EXPLORING DATA

ST101 – DR. ARIC LABARR


Why do we organize and explore our data?

A lot of insights can be drawn from just organizing, exploring, and looking at your data.

Different types of data need to be summarized differently.

EXPLORATION


TYPES OF VARIABLES

There are two main types of variables:

Qualitative – data with a measurement scale inherently categorical.

Quantitative – data that are numeric and define a value or quantity.


EXPLORING DIFFERENT TYPES OF VARIABLES

…

Date

Weekday

Season

Weather Type

Temperature

(°F)

Humidity 

(%)

# Casual Users

# Registered Users

1/1/2011

Saturday

Winter

Misty

46.7

80.6

331

654

1/2/2011

Sunday

Winter

Misty

48.4

69.6

131

670

1/3/2011

Monday

Winter

Clear / 

Partly Cloudy

34.2

43.7

120

1229

1/4/2011

Tuesday

Winter

Clear / 

Partly Cloudy

34.5

59.0

108

1454

1/5/2011

Wednesday

Winter

Clear / 

Partly Cloudy

36.8

43.7

82

1518


EXPLORING DIFFERENT TYPES OF VARIABLES

…

Date

Weekday

Season

Weather Type

Temperature

(°F)

Humidity 

(%)

# Casual Users

# Registered Users

1/1/2011

Saturday

Winter

Misty

46.7

80.6

331

654

1/2/2011

Sunday

Winter

Misty

48.4

69.6

131

670

1/3/2011

Monday

Winter

Clear / 

Partly Cloudy

34.2

43.7

120

1229

1/4/2011

Tuesday

Winter

Clear / 

Partly Cloudy

34.5

59.0

108

1454

1/5/2011

Wednesday

Winter

Clear / 

Partly Cloudy

36.8

43.7

82

1518

Qualitative – explore within a category or across categories.


Qualitative – explore within a category or across categories.

Example questions:

What do Saturdays look like?

What do clear days look like in comparison to rainy days?

Is the winter different than the summer?

EXPLORING QUALITATIVE DATA


EXPLORING DIFFERENT TYPES OF VARIABLES

…

Date

Weekday

Season

Weather Type

Temperature

(°F)

Humidity 

(%)

# Casual Users

# Registered Users

1/1/2011

Saturday

Winter

Misty

46.7

80.6

331

654

1/2/2011

Sunday

Winter

Misty

48.4

69.6

131

670

1/3/2011

Monday

Winter

Clear / 

Partly Cloudy

34.2

43.7

120

1229

1/4/2011

Tuesday

Winter

Clear / 

Partly Cloudy

34.5

59.0

108

1454

1/5/2011

Wednesday

Winter

Clear / 

Partly Cloudy

36.8

43.7

82

1518

Quantitative – explore center, spread, and “look” of variables.


Quantitative – explore center, spread, and “look” of variables.

Example questions:

What is the typical temperature in my data?

Is the number of users trending up or down?

What is the range of humidity values? Are they narrow or very spread out?

EXPLORING QUANTITATIVE DATA


A lot of insights can be drawn from just organizing, exploring, and looking at your data.

Different types of data need to be summarized differently.

Qualitative – explore within a category or across categories.

Quantitative – explore center, spread, and “look” of variables.


SUMMARY


DISPLAYING QUALITATIVE DATA

EXPLORING DATA


Qualitative – explore within a category or across categories.

Example questions:

What do Saturdays look like?

What do clear days look like in comparison to rainy days?

Is the winter different than the summer?

EXPLORING QUALITATIVE DATA


Qualitative – explore within a category or across categories.

Different graphs are used for different tasks:

Pie chart – comparison across all categories (distribution of categories).

Bar chart – comparison across specific categories

Regular

Side-by-side

Stacked

EXPLORING QUALITATIVE DATA


PIE CHART

Pie chart – graph in which a circle is divided into sections that each represent a proportion of the whole.

Best used when looking to show entire distribution (or set of categories) for a qualitative variable.


PIE CHART

Pie chart – graph in which a circle is divided into sections that each represent a proportion of the whole.

Best used when looking to show entire distribution (or set of categories) for a qualitative variable.

Donut chart is basically the same thing with the center missing.



PIE CHART

Donut charts allow us to compare different groups’ distributions across all categories.

Casual

Registered


BAR CHART

Bar chart – numerical values of variables are represented by the height or length of lines or rectangles of equal width.

Best used when looking to compare specific categories to each other.


BAR CHART

Bar chart – numerical values of variables are represented by the height or length of lines or rectangles of equal width.

Best used when looking to compare specific categories to each other.

Stacked bar charts break down the first categories into subcategories.


BAR CHART

Bar chart – numerical values of variables are represented by the height or length of lines or rectangles of equal width.

Best used when looking to compare specific categories to each other.

Side-by-side bar charts look at these comparisons across multiple categories.


Qualitative – explore within a category or across categories.

Pie chart – graph in which a circle is divided into sections that each represent a proportion of the whole.

Bar chart – numerical values of variables are represented by the height or length of lines or rectangles of equal width.


SUMMARY


DISPLAYING QUANTITATIVE DATA

EXPLORING DATA


Quantitative – explore center, spread, and “look” of variables.

Example questions:

What is the typical temperature in my data?

Is the number of users trending up or down?

What is the range of humidity values? Are they narrow or very spread out?

EXPLORING QUANTITATIVE DATA


Quantitative – explore center, spread, and “look” of variables.

Different graphs are used for different tasks:

Line graph – look at how a variable changes over time.

Scatterplot – comparison between different quantitative variables.

EXPLORING QUANTITATIVE DATA


LINE GRAPH

Line graph – uses lines to connect individual data points over time.

Best when wanting to see how things change across time.


LINE GRAPH

Line graph – uses lines to connect individual data points over time.

Best when wanting to see how things change across time.


LINE GRAPH

Line graph – uses lines to connect individual data points over time.

Best when wanting to see how things change across time.


LINE GRAPH

Line graph – uses lines to connect individual data points over time.

Best when wanting to see how things change across time.


SCATTERPLOT

Scatterplot – the values of two variables are plotted along two axes, the pattern of the resulting points revealing any relationship present.

Best used when trying to explore relationships between two quantitative variables.


SCATTERPLOT

Scatterplot – the values of two variables are plotted along two axes, the pattern of the resulting points revealing any relationship present.

Best used when trying to explore relationships between two quantitative variables.


Quantitative – explore center, spread, and “look” of variables.

Line graph – uses lines to connect individual data points over time.

Scatterplot – the values of two variables are plotted along two axes, the pattern of the resulting points revealing any relationship present.


SUMMARY


DESCRIBING CENTER

EXPLORING DATA


When exploring data, a good summary of a variable might be what a “typical” value of that variable would look like.

What is “typical” really mean?

Qualitative variable – most common category.

Quantitative variable – focus on the center of the values of the variable.


“TYPICAL” VALUE


MODE

Mode – the mode of a variable is the most common value.

Typically reported with qualitative variables more than quantitative variables.


In our data, the “typical” weather day (according to mode) is clear or cloudy.


MEAN

Mean – the mean of a variable is the sum of all the values divided by the number of values.


 

Number of the 

observations in

the sample


MEAN

Mean – the mean of a variable is the sum of all the values divided by the number of values.


 

Sum of the values

of the n observations


MEAN

Mean – the mean of a variable is the sum of all the values divided by the number of values.



 


MEAN

Mean – the mean of a variable is the sum of all the values divided by the number of values.


In our data, the “typical” weather day (according to mean) is 59.51°F.



 


MEDIAN

Median – value in the middle when the data items are arranged in ascending order.

For an odd number of observations:


26

30

27

22

24

29

13

Original Data


MEDIAN

Median – value in the middle when the data items are arranged in ascending order.

For an odd number of observations:


26

30

27

22

24

29

13

Original Data

13

22

24

26

27

29

30

Ascending Order


MEDIAN

Median – value in the middle when the data items are arranged in ascending order.

For an odd number of observations:


26

30

27

22

24

29

13

13

22

24

26

27

29

30

Median


MEDIAN

Median – value in the middle when the data items are arranged in ascending order.

For an even number of observations:


26

30

27

22

24

29

13

13

22

24

26

27

29

30

 

27

27


MEDIAN

Median – value in the middle when the data items are arranged in ascending order.


In our data, the “typical” weather day (according to median) is 59.76°F.



MEAN VS. MEDIAN

Whenever a data set has extreme values, the median is the preferred measure of center.

Mean is bothered by extreme values, while median is not.


26

30

27

22

24

29

13

13

22

24

26

27

29

30

Median = 26

Mean = 24.42


MEAN VS. MEDIAN

Whenever a data set has extreme values, the median is the preferred measure of center.

Mean is bothered by extreme values, while median is not.


26

300

27

22

24

29

13

13

22

24

26

27

29

300

Median = 26

Mean = 63


When exploring data, a good summary of a variable might be what a “typical” (or center) value of that variable would look like.

Mode – the mode of a variable is the most common value.

Mean – the mean of a variable is the sum of all the values divided by the number of values.

Median – value in the middle when the data items are arranged in ascending order.


SUMMARY


DESCRIBING SPREAD

EXPLORING DATA


Center can only get you so far with describing a variable’s “typical” value.

Typically, we also consider how spread out a data set is as well.

This is called variability or dispersion.



MEASURES OF VARIABILITY


RANGE

Range – difference between the largest and smallest values.


Highest temperature = 90.5°F

Lowest temperature = 22.6°F



RANGE

Range – difference between the largest and smallest values.


Highest temperature = 90.5°F

Lowest temperature = 22.6°F


Range = 90.5 – 22.6 = 67.9°F


RANGE

Range – difference between the largest and smallest values.

Very sensitive to observations with extreme values as it only focuses on the largest and smallest values in the data.


Highest temperature = 90.5°F

Lowest temperature = 22.6°F


Range = 90.5 – 22.6 = 67.9°F


RANGE

Range – difference between the largest and smallest values.


In our data, the “spread” of temperature (according to range) is 67.9°F.

Highest temperature = 90.5°F

Lowest temperature = 22.6°F


Range = 90.5 – 22.6 = 67.9°F


VARIANCE

Variance – measure of dispersion around the mean of the data set.

Average of the squared distances between each data value and mean.


 


VARIANCE

Variance – measure of dispersion around the mean of the data set.

Average of the squared distances between each data value and mean.


Temperature

(°F)

46.7

-12.8

163.8

48.4

-11.1

123.2

34.2

-25.3

640.1

34.5

-25.0

625.0

36.8

-22.7

515.3

…

…

…

72.5

13.0

169.0

 


VARIANCE

Variance – measure of dispersion around the mean of the data set.

Average of the squared distances between each data value and mean.


Temperature

(°F)

46.7

-12.8

163.8

48.4

-11.1

123.2

34.2

-25.3

640.1

34.5

-25.0

625.0

36.8

-22.7

515.3

…

…

…

72.5

13.0

169.0

 

Add together and divide by 730 (= 731 – 1)


VARIANCE

Variance – measure of dispersion around the mean of the data set.


In our data, the “spread” of temperature (according to variance) is 239.8°F squared.


Temperature

(°F)

46.7

-12.8

163.8

48.4

-11.1

123.2

34.2

-25.3

640.1

34.5

-25.0

625.0

36.8

-22.7

515.3

…

…

…

72.5

13.0

169.0


VARIANCE

Variance – measure of dispersion around the mean of the data set.


In our data, the “spread” of temperature (according to variance) is 239.8°F squared.


Temperature

(°F)

46.7

-12.8

163.8

48.4

-11.1

123.2

34.2

-25.3

640.1

34.5

-25.0

625.0

36.8

-22.7

515.3

…

…

…

72.5

13.0

169.0

???


STANDARD DEVIATION

The problem with variance is that it is in terms of squared units of the data.

To correct for this, we have the standard deviation, which is just the square root of the variance.


 


STANDARD DEVIATION

The problem with variance is that it is in terms of squared units of the data.

To correct for this, we have the standard deviation, which is just the square root of the variance.

In our data, the “spread” of temperature (according to standard deviation) is 15.5°F.



 


Variance (and standard deviation) possess two common characteristics:

If the variance equals zero, then all of the data in the data set has the same value.

All measures of spread are positive (or nonnegative if zero spread) in value.


2 CHARACTERISTICS OF VARIANCE


Don’t only look at center, but also variability of a variable.

Range – difference between the largest and smallest values.

Variance – measure of dispersion around the mean of the data set.

Standard deviation – the square root of the variance (helps with units of variance).

SUMMARY


Last modified: Monday, October 17, 2022, 1:01 PM