or less

Around 3 times more males than females responded that they hate school

Since they responded more favorably, the females in this study like school more than males do

Example 2a – Is there a correlation between attitude and performance? Larger version on next slide…

Example 2a – cont’d Most students answered “Very well” when asked

how well they were doing in school. There is only one student who selected “Poorly”

when asked how well she was doing in school. Of the four students who answered “I hate

school,” one claimed he was doing well. It appears that performance correlates with

attitude Is 27 out of 1 046 students enough to make a

valid inference? It depends on how they were chosen!

Example 2b – Examine all 1046 students

Example 2b - cont’d From the data, the following conclusions can be made: All students who responded “Very poorly” also

responded “I hate school” or “I don’t like school very much.”

A larger proportion of students who responded “Poorly” also responded “I hate school” or “I don’t like school very much.

It appears that there is a relationship between attitude and performance.

It CANNOT be said that attitude CAUSES performance, or performance CAUSES attitude without an in-depth study.

Drawing Conclusions

Do females seem more likely to be interested in student government?

Does gender appear to have an effect on interest in student government?

Is this a correlation? Is it likely that being

female causes interest?

0

10

20

30

40

50

Yes No

Students Interested in Student Government

FemaleMale