Stat 20: Intro to Probability and Statistics - Lecture 3: Types of Data ...

Stat 20: Intro to Probability and Statistics 

Lecture 3: Types of Data and Displays 

Tessa L. Childers-Day 

UC Berkeley 

28 January 2014

Today’s Goals Kinds of Data Displaying Qualitative Data 

Outline 

1 Today’s Goals 

2 Kinds of Data 

3 Displaying Qualitative Data 

2 / 27


By the end of this lecture... 

You will be able to: 

Define data types 

Classify a given response as a type of data 

Compare types of data 

Comprehend displays of qualitative data 

3 / 27


Example: High School Hobbies 

(Hypothetical:) Imagine we are interested in exploring what kinds 

of hobbies high school students have below. We construct a survey: 

(1) Circle your gender: Female Male 

(2) Circle your class level: Fresh Soph Jr Sr 

(3) What is your GPA (0.0-5.0)? 

(4) What is your height in inches? 

(5) What is your weight in pounds? 

(6) What is your favorite hobby? 

How do the questions look? How should we sample students? 

4 / 27


Now what? 

We have seen how to design experiments, observational studies, 

and surveys. After they are carried out, what do we have? 

Data: 

the individual bits of information or responses collected, e.g. a 

single person’s height is a data (point, value), singular 

a set or collection of information or responses, e.g. all of the 

heights collected in the course of an experiment is data (set), 

plural 

5 / 27


Example: High School Hobbies (cont.) 

A selection of the hypothetical raw data appear below: 

obs gender class level gpa height weight hobbies 

1 male jr 3.80 71 122 watching tv 

2 female soph 2.80 67 132 facebook 

3 female jr 3.90 62 148 baseball 

4 male jr 3.50 60 139 soccer 

5 male sr 2.60 66 133 yearbook 


7 male sr 0.70 71 138 facebook 

8 female fresh 4.80 60 143 gymnastics 

9 male sr 4.00 72 132 hanging out 

10 male jr 1.30 72 146 reading 

6 / 27


Ways to classify data 

Level of Measurement: 

Qualitative 

Nominal 

Ordinal 

Quantitative 

Interval 

Ratio 

Countability: 

Discrete 

Continuous 

7 / 27


Qualitative Data 

In general, qualitative data are: 

Categorical 

Linguistic 

Non-numeric 

May be subjective or objective 

Do we have categorical data in our example? 

8 / 27


Nominal Data 

A type of data that are simply names or labels. Cannot be ranked 

or ordered by value objectively. 

Rocks: igneous, metamorphic, sedimentary 

Clouds: cumulus, stratus, cirrus, nimbus 

Names: Adam, Andrew, Bethany, Christopher 

College Degree: yes/no 

Currently Married: yes/no 

Coin flip: heads/tails 

Do we have nominal data in our example? 

9 / 27


Ordinal Data 

A type of data that are names or labels which can be sensibly 

ordered or ranked. Nominal data plus an ordered scale. The 

“distances” between each category are not known, but their 

ordering is known. Ties are allowed. 

Cooking Ability: poor, adequate, fair, good, excellent 

Letter Grade: A, B, C, D, F 

Likert Scale: strongly disagree, disagree, neutral, agree, 

strongly agree 

Horse Race Results: first, second, third, fourth 

Frequency: never, sometimes, always 

Movie Review: 0 stars to 5 stars 

Do we have ordinal data in our example? 

10 / 27


Quantitative Data 

In general, quantitative data are: 

Numeric 

Non-linguistic 

Objectively Measurable 

Do we have quantitative data in our example? 

11 / 27


Interval Data 

A type of data that are numeric and are naturally ordered, but 

have no meaningful zero. Distances are meaningful. 

Temperature: 20 ◦ is the same amount hotter than 15 ◦ as 15 ◦ 

is to 10 ◦ , but 20 ◦ is not twice as hot as 10 ◦ 

Time: The same amount of time elapses between 4:05 and 

4:10 as between 5:12 and 5:17. 8:00 is not twice 4:00. 

Do we have interval data in our example? 

12 / 27


Ratio Data 

A type of data that are numeric, naturally ordered, and have a 

meaningful zero. Distances and ratios are meaningful. Often 

physical in nature. 

Speed in km/h, m/h, etc 

Money/debt in dollars, euros, etc 

Electrical charge in coulombs 

Do we have ratio data in our example? 

13 / 27


Countability 

Applies only to numeric data 

Discrete: countable, exactly measurable, equally spaced; e.g. 

number of coin flips that land heads, number of queens in a 

deck of cards, integers, money 

Continuous: not countable, not exactly measurable, arbitrarily 

close, infinitely divisible; e.g. weight, length are continuous, 

but our ability to measure is finite, so mostly 

round/approximate 

14 / 27


Example: High School Hobbies (cont.) 

A selection of the hypothetical raw data appear below: 

obs gender class level gpa height weight hobbies 

1 male jr 3.80 71 122 watching tv 

2 female soph 2.80 67 132 facebook 


4 male jr 3.50 60 139 soccer 

5 male sr 2.60 66 133 yearbook 


7 male sr 0.70 71 138 facebook 

8 female fresh 4.80 60 143 gymnastics 

9 male sr 4.00 72 132 hanging out 

10 male jr 1.30 72 146 reading 

15 / 27


Visual Displays of Information 

Aggregating the data and displaying it in a picture or summary of 

some sort is in order. 

What sorts of displays have you seen before? 

16 / 27


Visual Displays of Information (cont.) 

Today: Qualitative Data 

Data Tables 

Distribution Tables 

Contingency Tables 

Pie Charts 

Bar Charts 

Word Clouds 

Can work for quantitative data too, though not ideal 

17 / 27


Data Tables 

A frequency table (distribution table) simply displays the number 

(or percentage) of observations which meet a certain criteria. 

Gender Female Male Total 

Frequency 247 253 500 

Class Fresh. Soph. Junior Senior Total 

Frequency 122 125 130 123 500 

GPA 0-1 1-2 2-3 3-4 4-5 Total 

Frequency 51 80 167 123 79 500 

Height (in) 60-63 63-66 66-69 69-72 Total 

Frequency 106 173 141 80 500 

18 / 27


Data Tables (cont.) 

Contingency tables (or cross-tabulations) display two or more 

variables at once. The frequency listed at the intersection of the 

column and row tells the number of observations which meet both 

criteria, while the totals along the sides (marginal totals) provide 

frequency distributions. 

Class 

Gender Fresh. Soph. Junior Senior Total 

Female 58 61 63 65 247 

Male 64 64 67 58 253 

Total 122 125 130 123 500 

19 / 27


Pie Charts 

Pie charts represent proportion (percentage of total) as sections of 

a circular “pie”. The area of the “slice” is the same percentage of 

the total “pie” as the category. 

GPA 

Above A A B C D/F 

20 / 27


Pie Charts (cont.) 

The usage of pie charts is discouraged in statistics for the following 

reasons: 

Areas are difficult to compare between different shapes 

Angles are difficult to compare 

Enlarging a pie chart does not yield additional information 

Small portions are hard to see/compare 

What proportion do you think have a D/F compared with a C? 

21 / 27



GPA 


22 / 27



GPA 


16% 

10% 

16% 

25% 

33% 

23 / 27


Bar Charts 

Bar charts represent frequency by the height of the bar. Higher bar 

⇒ more observations in that category 

180 

160 

140 

120 

100 

80 

60 

40 

20 

GPA 

0 


24 / 27


Bar Charts (cont.) 

Compare this with the pie chart: 

Only comparing height–not shape, not angle, not area 

Horizontal lines can aid in height comparison 

Enlarging a bar chart makes the difference in height bigger 

Small portions still visible 

25 / 27


Word Clouds 

Word clouds display words or phrases, with font size proportional 

to usage/frequency. Not ideal, but hard to display phrases. 

Why not ideal? What could we do instead? 

26 / 27


Important Takeaways 

There are different kinds of data 

Qualitative/Quantitative 

Nominal/Ordinal/Interval/Ratio 

Discrete/Continuous 

Need to display data–hard to understand raw data, especially 

in large amounts 

Qualitative Data Displays 

Tables (distribution and contingency) 

Pie Charts 

Bar Charts 

Word Clouds 

Next time: Quantitative Data Displays 

27 / 27

Stat 20: Intro to Probability and Statistics - Lecture 3: Types of Data ...

Create successful ePaper yourself

Delete template?

Save as template?