Module 9.2

Data Distributions And Outliers

P. 389

What statistics are most affected by outliers?What shapes can data distributions have?

P. 389A Dot Plot is a data representation that uses a number line and Xs, dots, or other symbols to show frequency.

Twelve employees at a small company make the following annual salaries (in thousands of dollars): 25, 30, 35, 35, 35, 40, 40, 40, 45, 45, 50, and 60.

P. 390

P. 390

Is the extreme value of 150 an Outlier?

150 >? 𝑸𝟑 + MagicNumber150 >? 47.5 + 18.75150 >? 66.25Yes – So 150 is an Outlier.In fact, everything above 66.25 is an Outlier.

25, 30, 35, 35, 35, 40, 40, 40, 45, 45, 50, 60, 150

Median𝑸𝟏 𝑸𝟑

(45+50)/2 = 47.5(35+35)/2 = 35

IQR = 47.5 – 35 = 12.5

MagicNumber = 1.5*IQR = 1.5*12.5 = 18.75

P. 390

Is the extreme value of 16 an Outlier?

16

P. 390

𝑸𝟏 – MagicNumber = 16.25𝑸𝟑 + MagicNumber = 66.25

So…Everything below 16.25 and above 66.25 is an Outlier.

25, 30, 35, 35, 35, 40, 40, 40, 45, 45, 50, 60, 150

Median𝑸𝟏 𝑸𝟑

P. 391

1) Create a dot plot using an appropriate scale for the number line.

2) Determine whether the extreme values are outliers.

P. 391

1) Create a dot plot using an appropriate scale for the number line.

2) Determine whether the extreme values are outliers.

72, 80, 81, 84, 84 , 87 , 88, 89 , 90, 93, 100

Median𝑸𝟏 𝑸𝟑

IQR = 90 – 81 = 9

Is 72 an Outlier?

72

What statistics are most affected by outliers?

Outliers affect the mean more than the median, and they affect the standard deviation more than the IQR.

Mr. Morris gave his algebra class a test, the results of which are listed below.

68, 92, 74, 75, 86, 90,92, 81, 60, 82, 77, 80

Shania was absent on the day of the test and had to take the test late. She earned a score of 99. Which measure of the class's test results did Shania's score most change?

A. IQRB. MeanC. MedianD. Range

P. 391-392

P. 392

The mean age and median age are lower for the NFL than for the MLB, which means that NFL players tend to be younger than MLB players.

The IQR and standard deviation are smaller for the NFL than for the MLB, which means that the ages of NFL players are closer together than those of MLB players.

P. 392

18, 20, 25, 27, 30, 35, 39, 41, 46, 48

P. 392

21, 24, 26, 29, 32, 34, 36, 38, 39, 41

Median𝑸𝟏 𝑸𝟑

(30 + 35)/2 = 32.5

IQR = 41 – 25 = 16

Median𝑸𝟏

(32 + 34)/2 = 33

IQR = 38 – 26 = 12

𝑸𝟑 𝑸𝟑

Mean = 32.9 Mean = 32

P. 392

The mean is lower for the 1st/2nd game show, which means that contestants in the 1st/2nd game show are on average younger than contestants in the 1st/2nd

game show.

However, the median is lower for the 1st/2nd game show, which means that although contestants are on average younger on the 1st/2nd game show, there are more young contestants on the 1st/2nd game show.

Finally, the IQR and standard deviation are higher for the 1st/2nd game show, which means that the ages of contestants on the 1st/2nd game show are further apart than the age of contestants on the 1st/2nd game show.

22,24,26,26,26,28,28,31,31,32,33,35,39,40,46,49,51,56,57,58,59,62,64,69,71,76

Median𝑸𝟏

(39 + 40)/2 = 39.5

IQR = 58 – 28 = 30

𝑸𝟑

Mean = 43.81Standard Deviation = 16.42

P. 393

P. 393

What is the Mean?What is the Median?What is the IQR?

P. 393Compare the data.

The mean is lower for Arizona, which means that, on average, members of Congress tend to be younger in Arizona than in Illinois.

However, the median is lower in Illinois, which means that there are more young members of Congress in Illinois despite the differences in average age.

Finally, the IQR and standard deviation are lower for Arizona, which means that the ages of members of Congress are closer together than they are in Illinois.

26, 27, 32, 37, 42, 42, 46, 56, 58

22,24,26,26,26,28,28,31,31,32,33,35,39,40,46,49,51,56,57,58,59,62,64,69,71,76

P. 393

A data distribution can be described as Symmetric (aka Uniform), Skewed To The Left, or Skewed To The Right, depending on the general shape of the distribution in a dot plot or other data display.

In a Symmetric distribution, the Mean and Median are always approximately equal, because the values are equally distributed on either side of the center.

In a Skewed distribution, the Mean and Median are NOT always approximately equal, because the median will sometimes be closer to where the values cluster than the mean will be.

P. 393-394

P. 394

Number of Apples Sold by Grocery Store A

The distribution for Grocery Store A isleft-skewed/right-skewed/symmetric

This means that the number of apples sold each day isevenly/unevenly distributed about the mean.

Number of Apples Sold by Grocery Store B

The distribution for Grocery Store B isleft-skewed/right-skewed/symmetric

This means that the number of apples sold each day isevenly/unevenly distributed about the mean.

P. 395

Number of Free Throws Shot For Team A

The distribution for Team A isleft-skewed/right-skewed/symmetric

This means that the number of free throws shot isevenly/unevenly distributed about the mean.

Number of Free Throws Shot For Team B

The distribution for Team B isleft-skewed/right-skewed/symmetric

This means that more/less than half of the team members shot a number of free throws that were greater than the mean.