Transcript Stats 2-2 / Microsoft Office PowerPoint Presentation

Frequency Distribution
Objectives:
Create Frequency Distributions
Analyze Frequency Distribution
What is a Frequency Distribution?
• Allows us to understand and interpret the
nature of the distribution of a data set.
• Shows how data is partitioned among
classes by listing the classes along with
the number of data values in each.
PULSE RATES (BEATS PER MINUTE)
of FEMALES
76
80
64
72
76
80
88
68
76
60
72
76
72
96
76
68
72
80
80
68
104
64
72
88
68
64
60
68
80
76
72
72
88
80
60
72
88
88
124
64
Creating a Frequency Distribution
Table
• Lower Class Limits: smallest numbers that can
belong to the different classes
• Upper Class Limits: largest numbers ...
• Class Boundaries: numbers used to separate
the classes, but w/out the gaps created by class
limits
• Class Midpoints: values in the middle of the
classes
• Class width: difference b/w 2 consecutive
lower/upper class boundaries
n
Procedure:
• Determine the number of classes
– Will either be given or found by
– ALWAYS ROUND UP!
n
Calculate the Class Width
• Round up for convenience
class width 
maximum
- minimum
# of classes
Lower Class Limit
• Select either the lowest data value or a
convenient value below the minimum as
the first lower class limit.
Cont...
• Using the class width and the first lower
class limit begin listing the lower class
limits in a vertical column by adding the
class width.
Adding the upper class limits
• Identify the corresponding upper class
limits to each class making sure that the
classes do not overlap
Finish by...
• Taking the total values in each class and
listing them is column number 2
Things to watch out for:
• Confusing the class width and the class
boundaries
– Class width is the difference between lower or
upper class limits!
• Make sure you include all classes, even
those with 0 data values.
• The sum of column 2 should be the # of
values in data set
Example using Female Pulse
Rates
• Step 1: Find total # of
classes
– n=40
40  6 . 324 ...
• Round up: There are 7
classes
Pulse Rate Frequency
Calculate Class Width
•
class width 
maximum
- minimum
# of classes
class width 
124 - 60
7
 9 . 142 ...  10
Begin filling in table
• Choose 60 as the first lower class limit
because it is both the minimum value and
a convenient value
• Add the class width and record in following
rows
Pulse Rate
60708090-
100110120-
Frequency
Identify corresponding UCL
• Make sure you leave
no gaps where
numbers would fit in.
Pulse Rate Frequency
60-69
70-79
80-89
90-99
100-109
110-119
120-129
Finish by...
• Calculating frequency
for each class
• All values should be
included totals should
match up!
Pulse Rate Frequency
60-69
12
70-79
14
80-89
11
90-99
1
100-109
1
110-119
0
120-129
1
Relative Frequency Tables
• Same Classes
• Sum must be close to 1
relative
frequency

class frequency
 all
frequencie
s
Relative frequency distribution
tables
Pulse Rate
Relative Frequency
60-69
30%
70-79
40%
80-89
27.5%
90-99
2.5%
100-109
2.5%
110-119
0
120-129
2.5%
Cumulative Frequency
• Replace lower class
limits with “less
than...”
• Add each cell to
previous cells
Pulse Rate
Frequency
Less than 70
12
Less than 80
26
Less than 90
37
Less than 100
38
Less than 110
39
Less than 120
39
Less than 130
40
Interpreting Frequency
Distributions
Normal Distribution (Bell Curve) within a
frequency distribution table:
Frequencies start low, increase in
frequency, then return to low.
Distribution is approximately symmetric
IQ Scores of 1000 Adults
IQ score
50-69
Freq
Normal Dist
24 frequencies start low...
70-89
228
90-109
490 increase to maximum...
110-129
232
130-149
Relatively symmetric
26 decrease to be come low again.
Last Digits of Female Pulse Rates
•
Last
digit
0
1
2
3
4
5
6
7
8
Freq
9
0
8
0
6
0
7
0
10
Randomly Selected Pennies
Wt. (grams) of pennies
2.40-2.49
2.50-2.59
2.60-2.69
2.70-2.79
2.80-2.89
2.90-2.99
3.00-3.09
3.10-3.19
Frequency
18
19
0
0
0
2
25
8