Chpt 2 - Organizing and Graphing Data

Question 1

Why do we need to learn how to organize data?

Answer 1

Without organizing the raw data, we cannot obtain useful information

Question 2

What is data that is non-numerical, such as gender called?

Answer 2

Categorical

Also called qualitative

Question 3

What is data that is numerical, such as the ages of the people involved in the study?

Answer 3

Numerical

Also called quantitative

Question 4

What is a variable?

Answer 4

A variable is a characteristic that varies from one person or thing to another.

Examples include gender, age, marriage status, number of email accounts, monthly salary, height, weight, etc.

Basically all of the headings of the columns is considered a variable

Question 5

What is the formal definition of data?

Answer 5

The values of a variable in a sample.

Question 6

How can we categorize variables? How can these be further broken down?

Answer 6

Categorical (qualitative) or Numerical (quantitative)

Numerical variables can be further broken down to:
Discrete or continuous

Categorical variables can be further broken down to:
Nominal or ordinal

Question 7

What are the types of numerical variables?

Answer 7

Discrete or continuous

Question 8

What is a discrete variable? Give some examples

Answer 8

A numerical variable whose values can be listed

An example might be how many email addresses do you have? If you say 4, the person would be able to list out their 4 email addresses.

Question 9

What is a continuous variable? Give some examples

Answer 9

A numerical variable whose possible values from some interval of numbers

Height is a continuous variable because its possible value is any number from 40cm to 300cm. While the height may not change once we are adults, we often don’t measure it in just feet….we use feet and inches, making this continuous as a value

Other examples are weight, temperature, and length.

Question 10

Is age a discrete or continuous variable?

Answer 10

Age is also considered discrete because while you are constantly aging, we only list out age as whole numbers.

Anytime we are counting such as 1, 2, 3, it is considered discrete

That being said, with babies, we do measure the partial intervals, such as 1.5 years, or kids are only 5 days away from their next birthday…this context with looking forward and using increments, its considered a continuous variable

Question 11

What is a non-numerical variable that has no specified order called?

Give an example

Answer 11

Nominal

Marital status…there is no actual order in life that is set, you may get married, be common law, get separated, be single etc. without a defined order that everyone follows

Question 12

What is a non-numerical variable that has an order called?

Give an example

Answer 12

Ordinal

In many studies, there may be very like, like, neutral, dislike, or very dislike

Question 13

If in a study, they coded females as 1 and males as 2, does this make it a numerical variable?

How can you test if the value is numerical or non-numerical?

Answer 13

No, it’s still a categorial variable because the numbers are meaningless and have no mathematical meaning

To check, do some basic math operations, if it makes sense it’s a numerical variable, if not, it is a non-numerical value. For example, if females are 1 and males are 2, you cannot add two females together to make 1 male. haha

Question 14

What is the purpose of organizing data?

Answer 14

To analyze the distribution of a variable

Question 15

What methods can we use to organize categorical data?

Answer 15

Numerical methods (frequency and relative frequency tables)

Graphical methods (pie charts and bar charts that help visualize the frequency/relative frequency tables)

Question 16

What is the distribution of a variable?

Answer 16

A table or formula (he also said graph) that tells us:

1.What values this variable takes

2. How often it takes these values in a population

Question 17

If we are interested in the distribution of gender, what would we need to know?

Answer 17

1. What values this variable takes (so male/female)
2. How often it takes these values in a population (so number of males and number of females)

We might also include transmen, transwomen, and nonbinary as other values, this would mean that we would need to also know the number of transmen, transwomen, and nonbinary people exist in the population

Question 18

What is frequency?

What is the frequency of genders if the sample of 10 students has 6 girls and 4 boys in it?

Answer 18

A numerical method or organizing categorical data

It’s counting :) It’s the number of times a particular distinct value of a variable occurs in a sample

Frequency of males is 4
Frequency of females is 6

Question 19

What is relative frequency?

What is the relative frequency of genders if the sample of 10 students has 6 girls and 4 boys in it?

Answer 19

A numerical method of organizing categorical data

It’s the ratio of the frequency to the sample size. The relative frequency of a particular distinct value of a variable shows the percentage of this value occurs in a sample

Relative frequency = frequency/sample size

Females: 6/10 or 60%
Males: 4/10 or 40%

Question 20

Once we have determined the frequencies or relative frequencies, we can make a frequency/relative frequency table to show the distribution of the data. What are the steps to this?

Give an example using the possible genders of a group of 10 students with 6 women and 4 men

Answer 20

1. List out all the possible distinct values (male, female)
2. Find the frequencies (f) and relative frequencies (f/n) of the distinct values
   Females - f=6, f/n=6/10
   Males - f=4, f/n=4/10
   (this would be listed in a simple table…but I can’t put one in here)

Question 21

What are the graphical methods used to organize categorical data?

Answer 21

Pie charts

Bar charts

Question 22

What are the numerical methods to organize categorical data

Answer 22

Frequency/relative frequency tables

Question 23

What is pie chart?

Answer 23

A disk divided into wedge-shaped pieces proportional to the relative frequencies of the categorical data

Once slice is allotted for each category and the angle of the slice = relative frequency x 360 degrees

Question 24

A study of 10 students showed that 6 liked rom-com movies. How would this be expressed on a pie chart?

Answer 24

f = 6
f/n = 6/10 or 60%

Equation for pie chart:
angle = f/n x 360
angle = 0.60 x 360
angle = 216 degrees

Question 25

What is the notation for frequency?

Answer 25

f

Question 26

What is the notation for relative frequency?

Answer 26

f/n

Question 27

What is a bar chart?

Answer 27

A display of the distinct values of categorical data on a horizontal axis and the relative frequencies or frequencies (depending on what we want) of those values on a vertical axis

One bar is for one category

The height of the bar = relative frequency, or frequency, of a value (so we might have a frequency of 6, or a relative frequency of 0.6, depending on what we want to present)

Bars should be positioned so that they DO NOT TOUCH each other

Question 28

What is the difference between frequency/relative frequency tables and contingency tables?

Answer 28

Frequency and relative frequency tables summarize information of a SINGLE (univariate) categorical data

Contingency tables summarize information of TWO SETS (bivariate) of categorical data

Question 29

What method will help us answer the question of are there more divorced female residents or more divorced male residents of a sample?

What would this look like?

Answer 29

Contingency table

There are TWO SETS of data to be examined, gender and marital status

Gender and Marital status would both be titles; under gender we would split males to females, and then under marital status, we would use each type of status as a subheading (married, divorced etc.). We would count each group of participants to summarize the totals. So how many females are married, how many males etc. to fill in the tables. The totals would be counted both horizontally and vertically

Question 30

What are contingency tables?

Answer 30

Tables that allow us to summarize and analyze the relationship between TWO variables

Question 31

What is the relationship between 2 variables?

Answer 31

Association

Question 32

What is an assocaiton?

Answer 32

The relationship between 2 variables

Question 33

How do we know 2 variables are associated?

Answer 33

If knowing the values of one of the variables tells us something about the values of the other variables

Question 34

What are possible values of seasons? What about weather?

Are these 2 variables associated? explain.

Answer 34

Season - spring, summer, fall, winter

Weather - sunny, cloudy, snowy, windy, thunder, raining etc.

Yes they are associated. Given the information about the season, we know more about the weather. Like knowing it is cold and snowy in the winter

Question 35

What are possible values of clothing size? What about GPA?

Are these 2 variables associated? explain

Answer 35

Clothing size - S, M, L, XL

GPA - 0.00-4.00

No they are not associated because knowing your clothing size tells us nothing about GPA

Question 36

What are are some of the ways we can further examine the relationship between 2 variables if it is difficult to observe in a contingency table?

Answer 36

Apply other statistical methods such as side-by-side bar or pie charts, stacked bar charts, etc.