Work through the notes

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Work through the notes Then complete the class
work next to this document on the website For
the last page of the class work you will have to
roll two dice. There are several websites that
allow you to do this virtually two of them are
below https//www.math.duke.edu/education/postcal
c/probability/dice/index.html http//www.math.csu
sb.edu/faculty/stanton/m262/intro_prob_models/intr
o_prob_models.html
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Objectives
Find measures of central tendency and measures of
variation for statistical data. Examine the
effects of outliers on statistical data.
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Vocabulary
expected value probability distribution variance s
tandard deviation outlier
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Recall that the mean, median, and mode are
measures of central tendencyvalues that describe
the center of a data set.
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Example 1 Finding Measures of Central Tendency
Find the mean, median, and mode of the data.
deer at a feeder each hour 3, 0, 2, 0, 1, 2, 4
Mean
Median
0 0 1 2 2 3 4
2 deer
Mode
The most common results are 0 and 2.
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Check It Out! Example 1a
Find the mean, median, and mode of the data set.
6, 9, 3, 8
Mean
Median
3 6 8 9
Mode
None
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Check It Out! Example 1b
Find the mean, median, and mode of the data set.
2, 5, 6, 2, 6
Mean
Median
2 2 5 6 6
5
Mode
2 and 6
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A weighted average is a mean calculated by using
frequencies of data values. Suppose that 30
movies are rated as follows
weighted average of stars
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For numerical data, the weighted average of all
of those outcomes is called the expected value
for that experiment.
The probability distribution for an experiment is
the function that pairs each outcome with its
probability.
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Example 2 Finding Expected Value
The probability distribution of successful free
throws for a practice set is given below. Find
the expected number of successes for one set.
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Example 2 Continued
Use the weighted average.
Simplify.
The expected number of successful free throws is
2.05.
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Check It Out! Example 2
The probability distribution of the number of
accidents in a week at an intersection, based on
past data, is given below. Find the expected
number of accidents for one week.
Use the weighted average.
expected value 0(0.75) 1(0.15) 2(0.08)
3(0.02)
0.37
Simplify.
The expected number of accidents is 0.37.
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A box-and-whisker plot shows the spread of a data
set. It displays 5 key points the minimum and
maximum values, the median, and the first and
third quartiles.
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The quartiles are the medians of the lower and
upper halves of the data set. If there are an odd
number of data values, do not include the median
in either half.
The interquartile range, or IQR, is the
difference between the 1st and 3rd quartiles, or
Q3 Q1. It represents the middle 50 of the data.
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Example 3 Making a Box-and-Whisker Plot and
Finding the Interquartile Range
Make a box-and-whisker plot of the data. Find the
interquartile range. 6, 8, 7, 5, 10, 6, 9, 8, 4
Step 1 Order the data from least to greatest. 4,
5, 6, 6, 7, 8, 8, 9, 10
Step 2 Find the minimum, maximum, median, and
quartiles.
4, 5, 6, 6, 7, 8, 8, 9, 10
Mimimum
Median
Maximum
Third quartile 8.5
First quartile 5.5
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Example 3 Continued
Step 3 Draw a box-and-whisker plot.
Draw a number line, and plot a point above each
of the five values. Then draw a box from the
first quartile to the third quartile with a line
segment through the median. Draw whiskers from
the box to the minimum and maximum.
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Example 3 Continued
IRQ 8.5 5.5 3
The interquartile range is 3, the length of the
box in the diagram.
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Check It Out! Example 3
Make a box-and-whisker plot of the data. Find the
interquartile range. 13, 14, 18, 13, 12, 17, 15,
12, 13, 19, 11, 14, 14, 18, 22, 23
Step 1 Order the data from least to greatest. 11,
12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18, 18,
19, 22, 23
Step 2 Find the minimum, maximum, median, and
quartiles.
11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18,
18, 19, 22, 23
Mimimum
Median
Maximum
First quartile 13
Third quartile 18
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Check It Out! Example 3 Continued
Step 3 Draw a box-and-whisker plot.
IQR 18 13 5
The interquartile range is 5, the length of the
box in the diagram.
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Example 1 Wildlife Application
A researcher is gathering information on the
gender of prairie dogs at a wildlife preserve.
The researcher samples the population by catching
10 animals at a time, recording their genders,
and releasing them.
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Since there were 24 males in the sample, and 16
females, he estimates that the ratio of males
tofemales is 32.
Continued Example 1 Wildlife Application
How can he use this data to estimate the ratio of
males to females in the population?
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Check It Out! Example 1
Identify the population and the sample.
1. A car factory just manufactured a load of
6,000 cars. The quality control team randomly
chooses 60 cars and tests the air conditioners.
They discover that 2 of the air conditioners do
not work.
population 6,000 total cars sample 60 cars
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Example 2A Identifying Potentially Biased Samples
Decide whether each sampling method could result
in a biased sample. Explain your reasoning.
A. A survey of a citys residents is conducted by
asking 20 randomly selected people at a grocery
store whether the city should impose a beverage
tax.
Residents who do not shop at the store are
underrepresented, so the sample is biased.
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Example 2B Identifying Potentially Biased Samples
B. A survey of students at a school is conducted
by asking 30 randomly selected students in an
all-school assembly whether they walk, drive, or
take the bus to school.
No group is overrepresented or underrepresented,
so the sample is not likely to be biased.