homework quiz 9/30 find the standard deviation of: 8, 4, 3, 2
TRANSCRIPT
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Homework Quiz 9/30Find the standard deviation of: 8, 4, 3, 2
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Relative Standing and
BoxplotsSection 3-4
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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z-ScoresWhat does it mean How do you find it
The z-Score for a particular data point tells you the number
of standard deviations the point
is away from the mean
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ExampleA man is 76.2 in tall and 237.1 lb heavy. Which
of these measurements is more extreme?
Consider that the mean height is 68.34 in with a standard deviation of 3.02 in. Also the mean weight is 172.55 lb with a standard deviation of 26.33 lb.
ROUND-OFF RULE: Round z-Scores to the nearest hundredth, as that is how they are typically plugged into statistical tables.
𝑧=𝑥−𝑥𝑠
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z Scores and Usual Values
Whenever a data value is less than
the mean, its corresponding z
score is negative.
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Agendaz-Scores
Finding Percentiles
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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PercentileWhat does it mean How do you find it
A percentile tells you what percentage of the data is less than
a particular data value
ROUND-OFF RULE: Round off to the nearest whole number.
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ExampleThe scores on the most recent quiz are posted in
the table below. Assume you are the person that scored a 93, and calculate your percentile.
78 100 99 98 21 57
68 75 85 88 87 86
39 2 95 97 93 77
87 88 86 85 82 81
79 62 65 99 100 88
𝑃𝑥=( ¿𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠<𝑥𝑛 )⋅100
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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QuartilesWhat does it mean How do you find it
Quartiles are denoted by They
divide the data into 4 groups that each
contain about 25% of the data.
*The data must be ordered least
to greatest first.
ROUND-OFF RULE: Round L to the nearest whole number unless it is exactly at .5, then find the average of the #’s it is in between.
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5-Number SummaryWhat does it mean Why do we do it?
The 5-Number Summary of a data set is a table that
gives the minimum value, , and the maximum value
The 5-Number Summary gives us all of the information we
need in order to create a box plot
(which we will learn next)
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ExampleFind the 5-Number Summary for the following data set:
3 5 7 4
2 1 6 5
1 4 8 7
𝐿=𝑘4∙𝑛
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Important – Remember the Difference!
Statistic Parameter
Mean
Standard Deviation
s
Variance
z score
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HomeworkP.127-128: #7, 8, 15-18, 27(only complete 5 #
summary)
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Section 3.4Day 2
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Homework Quiz 10/2Write down all of your work for problem #8
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
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Box PlotsHow to construct it Why do we do it?
1. On a number line, plot each of the values from your 5-Number Summary
2. Place vertical lines at
3. Connect the tops and bottoms of
• Gives us an idea about the distribution, spread, and center of the data
• Great for comparing two sets of data
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ExampleCreate a box plot using the following data about
the number of times Abena solved a rubik’s cube in a single minute.
1 5 2 3 8 3
4 4 1 9 9 12
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MATH SWAGG – CALCULATOR SKILLZ
1 5 2 3 8 3
4 4 1 9 9 12
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Critical ThinkingCompare the given data sets
Each plot represents a different lottery years and the average earnings for the winning contestants.
Lottery 1 is in 2010Lottery 2 is in 2011Lottery 3 is in 2012
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Critical ThinkingCompare the given data sets
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
![Page 27: Homework Quiz 9/30 Find the standard deviation of: 8, 4, 3, 2](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649ec55503460f94bd0ef6/html5/thumbnails/27.jpg)
Interquartile RangeHow to find it Why do we do it?
• It helps us indicate any outliers.
• Anything greater than or less than is considered an outlier.
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Agendaz-Scores
Finding Percentile
Finding Quartiles
Box Plots
Interquartile Range
Modified Box Plots
![Page 29: Homework Quiz 9/30 Find the standard deviation of: 8, 4, 3, 2](https://reader036.vdocuments.mx/reader036/viewer/2022062314/56649ec55503460f94bd0ef6/html5/thumbnails/29.jpg)
Modified Box PlotWhat is it? Why do we do it?
A modified box plot follows the same procedure as a normal box plot, except you distinguish outliers using asterisks and stop your line at the least and greatest values that aren’t outliers.
• Outliers can significantly effect the shape of the data, so using the modified box plot makes are representation resistant.
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ExampleCreate a modified box plot using the following data about the number of times Ms. P served an
ace against Mitch after school at the tennis courts.
ACES 32 35 37 28 30
42 45 41 49 29 120
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HomeworkP.126-128: #4, 11, 14, 27, 28