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Section 2.2 Homework

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After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?

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If percentages are used, the sum should be 100%. If proportions are used, the sum should be 1.

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Identify the class width, class midpoints, and class boundaries for the given frequency distribution.
Daily Low
Temperature
(degrees°F)
40-42
43-45
46-48
49-51
52-54
55-57
58-60
Frequency
1
3
5
11
7
7
1
a) What is the class width?
b) What are the class midpoints?
c) What are the class boundaries?

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a) 3
b) 41, 44, 47, 50, 53, 56, 59
c) 39.5, 42.5, 45.5, 48.5, 51.5, 54.5, 57.5, 60.5

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Identify the class width, class midpoints, and class boundaries for the given frequency distribution.
Height (inches)
65.0-68.9
69.0-72.9
73.0-76.9
77.0-80.9
81.0-84.9
85.0-88.9
89.0-92.9
93.0-96.9
97.0-100.9
101.0-104.9
Frequency
4
25
9
1
0
0
0
0
0
1
a) What is the class width?
b) What are the class midpoints?
(Use ascending order. Round to two decimal places as needed.)
c) What are the class boundaries?
(Use ascending order. Round to two decimal places as needed.)

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a) 4
b) 66.95, 70.95, 74.95, 78.95, 82.95, 86.95, 90.95, 94.95, 98.95, 102.95
c) 64.95, 68.95, 72.95, 76.95, 80.95, 84.95, 88.95, 92.95, 96.95, 100.95,
104.95

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Does the frequency distribution appear to have a normal distribution? Explain.
Temperature (degrees°F)
40-44
45-49
50-54
55-59
60-64
65-69
70-74
Frequency
1
3
10
12
10
2
1

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Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric. Bell-shaped.

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How to solve for a relative frequency table.

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Look at both frequency tables and put 0 where data is missing. Find the total of both. Divide total by number given and multiply by 100.

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How to solve for a cumulative frequency distribution.

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rewrite the table as less than the lower class boundary of the next class. EX: 20-29, 30-39 you would use "less than 30" Make sure to add the frequencies less than the number next to the phrase "less than"

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Which characteristic of data is a measure of the amount that the data values vary?

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Variation

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Fill in the blank.
_______ are sample values that lie very far away from the majority of the other sample values.

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Outliers are sample values that lie very far away from the majority of the other sample values.

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Fill in the blank.
A _______ helps us understand the nature of the distribution of a data set.

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A frequency distribution helps us understand the nature of the distribution of a data set.

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Fill in the blank.
Class width is found by _______.

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subtracting a lower class limit from the next consecutive lower class limit.

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Fill in the blank.
In a _______ distribution, the frequency of a class is replaced with a proportion or percent.

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In a relative frequency distribution, the frequency of a class is replaced with a proportion or percent.

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Section 2.3 Homework

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The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?

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With a data set that is so small, the true nature of the distribution cannot be seen with a histogram.

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Fill in the blank.
The heights of the bars of a histogram correspond to _______ values.

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The heights of the bars of a histogram correspond to
frequency values.

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Fill in the blank.
The bars in a histogram _______.

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The bars in a histogram
touch.

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Fill in the blank.
A histogram aids in analyzing the _______ of the data.

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A histogram aids in analyzing the
shape of the distribution of the data.

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Fill in the blank.
A _______ histogram has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

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A relative frequency histogram has the same shape and horizontal scale as a histogram but the vertical scale is marked with relative frequencies instead of actual frequencies.

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Fill in the blank.
A(n) _______ distribution has a "bell" shape.

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A(n) normal distribution has a "bell" shape.

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Section 2.4 Homework

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A bar chart and a Pareto chart both use bars to show frequencies of categories of categorical data. What characteristic distinguishes a Pareto chart from a bar chart, and how does that characteristic help us in understanding the data?

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In a Pareto chart, the bars are always arranged in descending order according to frequencies. The Pareto chart helps us understand data by drawing attention to the more important categories, which have the highest frequencies.

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Fill in the blank.
A(n) _______ uses line segments to connect points located directly above class midpoint values.

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A(n) frequency polygon uses line segments to connect points located directly above class midpoint values.

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Fill in the blank.
A _______ is a graph of each data value plotted as a point.

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A dotplot is a graph of each data value plotted as a point.

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Fill in the blank.
We utilize statistical _______ to look for features that reveal some useful or interesting characteristics of the data set.

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We utilize statistical graphs to look for features that reveal some useful or interesting characteristics of the data set.

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Fill in the blank.
A _______ is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.

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A scatter-plot is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.

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Which of the following is NOT true about statistical graphs?

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They utilize areas or volumes for data that are one-dimensional in nature.

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Fill in the blank.
In a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as _______.

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In a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as
a nonzero axis.

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Fill in the blank.
When drawings of objects are used to depict data, false impressions can be made. These drawings are called _______.

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When drawings of objects are used to depict data, false impressions can be made. These drawings are called
pictographs.

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Which of the following is a common distortion that occurs in graphs?

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Using a two-dimensional object to represent data that are one-dimensional in nature

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Why is it important to learn about bad graphs?

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So that we can critically analyze a graph to determine whether it is misleading