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1.1 Displaying Data Visually

Learning goal: Classify data by typeCreate appropriate graphs

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

Chapter 1 Problem

Log on to a computer You may pair up if no computers are available

Click MDM4U.LIEFF.CA Save the file MDM4U CP1.PDF to your M:\

drive Create a MDM4U folder Create a Ch1 folder

Answer CP1 and CP2 in a Word document

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

E.g. age, height, weight, number of siblings

a) Discrete Data Data where a fraction/decimal is impossible E.g., Age, Number of siblings

b) Continuous Data Data where fractions/decimals are possible E.g., Weight, Height, Academic average

2) Qualitative – cannot be measured numerically E.g. eye colour, hair colour, favourite band

Who do we collect data from? Population - the entire group from which we can

collect data / draw conclusions NOTE: 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 some members of the pop’n (min. 10%) A good sample must be representative of the pop’n Sampling methods in Ch2

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 107112 114 115 115121 123 125 127 127133 134 134 136 137 138141 144 146 146 146152 152 154 159165 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, and is 10 units here 100-109, 110-119, 120-129, etc. No decimals req’d

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

Measures of Central Tendency Used to indicate one value that best represents a

group of values Mean (Average)

Add all numbers and divide by the number of values Affected greatly by outliers (values that are significantly

different from the rest) Median

Middle value Place all values in order and choose middle number For an even # of values, average the 2 middle ones Not affected as much by outliers

Mode Most common number There can be none, one or many modes Only choice for Qualitative data

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 is important. Why?

Displaying Data –Pie / Circle Graphs A circle divided up

to represent the data

Shows each category as a portion of the whole

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

Scatter Plot

A scatter plot shows the relationship between two numeric variables

This relationship, called a correlation, can be positive, negative or none

A line or curve of best fit (regression line) can be used to model the relationship

Examining Trends

A line graph shows long-term trends over time e.g. stock price, currency, moving average

Examining the spread of data

A box and whisker plot shows the spread of data

Divided into 4 quartiles with 25% of the data in each

Instructions for creating these may be found on page 9 of the text or at:http://regentsprep.org/Regents/math/data/boxwhisk.htm

MSIP / Home Learning

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

Mystery Data

Gas prices in the GTA

3-Jan-08

22-Feb-08

12-Apr-08

1-Jun-08

21-Jul-0

8

9-Sep-08

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 determine what type of data this is 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 The data is numerical, so at least Interval

data. It has an absolute starting point, so it is ratio data.

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

MSIP / Home LearningRead pp. 16–19Complete 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

What conclusions are possible? To draw a conclusion, a number of conditions

must apply data must be representative of the population sample size must be large enough data must address the question

Types of statistical relationships Correlation

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 usually requires an in-depth study i.e. WE WILL NOT DO

THIS IN THIS COURSE!!! e.g., incidence of cancer among smokers

Do not use the P-word!!!

Example 1 – Split bar graph

Do females like school more than males do?

Example 2 – Is there a correlation between attitude and performance?

Example 3 – Examine all 1046 students

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?

01020304050

Yes No

Students Interested in Student Government

FemaleMale

References

Calkins, K. (2003). Definitions, Uses, Data Types, and Levels of Measurement. Retrieved August 23, 2004 from http://www.andrews.edu/~calkins/math/webtexts/stat01.htm

James Cook University (n.d.). ICU Studies Online. Retrieved August 23, 2004 from http://www.jcu.edu.au/studying/services/studyskills/scientific/data.html