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0904 Variability.notebook March 12, 2014

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#33 & 28




What are the possible values for xin the data set 22, 12, 33, 25, andx if the median is 25? any numbergreater than or equal to 25


Math Bookpage 476

OH Academic Content Standards8.1.6; 8.5.9

(pp 18)

Learning ObjectiveStudent will learn to find measures of variability and show understanding through class work.



first quartile The median of the lower half of a set of data; also called the lower quartile.

variability The spread of values in a set of data. The data set 1, 5, 7, 10, 25 has greater variability than the data set 8, 8, 9, 9, 9

third quartile The median of the upper half of a set of data; also called the upper quartile.


Introduce to variability. Remember the three measures of central tendency: mean, median, and mode. Measure of central tendency tells where the data is centered.

Does mean, median, or mode gives any indication of how a set of data is spread out?

The topic of the new lesson will address how a data set is spread out.


Box & Whisker Plot



Quartile 1 = 69 Median = 85 Quartile 3 = 93








(pp 19)


31, 23, 33, 35, 26, 24, 31, 29

Use the given data to make a boxandwhisker plot.



Lesson


(pp 19)






Interquartile range: 10 4 = 6

IQR


A boxandwhisker plot shows the variability of a data set, or how the data set is distributed. One important measure of this is the interquartile range ﴾IQR﴿. The IQR is the difference between the third quartile ﴾Q3﴿ and the first quartile ﴾Q1﴿. The IQR is represented on the plot by the length of the box.

If a whisker appears very long compared to the length of the box, then there may be one or more outliers on that whisker.

Outliers can be mathematically identified as follows: Subtract 1.5 times the IQR from the first quartile. Any value less than that difference is an outlier. Add 1.5 times the IQR to the third quartile. Any value greater than that sum is an outlier.


Comparing Data Sets Using

BoxandWhisker Plots

Comparing Data Sets Using

BoxandWhisker Plots


These boxandwhisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office.

The median for the first ten presidents is slightly greater. The range for the last ten presidents is greater.

A. Compare the medians and ranges.


Box and Whisker Plot Questions

Use the arrows at the bottom to start and to move between questions


1 What does the point labeled C represent on the box plot?

A Mean

B Median

C Mode

D Range


2 What do the points labeled B and D represent on the box plot?

A Mean and mode

B Mean and median

C Least and greatest value

D Lower and upper quartile


3 What do the points labeled A and E represent on the box plot?

A Mean and mode

B Mean and median

C Least and greatest value

D Lower and upper quartile


4 What does the length of the box plot tell you about the data set?

A How many quartiles the box plot has.

B How many data points are in the data set.

C How close or far apart the data is grouped.

D How many times a certain data value occurs.


5 What is the median of the data set?

A 8

B 12

C 15

D 19


6 What is the least and greatest value of the data set?

A 6 and 8

B 6 and 19

C 8 and 15

D 15 and 19


7 What is the range of the data set?

A 6

B 12

C 13

D 19


8 Data points in the first quartile are between which two points?

A 6 and 8

B 8 and 12

C 12 and 15

D 15 and 19


9 Which data point is part of Q3?

A 16

B 19

C 21

D 23


10 Which statement is true?

A There are more data points in Q2 than in Q3.

B There are fewer data points in Q2 than in Q3.

C Data points in Q2 are more spread out than in Q3.

D Data points in Q2 are more bunched than in Q3.


Problems


B. Compare the interquartile ranges.

The interquartile range is greater for the last ten presidents.


These boxandwhisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters.


Compare the medians and the ranges.

The median for Tampa Bay is significantly greater, and the range for Tampa Bay is slightly greater.


Compare the interquartile ranges.

The interquartile range is slightly greater for Oakland.


Math HumorWhy did the student shave after reviewing his homework? The teacher took off points because his whiskers were too long.




Complete Packet pg. 20

#16



19 23 29 32 33 34 42 47 59

11 21 26 32 38 41 54 56 58

l l l l l l l l l l 15 20 25 30 35 40 45 50 55 60

l l l l l l l l l l l10 15 20 25 30 35 40 45 50 55 60


The range of the middle half of the data is greater for data set B.

The medians are equal, but data set B has a much greater range.




Homework

Packet p 2122#111

Packet p 2122#111

Homework


the rule is every third student

both the grocery store and the customersfrom the stores are chosen at random

population: Friday’s customers; sample: customers asked by the restaurant owner: possible bias; not all customers are likely to order food with salsa.

Population: customers; sample: customers who rent dramas; possible bias: the customers who choose their favorite movie are the people who like dramas.







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