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Data Analysis: Summarizing and Graphing Qualitative and Quantitative Data, Summaries of Advanced Data Analysis

This chapter from a statistics textbook covers the basics of summarizing and graphing both qualitative and quantitative data. Topics include raw data, variables, observational units, explanatory and response variables, classifying and summarizing qualitative data, and describing quantitative data using stem-and-leaf plots and histograms.

What you will learn

  • What is the purpose of using stem-and-leaf plots to describe quantitative data?
  • What is the difference between explanatory and response variables?
  • How do you calculate class relative frequency for qualitative data?

Typology: Summaries

2021/2022

Uploaded on 09/12/2022

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Chapter 2: Summarizing and Graphing
Data
More Basic Terms
Raw data --- numbers and category labels that
are collected, but not yet processed
Variable --- a characteristic that differs from
one individual to the next
Observational unit (observation) --- single
individual who participates in a study
2
Explanatory and Response Variables
Many questions are about the relationship
between two variables.
It is useful to identify one variable as the
independent variable (explanatory variable,
predictor, covariate) and the other variable as
the dependent variable (response variable).
Generally, the value of the independent variable
for an individual is thought to partially explain
the value of the dependent variable for that
individual.
3
Describing Qualitative Data
Class---a category into which qualitative data can
be classified
Class frequency---number of observations in the
data set falling in a given class
Class relative frequency---class frequency
divided by the total number of observations in the
data set
class frequency
class relative frequency = n
4
Describing Qualitative Data
Numerical summaries for one or two
categorical variables
Count how many fall into each category.
Calculate the percent in each category.
pf3
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1

Chapter 2: Summarizing and Graphing

Data

More Basic Terms

Raw data --- numbers and category labels that

are collected, but not yet processed

Variable --- a characteristic that differs from

one individual to the next

Observational unit (observation) --- single

individual who participates in a study

2

Explanatory and Response Variables

Many questions are about the relationship

between two variables.

It is useful to identify one variable as the

independent variable (explanatory variable,

predictor, covariate) and the other variable as

the dependent variable (response variable).

Generally, the value of the independent variable

for an individual is thought to partially explain

the value of the dependent variable for that

individual.

3

Describing Qualitative Data

Class ---a category into which qualitative data can

be classified

Class frequency ---number of observations in the

data set falling in a given class

Class relative frequency ---class frequency

divided by the total number of observations in the

data set

class frequency

class relative frequency =

n

4

Describing Qualitative Data

Numerical summaries for one or two

categorical variables

Count how many fall into each category.

Calculate the percent in each category.

5 6

Describing qualitative data

2_Rarely 8.2%

4_Mosttimes 19.0%

5_Always 55.4% (^) 3_Sometimes 13.6%

1_Never 3.8%

7

Describing qualitative data—Bar Graph

Seat Belt Use

0

20

40

60

Always Most TimesSometimes

Rarely Never

Usage

Percentage

8

If working with two variables, have the categories of the explanatory variable define the rows and compute row percentages.

13

Describing Quantitative Data

• Data arranged in

ascending order

• Easy to identify

individual measurements

14

Describing Quantitative Data

Histograms

¾ x -axis divided into intervals (best to use

equal class/interval sizes); between 6 and 15

intervals is a good number

¾ y -axis gives the frequency (count) or

relative frequency of the measurements that

fall into each interval

• Draw a bar with corresponding height

• Decide rule to use for values that fall

on the border between two intervals

15

Describing Quantitative Data

Histograms (continued)

¾ The proportion of total area under the

histogram that falls above a particular

interval on the x -axis equals the relative

frequency of measurements contained in the

interval

¾ Cannot identify individual measurements

16

Describing Quantitative Data--Histogram

50 60 70 80 90 100 temperature

0

10

20

30

40

Frequency

17

Describing Quantitative Data--Histogram

57 61 65 69 73 77 81 85 89 93 97 temperature

0

5

10

15

20

Frequency

18

WhiteBCC

19

3.1 3.6 4.1 4.6 5.1 5.6 6. RedBCC

0.

2.

5.

7.

10.

12.

15.

20

Hemoglobin

25

Describing Quantitative Data—Scatterplot

Daily High Temperatures

50

55

60

65

70

75

80

85

90

50 60 70 80 90 Predicted High (Degrees F)

Actual High Temp

(Degrees F)