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# the interquartile range of the data set is 4. 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12 which explains whether or not 12 is an outlier? twelve is an outlier because it is greater than the sum of 7 and 4. twelve is an outlier because it is less than the sum of 7 and 6. twelve is not an outlier because it is greater than the sum of 7 and 4. twelve is not an outlier because it is less than the sum of 7 and 6.

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### James

Guys, does anyone know the answer?

get the interquartile range of the data set is 4. 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12 which explains whether or not 12 is an outlier? twelve is an outlier because it is greater than the sum of 7 and 4. twelve is an outlier because it is less than the sum of 7 and 6. twelve is not an outlier because it is greater than the sum of 7 and 4. twelve is not an outlier because it is less than the sum of 7 and 6. from EN Bilgi.

## The interquartile range of the data set is 4. 2, 2

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## The interquartile range of the data set is 4. 2, 2, 3, 3, 4, 5, 5, 6, 7, 9, 12 Which explains whether or not 12 is an outlier? Twelve is an outlier because it is greater than the sum of 7 and 4.. Twelve is an outlier because it is less than the sum of 7 and 6. Twelve is not an outlier because it is greater than the sum of 7 and 4. Twelve is not an outlier because it is less than the sum of 7 and 6.

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Sara was studying the relationship between rainfall,  r mm, and humidity, h%,  in the UK. She takes a random sample of 11 days from May 1987 for Leuchars from the large data set.

She obtained the following results.

b9786959786949797879786r1.10.33.720.6002.41.10.10.90.1

Sara examined the rainfall figures and found

Q1=0.1 Q2=0.9 Q3=2.4

A value that is more than 1.5 times the interquartile range (IQR) above Q3 is called an outlier.

Show that r=20.6 is an outlier.

It is an outlier because it is greater than

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## Box Plots

Geometry chapter 11 Learn with flashcards, games, and more — for free.

## Box Plots - assignment, quiz

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The data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. What is the interquartile range of the data?

14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28

Click card to see definition 👆

* 12

Click again to see term 👆

Which data sets have outliers? Check all that apply.

14, 21, 24, 25, 27, 32, 35

15, 30, 35, 41, 44, 50, 78

16, 32, 38, 39, 41, 42, 58

17, 23, 28, 31, 39, 45, 75

18, 30, 34, 38, 43, 45, 68

Click card to see definition 👆

* 16, 32, 38, 39, 41, 42, 58 (16 & 58)

* 18, 30, 34, 38, 43, 45, 68 (68)

Click again to see term 👆

1/18 Created by sandiwall2211 Geometry chapter 11

### Terms in this set (18)

The data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. What is the interquartile range of the data?

14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28

* 12

Which data sets have outliers? Check all that apply.

14, 21, 24, 25, 27, 32, 35

15, 30, 35, 41, 44, 50, 78

16, 32, 38, 39, 41, 42, 58

17, 23, 28, 31, 39, 45, 75

18, 30, 34, 38, 43, 45, 68

* 16, 32, 38, 39, 41, 42, 58 (16 & 58)

* 18, 30, 34, 38, 43, 45, 68 (68)

The data set below represents the number of televisions repaired in a service shop over an 11-week period.

1, 48, 50, 25, 21, 19, 26, 30, 18, 17, 3

Find the outlier. * 50

If a data set has only one outlier, which value will always change when the outlier is excluded?

the median the range

the interquartile range

the upper quartile * the range

Charles wants to analyze his last 9 months of math test scores with a box plot to see how spread out they are.

92 86 80 94 90 84 87 91 100

Arrange the scores in lowest to highest order.

* 80 84 86 87 90 91 92 94 100

* the median is 90

Q1 = 85 (84+86=170/2)

Q3 = 93 (92+94=186/2)

IQR = 8 (93-85) range = 20 (100-80)

Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.

Compare the box plots. Which statements are true? Check all that apply.

*Ben has the smaller range of test scores.

*The lower quartile and upper quartile of Nadia's data are both higher than the lower quartile and upper quartile of Ben's data.

*The median of Nadia's data is equal to the median of Ben's data.

*Ben's lowest score was equal to Nadia's lowest score.

* The median of Nadia's data is equal to the median of Ben's data.

A football coach compared the yards per game of two of his running backs over the course of 10 games. Based on the data represented in the box plots, which football player had greater success during the 10 games?

*Nasir was more successful because he had the greatest number of yards in one game.

*Nasir was more successful because he had the greater measure of center.

*Aaron was more successful because he had an outlier.

* Nasir was more successful because he had the greater measure of center.

A basketball player recorded her points for 11 consecutive games. Her points are listed below.

13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27

How many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?

*23

Which statement is true about the box plots?

* The ranges for the box plots are the same, but their interquartile ranges are different.

The data set below has a lower quartile of 13 and an upper quartile of 37.

1, 12, 13, 15, 18, 20, 35, 37, 40, 78

Which statement is true about any outliers of the data set?

*The data set does not have any outliers.

*The lowest value, 1, is the only outlier.

*The greatest value, 78, is the only outlier.

*Both 1 and 78 are outliers.

* The greatest value, 78, is the only outlier.

The box plot represents the number of minutes it takes for the students in a class to run a mile.

What is the minimum of the data?

0 5 7 13 *5

The data set represents the number of miles Mary jogged each day for the past nine days.

6, 7, 5, 0, 6, 12, 8, 6, 9

What is the outlier of the data?

* zero

Which statement is true about the ranges for the box plots?

Number of sales in morning and afternoon

Morning = 3-15 Afternoon = 4-16 (range 12 for both)

* The range of the Morning box plot is the same as the range of the Afternoon box plot.

The box plots compare the number of students in Mr. Ishimoto's classes and in Ms. Castillo's classes over the last two semesters.

Which statement is true about the box plots? Select three options.

*Both box plots show the same range.

*Both box plots show the same interquartile range.

*The data for Mr. Ishimoto has an outlier.

*Mr. Ishimoto had the class with the greatest number of students.

*The smallest class size was 24 students.

Source : quizlet.com

## Identifying outliers with the 1.5xIQR rule (article)

Box and whisker plots

## Identifying outliers with the 1.5xIQR rule

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An outlier is a data point that lies outside the overall pattern in a distribution.

The distribution below shows the scores on a driver's test for

19 19 19

applicants. How many outliers do you see?

0 0 5 5 10 10 15 15 20 20 25 25 Scores

Some people may say there are

5 5 5

outliers, but someone else might disagree and say there are

3 3 3 or 4 4 4

outliers. Statisticians have developed many ways to identify what should and shouldn't be called an outlier.

A commonly used rule says that a data point is an outlier if it is more than

1.5\cdot \text{IQR} 1.5⋅IQR

1, point, 5, dot, start text, I, Q, R, end text

above the third quartile or below the first quartile. Said differently, low outliers are below

\text{Q}_1-1.5\cdot\text{IQR}

Q 1 ​ −1.5⋅IQR

start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text

and high outliers are above

\text{Q}_3+1.5\cdot\text{IQR}

Q 3 ​ +1.5⋅IQR

start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text

.

Let's try it out on the distribution from above.

## Step 1) Find the median, quartiles, and interquartile range

Here are the 19 19 19 scores listed out. 5 5 5 , 7 7 7 , 10 10 10 , 15 15 15 , 19 19 19 , 21 21 21 , 21 21 21 , 22 22 22 , 22 22 22 , 23 23 23 , 23 23 23 , 23 23 23 , 23 23 23 , 23 23 23 , 24 24 24 , 24 24 24 , 24 24 24 , 24 24 24 , 25 25 25

What is the median?

\text{median}= median=

start text, m, e, d, i, a, n, end text, equals

What is the first quartile?

\text{Q}_1= Q 1 ​ =

start text, Q, end text, start subscript, 1, end subscript, equals

What is the third quartile?

\text{Q}_3= Q 3 ​ =

start text, Q, end text, start subscript, 3, end subscript, equals

What is the interquartile range?

\text{IQR}= IQR=

start text, I, Q, R, end text, equals

Step 2) Calculate

1.5\cdot\text{IQR} 1.5⋅IQR

1, point, 5, dot, start text, I, Q, R, end text

below the first quartile and check for low outliers.

Calculate

PROBLEM A

\text{Q}_1-1.5\cdot\text{IQR}

Q 1 ​ −1.5⋅IQR

start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text

\text{Q}_1-1.5\cdot\text{IQR}=

Q 1 ​ −1.5⋅IQR=

start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text, equals

PROBLEM B

How many data points can we say are low outliers?Step 3) Calculate

0 0 5 5 10 10 15 15 20 20 25 25 Scores Choose 1 answer: Choose 1 answer: 1.5\cdot\text{IQR} 1.5⋅IQR

1, point, 5, dot, start text, I, Q, R, end text

above the third quartile and check for high outliers.

Calculate

PROBLEM A

\text{Q}_3+1.5\cdot\text{IQR}

Q 3 ​ +1.5⋅IQR

start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text

\text{Q}_3+1.5\cdot\text{IQR}=

Q 3 ​ +1.5⋅IQR=

start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text, equals

PROBLEM B

How many data points can we say are high outliers?

0 0 5 5 10 10 15 15 20 20 25 25 Scores Choose 1 answer: Choose 1 answer:

## Bonus learning: Showing outliers in box and whisker plots

Box and whisker plots will often show outliers as dots that are separate from the rest of the plot.

Here's a box and whisker plot of the distribution from above that does not show outliers.

Scores 0 0 5 5 10 10 15 15 20 20 25 25

Here's a box and whisker plot of the same distribution that does show outliers.

Scores 0 0 5 5 10 10 15 15 20 20 25 25

Notice how the outliers are shown as dots, and the whisker had to change. The whisker extends to the farthest point in the data set that wasn't an outlier, which was

15 15 15 .

Here's the original data set again for comparison.

0