Math 20: Foundations FM20.6 Demonstrate an understanding of normal distribution, including standard...
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Math 20: Foundations FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores. FM20.7 Demonstrate understanding
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
Slide 2
Getting Started! Comparing Salaries p. 208
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What do YOU Think? p. 209
Slide 5
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.
Slide 10
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
Slide 13
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?
Slide 28
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?
Slide 32
Summary p.220
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Practice Ex. 5.2 (p. 221) #1-9 #3-12
Slide 35
3. Standard Deviation FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
Slide 36
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.
Slide 37
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
Slide 48
4. Normal Distribution FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
Slide 49
a) b) c) d)
Slide 50
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
Slide 51
Normal Distribution (Bell Curve)
Slide 52
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?
Slide 57
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?
Slide 58
Mean Median Mode
Slide 59
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
Slide 74
5. Working with Z-Scores FM20.6 Demonstrate an understanding of
normal distribution, including standard deviation and
z-scores.
Slide 75
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.
Slide 76
For any given score, x, from a normal distribution x = +z Where
z is the number of standard deviations away from the mean
Slide 77
We can rearrange this formula to solve for the number of
standard deviations away from the mean a score is.
Slide 78
This is the formula we use to find the z-score
Slide 79
Again, the z-score is the number of standard deviations away
from the mean for a certain score
Slide 80
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
Slide 100
6. How Confident are You? FM20.7 Demonstrate understanding of
the interpretation of statistical data, including: confidence
intervals, confidence levels, margin of error.
Slide 101
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%.
Slide 102
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%.
Slide 103
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.
Slide 104
Slide 105
Based on this survey, what is the range for 18- to 34-year-olds
who do not have a social networking account?
