Transcript PowerPoint Slides that accompany the lecture

Statistics
Describing Data Using Tables and Graphs
Assignment 2
Example Problems
Frequency Distributions
• Objective: Identify the class width, class
midpoints, and class boundaries for the given
frequency distribution
Daily Low
Temperature
(°F)
50-53
54-57
58-61
62-65
66-69
70-73
74-77
Frequency
1
3
5
11
7
7
1
Frequency Distributions
• Class width is the difference between two consecutive
lower class limits or two consecutive lower class
boundaries and thus 53, 52, 51, 50 is a width of 4
Daily Low
Temperature
(°F)
50-53
54-57
58-61
62-65
66-69
70-73
74-77
Frequency
1
3
5
11
7
7
1
Frequency Distributions
– Class midpoints are the values in the middle of the
class. Because there is no “exact” middle we find by
averaging the class width, that is (53-50)/2 = 1.5
• So each lower value, add 1.5 to get the midpoints of
51.5
55.5
59.5
63.5
67.5
71.5
75.5
Daily Low
Temperature
(°F)
50-53
54-57
58-61
62-65
66-69
70-73
74-77
Frequency
1
3
5
11
7
7
1
Frequency Distributions
– Class boundaries are the numbers used to separate the
classes, but without the gaps created by the class limits
• Find the center of the gaps and don’t forget about the lower
boundary
49.5
53.5
57.5
61.5
65.5
69.5
73.5
77.5
Daily Low
Temperature
(°F)
50-53
54-57
58-61
62-65
66-69
70-73
74-77
Frequency
1
3
5
11
7
7
1
Interpret Frequency Distributions
• Question: The data represents the daily
rainfall (in inches) for one month. Construct a
frequency distribution beginning with a lower
class limit of 0.00 and use a class width of
0.20. Does the frequency distribution appear
to be roughly a normal distribution?
Daily Rainfall
(in inches)
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
0.51
0
0
0.23
0
0.00-0.19
0.20-0.39
0.40-0.59
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39
Frequency
Interpret Frequency Distributions
• Answer: What I would do is put the data in
numerical ascending order first. Because the
frequency is the count and you want to
“count” how many data items there are in the
range 0.00-0.19. I have them highlighted
below (but notice how much easier it would
have been if they were sorted)
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
0.51
0
0
0.23
0
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
22
0.40-0.59
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39
Interpret Frequency Distributions
• Now continue to the 0.20-0.39
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
• I find 5 values in this range
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
22
5
0.40-0.59
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39
0.51
0
0
0.23
0
Interpret Frequency Distributions
• Then to 0.40-0.59
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
0.51
0
0
0.23
0
• I find two values. I also notice all that is left is
1.34 for I put this “one” in the last row
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
22
5
2
0
0
0
1
0.40-0.59
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39
Interpret Frequency Distributions
• For the second part of the problem:
– Does the frequency distribution appear to be
roughly a normal distribution?
• Answer: Remember graphically this would be
a bell curve. If I visually thought about 22
values in the tail end certainly this is not
normal. Normal would have more in the
middle and less in the ends.
– In other words No, the distribution is not
symmetric and the frequencies do not start off
low.
Graphing Frequency Distributions
• What if you wanted to actually
see the graph of this data in your
calculator?
– First you need to enter the data in
your calculator
• Press Stat / Edit and press Enter
Graphing Frequency Distributions
• You are now
looking at a list
where you can
enter each value
– Enter each value
from our example
and press enter
after each value
entered
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
0.51
0
0
0.23
0
Graphing Frequency Distributions
• You are now
looking at a list
where you can
enter each value
– Enter each value
from our example
and press enter
after each value
entered
0.35
0
0.19
0.18
0
0
0.24
0
0.56
0.17
0
0
0.02
0
0
0.21
0
0
0.02
0
0
1.34
0.23
0
0.11
0.51
0
0
0.23
0
Interpret Frequency Distributions
• Next we will set up the
Histogram Window
– Press Window
• We saw from our frequency
distribution that our values are
between 0 and 1.39. However, we
want to have a little room to right
and left
– I set my Xmin = -0.5 and Xmax = 1.45
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
0.40-0.59
0.60-0.79
22
5
2
0
0
0
1
0.80-0.99
1.00-1.19
1.20-1.39
Graphing Frequency Distributions
• The y values are the vertical direction and in
our case the frequencies
– These ranged from 0 to 22
• Again make a little more room as I set
mine to -0.5 and 22.5 for the
Ymin and Ymax
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
22
5
2
0
0
0
1
0.40-0.59
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39
Graphing Frequency Distributions
• Next we will set the Stat Plot
– Press 2nd and then Y= to get to
the Stat Plot
• The first plot should be selected
so press ENTER
Graphing Frequency Distributions
• Turn the Stat Plot On by pressing enter
– Down arrow and then to the right to
select histogram and press enter
– The Xlist: L1 is where the data is located
• Remember you typed this in the list 1 column
• Press Graph
Daily Rainfall
(in inches)
Frequency
0.00-0.19
0.20-0.39
0.40-0.59
22
5
2
0
0
0
1
0.60-0.79
0.80-0.99
1.00-1.19
1.20-1.39