Transcript 2.2 Power Point

Chapter 2: Organizing
Data
Section 2: Frequency Distribution
and Histograms
Frequency Distribution
Lists the number of occurrences for
each category of data
Classes
Categories of data created by using
intervals of numbers

Usually 5 to 15 classes.
Class Width
The difference between consecutive lower
class limits
To find the class width…
1. largest data value – smallest data value
desired number of classes
2.
Increase result to next whole number
Class Limits
The smallest value
within the class.
The largest value
within the class .
Relative Frequency
Distribution
the relative
frequency is listed,
found by dividing the
frequency (f) of each
class by the sum of all
the frequencies (n).
class frequency (f)
total of all frequencies (n)
Class Mark (Mid-Point)
The number halfway between the lower
and upper class limits of a class.
To find the class mark…
lower class limit + upper class limit
2
Graphic representations of
(Grouped) Frequency Distributions
Histogram- A type of bar graph.
- Horizontal axis represents classes by labeling
the class boundaries
- vertical axis represents frequency or relative
frequency
- no space between bars

- bars must be the same width
- width of bar represents a quantitative value,
rather than a category
Class Boundary
the halfway point between the upper
limit of one class and the lower limit of
the next class

used as endpoints of the bars in a
histogram
Fr
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q
u
e
n
c
y
Three Classes
Histogram Examples
(Cont).
frequencyFive Classes
F
F
F
F
F
F
Ten Classes
F
F
F
F
F
F
F
Frequency Polygon
type of line graph, horizontal axis
labeled with class marks, vertical axis
represents frequencies
Frequency Polygon
Relative frequency distribution for Scores on
a Scientific Achievement Test
Limits
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85-89
Tallies
II
III
IIIII I
IIII
IIIII IIII
IIIII III
III
IIII
I
Frequency
2
3
6
4
9
8
3
4
1
Relative
Frequency
Relative frequency distribution for Scores on
a Scientific Achievement Test
Limits
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85-89
Tallies
II
III
IIIII I
IIII
IIIII IIII
IIIII III
III
IIII
I
Frequency
2
3
6
4
9
8
3
4
1
Relative
Frequency
0.05
0.075
0.15
0.10
0.225
0.20
0.075
0.10
0.025
Uniform/Rectangular
Distribution
Number of Students
Number of Students in Math Classes
35
30
25
20
15
10
5
0
Probability & Statistics
Transition to College
Math
Classes
Advanced Math II
Bell
Shaped/Symmetrical
Distribution
Students' Grades on a Math Final
Number of Students
12
10
8
6
4
2
0
A
B
C
Grade
D
F
Skewed to the Left
Distribution
Number of Students
Grade Level of Students in TCM
16
14
12
10
8
6
4
2
0
freshman
junior
sophomore
Grade
senior
Skewed to the Right
Distribution
Number of Students
Grade Level of Students in Algebra I
16
14
12
10
8
6
4
2
0
freshman
sophomore
Grade
junior
senior