Example: Ages of wealthiest people
Ages of the 50
Wealthiest people
worldwide (2009) Data:
89,
83,
78,
72,
66,
61,
54,
49,
36,
89,
83,
77,
69,
65,
60,
54,
47,
35
87,
82,
76,
69,
65,
59,
53,
46,
86,
81,
73,
68,
64,
58,
53,
44,
86,
80,
73,
67,
63,
57,
51,
43,
Class
35 - 41
42 - 48
49 - 55
56 - 62
63 - 69
70 - 76
77 - 83
84 - 90
85,
78,
73,
66,
61,
56,
51,
42,
(University of Utah)
Notes
Frequency distribution
table:
Frequency, f
2
5
7
7
10
5
8
6
Math 1040
1/6
Frequency Distribution
Notes
Main terms:
A frequency distribution is a table that shows classes of data entries
with frequencies, f , the number of data entries in the class.
The tables can be extended to summarize features such as
class midpoints, relative frequency, and cumulative frequency.
I
Each class must have upper and lower limits.
I
It is best when each class has the same class width.
I
All classes must cover the range of the data entries.
(University of Utah)
Math 1040
2/6
Frequency Distribution
Notes
Range: The difference between the maximum and minimum data
entries.
Ex: 89 - 35 = 54. The range is 54.
Number of classes: We decide between 5 and 20, whichever helps
detect patterns.
Ex: Choose 8 for this example.
Class width: Range ÷ Number of Classes.
Add 1 if you get a whole number. Otherwise, round up.
Ex: 54 ÷ 8 = 6.75. Round 6.75 ↑ 7. If the number of classes was 9,
54 ÷ 9 = 6, and then use ↑ 7 as the class width again.
(University of Utah)
Math 1040
3/6
Frequency Distribution
Notes
Class limits: Use the minimum data entry as the first class lower
limit. Then add the class width to get the next class lower limits.
Find the first class upper limit. Classes cannot overlap! The add the
class width to get the next class upper limits.
Ex: Min = 35. Add 7 each time. The lower limits for each class are
35, 42, 49, 56, 63, 70, 77, 84.
The first class lower limit is 41. The upper limits for each class are
41, 48, 55, 62, 69, 76, 83.
Count the entries for each class range. The total frequency for each
class is the frequency, f used for the table.
(University of Utah)
Math 1040
4/6
Additional Features
Notes
Class midpoints are averages of the class lower limit and class upper
limit.
I
Each class has a midpoint.
I
Find the first midpoint, then add the class width to get the next.
I
We will use the midpoints as lables for a graph.
Relative frequency of a class is the percentage of data entries that are
in each class.
Cumatlive frequency of a class is the sum of frequencies of that class
and each previous class frequency.
Relative cumulative frequency of a class is the sum of the relative
frequency of that class and the relative frequency of each previous
class.
(University of Utah)
Math 1040
5/6
Assignment
Notes
For May 28:
I
Homework §2.1: #29, #30 (due May 30)
Suggested Exercises: 2, 3, 4, 5, 15, 17
You should be able to:
I
Construct a frequency distribution from a data set.
I
Terms: limits, midpoints, relative frequencies,
cumulative frequencies, boundaries.
(University of Utah)
Math 1040
6/6