Homework Quiz 9/30Find the standard deviation of: 8, 4, 3, 2

Relative Standing and

BoxplotsSection 3-4

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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

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

z Scores and Usual Values

Whenever a data value is less than

the mean, its corresponding z

score is negative.

Agendaz-Scores

Finding Percentiles

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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.

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

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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.

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)

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

Important – Remember the Difference!

Statistic Parameter

Mean

Standard Deviation

s

Variance

z score

HomeworkP.127-128: #7, 8, 15-18, 27(only complete 5 #

summary)

Section 3.4Day 2

Homework Quiz 10/2Write down all of your work for problem #8

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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

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

MATH SWAGG – CALCULATOR SKILLZ

1 5 2 3 8 3

4 4 1 9 9 12

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

Critical ThinkingCompare the given data sets

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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.

Agendaz-Scores

Finding Percentile

Finding Quartiles

Box Plots

Interquartile Range

Modified Box Plots

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.

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

HomeworkP.126-128: #4, 11, 14, 27, 28