Elem Stat- Section 2

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Section 2.2 Homework

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

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

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?

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

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.)

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

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

​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.

How to solve for a relative frequency table.

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.

How to solve for a cumulative frequency distribution.

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"

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

Variation

Fill in the blank.

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

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

Fill in the blank.

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

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

Fill in the blank.

Class width is found by​ _______.

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

Fill in the blank.

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

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

Section 2.3 Homework

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?

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

Fill in the blank.

The heights of the bars of a histogram correspond to​ _______ values.

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

Fill in the blank.

The bars in a histogram​ _______.

The bars in a histogram touch.

Fill in the blank.

A histogram aids in analyzing the​ _______ of the data.

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

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.

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.

Fill in the blank.

​A(n) _______ distribution has a​ "bell" shape.

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

Section 2.4 Homework

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?

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.

Fill in the blank.

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

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

Fill in the blank.

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

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

Fill in the blank.

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

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

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.

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.

Which of the following is NOT true about statistical​ graphs?

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

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​ _______.

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.

Fill in the blank.

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

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

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

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

Why is it important to learn about bad​ graphs?

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

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