presented how to use the range to describe the spread of a data set Another similar statistic which

gives a measure of spread is the interquartile range or IQR. Th e IQR is the range of the middle half of the data.

Th e following data lists the average points per game of members of the Portland trail Blazers in 2006-2007. Source: nba.com

2.0, 3.5, 3.8, 3.9, 4.8, 6.5, 7.0, 8.4, 8.9, 9.0, 12.0, 16.8, 23.6 a. Find the fi ve-number summary for the data set.

b. Find the range and interquartile range of the averages.

a. Th e middle number of the data set (the median) is 7.0. Th e medians of the lower and

upper halves, Q1 and Q3, are 3.85 and 10.5, respectively. Th e minimum is 2.0 and the maximum is 23.6.

2.0 , 3.5, 3.8, | 3.9, 4.8, 6.5, 7.0 , 8.4, 8.9, 9.0, | 12.0, 16.8, 23.6

3.85 _10.5

min Q1 Median Q3 max

Th e fi ve-number summary for the data is 2.0 ~ 3.85 ~ 7 ~ 10.5 ~ 23.6

b. Find the range of the data. Range = Maximum – Minimum = 23.6 – 2.0 = 21.6

Find the interquartile range. IQR = Q3 – Q1 = 10.5 – 3.85 = 6.65

exercises

1.

Misty found the fi ve-number summary for the following set of data. Number of students in each Algebra class:

19, 23, 23, | 25, 26, 26, 27, 27, | 28, 28, 30 19 ~ 24 ~ 26 ~ 27.5 ~ 30

a. Antwan tells Misty her answer is only partly correct. Which part(s) did she have

right?

b. Which parts did she get wrong? Fix her errors and give the correct fi ve-number

summary.

c. What is the range of the class sizes? What is the interquartile range (IQR)?

d. About ___% of Algebra classes have 23 or fewer students in them.

e. One-half of the Algebra classes have more than ___ students.

example 3

s

olutions

Find the five-number summary for each data set.

2.

7, 14, 15, 19, 20, 25, 27

3.

40, 43, 45, 47, 54, 60

4.

12, 15, 12, 20, 16, 12, 8, 19, 18, 5

5.

74, 76, 79, 68, 52, 59, 76, 60, 78

6.

20, 22, 22, 23, 27, 32, 35, 40, 42, 45, 48, 50

7.

−5, 1, 0, 5, 0, 10, −6, −5, 9, 7, −9

given the five-number summaries, find the interquartile range (IQr) for each data set.

8.

21 ~ 23 ~ 24 ~ 29 ~ 35

9.

16 ~ 28 ~ 34 ~ 37 ~ 40

10.

67 ~ 74 ~ 81 ~ 88 ~ 95

11.

Wendy’s pig had a litter of piglets. The five-number summary of the piglets' weights in pounds is given below.

2.1 ~ 2.4 ~ 2.6 ~ 2.9 ~ 3.0

a. Fifty percent of the piglets weighed less than or equal to ___ pounds. b. ___% of the piglets weighed 2.4 pounds or more.

c. The middle 50% of the piglets weighed between ___ and ___ pounds.

12.

A pair of dice were rolled 15 times and the sums were tallied in the table below.

sum 2 3 4 5 6 7 8 9 10 11 12

Frequency | || | || ||| ||| | | |

a. List the outcomes of the fifteen rolls.

b. What is the five-number summary of the data? c. What is the IQR of the data?

d. What percent of the sums were between the first and third quartile (Q1 and Q3)? use the given information to complete each ordered data set.

13.

___, 4, 7, 9, 10, ___, ___ Five-number-summary = 2 ~ 4 ~ 9 ~ 11 ~ 15

14.

___, ___, 10, 11, 14, ___, ___, 15, 17 Mode = 15 Q1 = 9 Range = 11

15.

___, 14, 18, 20, 23, 23, ___, 30 Range = 16 IQR = 10

16.

68, 74, ___, 81, 82, 82, ___, 95, ___ Q1 = 75 Range = 31 Mean = 83

70

Lesson 12 ~ Five - Number Summaries Of Data

review

17.

Michael went fishing with his dad the last six weekends. He caught the following number of fish.

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6

1 0 2 9 0 1

a. Find the mean, median and mode of the data. b. Are there any outliers? Explain.

c. Which measure of center best represents how many fish Michael can

expect to catch when he goes fishing? Explain.

Which measure of center (mean, median or mode) best represents each data set? explain.

18.

the price of gas at ten gas stations

19.

the ages of all people in a classroom, including the teacher

20.

the weight of fifteen cats at the

21.

the first three digits of students’ telephone numbers veterinary clinic

22.

The Career Counseling department at Mayfield High School collected data about what occupational fields their students want to go into. The following pictograph shows the results.

social services Business health services Computers engineering = 10 students

a. How many students want to go into Computers?

b. How many more students are interested in Business than Health Services?

c. How many times more students are interested in Social Services than Engineering? d. What is the range of the most popular field to the least popular field?

e. How many students were included in this data?

f. Mayfield HS has 1,200 students. About how many would be interested in the Health Services field

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Create three quatrain poems to help you remember the diff erence between the mean, median and mode. Write one quatrain for each measure of center.

An example of a quatrain in rhyming scheme 3.

Quatrain

A quatrain is a poem consisting of four lines of verse with a specifi c rhyming scheme. Examples of quatrain rhyming schemes:

1. abab 2. abba -- envelope rhyme 3. aabb

Th e fi ve-number summary tells the data’s spread. When it is found there’s little more to be said. Minimum, maximum, quartiles and median too,

can help separate what is false from true.

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B

roch u r e

A new student has just joined the class. Make a brochure showing them how to fi nd the fi ve-number summary of a data set. Be sure to include data sets with an even and odd number of values.

Include some practice problems that the new student could try on their own at the end of the brochure. Include the solutions for the practice problems so that they can check their work.

72

Lesson 13 ~ Finding Outliers

Y

ou have seen how a very large or very small number in a data set can aff ect the mean of that data set. For example, look at some data from the Los Angeles Lakers’ 2006-2007 team. Notice how Kobe Bryant’s point total aff ected the mean of the data.

Player Kwame _Brown Andrew _Bynum Maurice _{Evans Walton}Luke Lamar _Odom Smush _{Parker Bryant}Kobe Points

scored 345 637 638 684 890 907 2430

Source: NBA.com

Mean = 933 Median = 684 Mean without Kobe = 683.5

Outliers can greatly aff ect the mean of a data set. It is helpful to be able to identify them. Outliers were defi ned in Lesson 10 as values that vary greatly from most of the other values in a data set. Th is defi nition can cause disagreement about what qualifi es as an outlier.

For example, a class did a survey on how many diff erent TV shows each student watched on a weekly basis. Th e class put the results in order. Number of TV shows watched weekly: 1, 5, 5, 5, 5, 6, 7, 7, 7, 8, 9

Ian and Annika discussed whether there were any outliers in the data. Ian: “I think the number 1 is an outlier because it’s quite a bit lower than the other numbers.”

Annika: “I disagree. One is only four smaller than 5. Th e other numbers go all the way to 9. I don’t think 1 is all that diff erent from the others.”

What do you think? Both students make a good argument. Statisticians have numerous ways to determine whether a number is an outlier or not. One common method for determining outliers is the IQR Method.

In document BLoCK 2 ~ data AnALYsIs (Page 34-38)