Math 20: Foundations FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and z-scores.
FM20.7 Demonstrate understanding of the interpretation of
statistical data, including: confidence intervals, confidence
levels, margin of error. G. You Can use Statistics to Make Many
Important Decisions
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Getting Started! Comparing Salaries p. 208
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What do YOU Think? p. 209
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Outlier - A value in a data set that is very different from
other values in the set.
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1. Sifting Through the Data FM20.6 Demonstrate an understanding
of normal distribution, including standard deviation and
z-scores.
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Mean, median and mode are about the same for both. However, the
range for X is more than double Y. Y batteries are closer to mean
on the line plot. Brand X has 4 extreme outliers. Brand Y seems
like the safer choice.
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Dispersion - A measure that varies by the spread among the data
in a set; dispersion has a value of zero if all the data in a set
is identical, and it increases in value as the data becomes more
spread out.
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Reflection p.210
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Summary p.211
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Practice Ex. 5.1 (p.211) #1-3
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2. Frequency Tables, Polygons and Histograms FM20.6 Demonstrate
an understanding of normal distribution, including standard
deviation and z-scores.
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2. Frequency Tables, Polygons and Histograms
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Frequency Table How to select you intervals?
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We could also use a Histogram or a Polygon Graph (line graph)
to solve this problem. Lets use a new frequency table to solve
using the Histogram or a Polygon Graph
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Histogram
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Frequency Polygon
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We use a different interval width in our frequency table then
we did with our two graphs. How did this affect the
distribution?
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If we used an interval width of 200 would that have made it
easier to see the flood years in our frequency?
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Would 2000 be a better interval?
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Example 2
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What other factors should be considered besides the rickter
scale reading?
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Summary p.220
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Practice Ex. 5.2 (p. 221) #1-9 #3-12
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3. Standard Deviation FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
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3. Standard Deviation Deviation - The difference between a data
value and the mean for the same set of data. Standard Deviation - A
measure of the dispersion or scatter of data values in relation to
the mean; a low standard deviation indicates that most data values
are close to the mean, and a high standard deviation indicates that
most data values are scattered farther from the mean.
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Investigate the Math p.226
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B-E)
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F-G)
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Reflecting p.228
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Example 1
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Example 2
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Example 3
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Summary p. 232
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Practice Ex. 5.3 (p.233) #2-12 #3-14
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4. Normal Distribution FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
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a) b) c) d)
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A normal distribution curve is a symmetrical curve that
represents the normal distribution; also called a Bell Curve Data
that, when graphed as a histogram or frequency polygon, results in
a unimodal symmetric distribution around the mean it is referred to
as a Normal Distribution
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Normal Distribution (Bell Curve)
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If we rolled 2 dice 50,000 times adding the two dice together
each time then graphed the results what do you think the graph
would look like?
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What if we rolled three dice?
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Well lets take a look. Grab a partner and two dice and roll the
two dice 50 times each adding the total each time. When you are
done see put your results into a histogram. Do you get a bell curve
(normal distribution)? What if we add all the results from the
class together?
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The more data the is collected the more likely your data will
be distributed normally. When your data is distributed normally, if
you where to draw a line of symmetry right in the middle what value
would this line have?
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Mean Median Mode
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When your data is distributed normally your mean, median and
mode are all the same
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Example 1
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Example 2
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Example 3
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a) b)
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Example 4
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What is the probability that it will last less than 18
months?
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Summary p. 250
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Practice Ex. 5.4 (p. 251) #1-13 #3-16
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5. Working with Z-Scores FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
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5. Working with Z-Scores Z-Score - A standardized value that
indicates the number of standard deviations of a data value above
or below the mean. Standard Normal Distribution - A normal
distribution that has a mean of zero and a standard deviation of
one.
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For any given score, x, from a normal distribution x = +z Where
z is the number of standard deviations away from the mean
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We can rearrange this formula to solve for the number of
standard deviations away from the mean a score is.
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This is the formula we use to find the z-score
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Again, the z-score is the number of standard deviations away
from the mean for a certain score
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Example 1
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Which one of Serges runs was better?
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Why would a lower z-score mean a lower time? What does a
negative z-score mean? What does a positive z-score mean? What does
a 0 z-score mean?
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Example 2
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The z-score table gives you the % from 0% to the score you are
looking at.
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Example 3
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Example 4
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Example 5
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Summary p. 263
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Practice Ex. 5.5 (p. 264) #1-13 #6-17, 20, 22
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6. How Confident are You? FM20.7 Demonstrate understanding of
the interpretation of statistical data, including: confidence
intervals, confidence levels, margin of error.
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6. How Confident are You? Margin of Error - The possible
difference between the estimate of the value youre trying to
determine, as determined from a random sample, and the true value
for the population; the margin of error is generally expressed as a
plus or minus percent, such as 65%.
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Confidence Interval - The interval in which the true value
youre trying to determine is estimated to lie, with a stated degree
of probability; the confidence interval may be expressed using
notation, such as 54.0% 3.5%, or ranging from 50.5% to 57.5%.
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Confidence Level - The likelihood that the result for the true
population lies within the range of the confidence interval;
surveys and other studies usually use a confidence level of 95%,
although 90% or 99% is sometimes used.
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Based on this survey, what is the range for 18- to 34-year-olds
who do not have a social networking account?