1. Class Data (Major) Ungrouped data:
Public Health
Other
Psychology
Cog Science
Biology
Biology
Psychology
Public Health
Other
Cog Science
Cog Science
Psychology
Other
Biology
Public Health
Other
Psychology
Public Health
Biology
Cog Science
Ungrouped data:
A set of scores or categories distributed individually, where the frequency for each individual score or category is counted.
Natural, distinct
Categories/groupings
What kind of data is this? What is the scale of measurement?

2. Class Data (Major)
Major
Count of Major
Psychology 22
Biology 17
Cognitive Science 12
Public Health
Other
Total 80
Notice: each category is represented by a different rectangle.
Also notice: each rectangle does not touch along the x-axis. This is meant to show that they are discrete, distinct categories.
A bar chart is a graphical display used to summarize the frequency of discrete and categorical data that are distributed in whole units or classes.

3. Class Data (Major)
Major
Count of Major
Psychology 22
Biology 17
Cognitive Science 12
Public Health
Other
Total 80
A graphical display is the shape of a circle that is used to summarize the relative percent of categorical data.

4. Class Data (Year) Natural, distinct Categories/groupings Ordered?
Sophomore
Senior
Freshman
Junior
Sophomore
Freshman
Junior
Sophomore
Junior
Freshman
Sophomore
Freshman
Junior
Senior
Natural, distinct
Categories/groupings
Ordered?
What kind of data is this? What is the scale of measurement?

5. Class Data (Year) Year Count of Year Freshman 11 Sophomore 60 Junior 7
Senior 2
Total 80

6. Definitions Grouped data: Interval:
A set of scores distributed into intervals, where the frequency of each score can fall into only one interval.
Interval:
A range of values within which the frequency of a subset of scores is contained.

7. Steps to Summarize Grouped Data
Step 1: Find the real range
The real range is one more than the difference between the largest and smallest value in a list of data
Step 2: Find the interval width
The interval width is the range of scores in each interval
There should be between 5 and 20 intervals.
Step 3: Construct the frequency distribution

8. Steps to Summarize Grouped Data
Step 1: Find the real range
The range is
= 65.
The real range is
= 66 94 84 95 65 90 62 92 58 88 86 97 96 73 93 91 64 71 78
100 87 85 47 35 81 69 53 77

9. Steps to Summarize Grouped Data (cont.)
Step 2: Find the interval width
Number of intervals is 6
Interval width is real range divided by the number of intervals: 66/6 = 11
Step 3: Construct the frequency distribution

10. Steps to Summarize Grouped Data (cont.)
Intervals
f(x)
90-100 17
79-89 10
68-78 5
57-67
46-56 2
35-45 1
Total 40
Intervals
f(x) 17 10 5 2 1
Total 40
Rules for a simple frequency distribution:
Each interval is defined
Each interval is equal length
No interval overlaps
Book version: slightly easier
to construct and understand
My version: used for
creating the visualization

11. Cumulative Frequency
Distributes the sum of frequencies across a series of intervals
Add from bottom up:
Discuss in terms of “less than”, “at or below” a certain value, or “at most”
Add from top down:
Discuss in terms of “greater than”, “at or above” a certain value, or “at least”
Intervals
f(x)
Cum. Freq. (bottom up)
Cum. Freq. (top down)
90-100 17 40
79-89 10 23 27
68-78 5 13 32
57-67 8 37
46-56 2 3 39
35-45 1
Total

12. Relative Frequency
Distributes the proportion of scores in each interval
Equals the frequency in an interval divided by the total number of frequencies
Often used to summarize large data sets
Intervals
f(x)
Relative Frequency
Cum. Rel. Frequency
90-100 17
0.425
1.000
79-89 10
0.250
0.575
68-78 5
0.125
0.325
57-67
0.200
46-56 2
0.050
0.075
35-45 1
0.025
Total 40

13. Class Data (Excitement)3 4 2 5 1 4 5 3 2 4 3 1 5 3 5 2 4 1
In the perspective of scores
on a continuum from 1 to 5,
categories/groupings arbitrary

14. Creating a Histogram Histogram: Rules for creating a histogram:
Summarizes the frequency of continuous, grouped (or ungrouped) data.
Rules for creating a histogram:
Rule 1:
Vertical rectangles represent each interval, and the height of the rectangle equals the frequency recorded for each interval.
Rule 2:
The base of each rectangle begins and ends at the upper and lower boundaries of each interval.
Rule 3:
Each rectangle touches adjacent rectangles at the boundaries of each interval.

15. Class Data (Excitement)
Intervals
f(x)
1-5 80
Total
Frequency =
Number of observations
80 observations between
0.5 and 5.5 (i.e., all data)
Not very useful
Intervals
f(x) 80
Total
Point out why we set the boundaries as .5s even though we don’t actually have that as options, clearer on next slide

16. Class Data (Excitement)
Intervals
f(x)
5-6 10
3-4 61
1-2 9
Total 80
More informative
e.g., 61 observations
between 2.5 and 4.5
(i.e., 3’s and 4’s)
Intervals
f(x) 10 61 9
Total 80

17. Class Data (Excitement)
Intervals
f(x) 5 10 4 17 3 44 2 6 1
Total 80
Even more informative
e.g., 10 observations
between 4.5 and 5.5
(i.e., 5’s)
Intervals
f(x) 10 17 44 6 3
Total 80

18. Class Data (Excitement)
Relative Frequency
= Frequency/Total
e.g. 10/80 = 0.125

19. Definitions Frequency polygon: Ogive:
A figure that summarizes the frequency of continuous data at the midpoint of each interval.
Ogive:
A figure that summarizes the cumulative frequency of continuous data at the upper boundary of each interval.

20. Class Data (Excitement)
Connect midpoints
of each class/group

21. Class Data (Excitement)
Frequency Polygon
by itself

22. Class Data (Excitement)
e.g., cumulative frequency up to 3.5 is = 53
Ogive always starts at 0 and ends at total

23. Class Data (Excitement)
e.g., cumulative relative frequency up to 3.5 is =
Relative Frequency Ogive always starts at 0 and ends at 1

24. Scatterplot Scatterplot (called a scattergram in the book):
A display of paired data points (x, y) that summarizes the relationship between two variables.
Data points are plotted to see whether a pattern emerges.

25. Measures on Central Tendency
The “center” of a distribution.
A measure of central tendency is a statistical measure that tends toward the center of a distribution.
They are used to locate a single score that is most representative or descriptive of all the scores in a distribution.
They can help us know if the distribution tends to be composed of high or low scores.
The types:
Mean
Median
Mode

26. Mode Most frequent value in a data set
53, 67, 75, 75, 84, 91, 91, 91, 94, 99
Mode = 91 (one mode)
53, 75, 75, 75, 84, 91, 91, 91, 94, 99
Mode = 75 and 91 (two modes)
53, 72, 73, 75, 84, 91, 92, 93, 94, 99
Mode = none (no mode)