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Find the inter quartile range, which is IQR = Q3 - Q1, where Q3 is the third quartile and Q1 is the first quartile. Then find these two numbers:

a) Q1 - 1.5*IQR

b) Q3 + 1.5*IQR

Any observation that is below a) or above b) can be considered an outlier.

Chadwick, quartiles are considered robust, meaning that they are not highly effected by outliers. This is because it takes location into account, not the values. Let's look at your data set (sorted).

2 3 6 9 13 18 21 106

position of Q1 = (8+1)/4 = 2.25

Q1 = 0.75(3)+0.25(6) = 3.75

position of Q2 = (8+1)/2 = 4.5

Q2 = (9+13)/2 = 11

position of Q3 = 3(8+1)/4 = 6.75

Q3 = 0.25(18)+0.75(21) = 20.25

Notice that none of these actually use the value 106. Let's continue.

So IQR = Q3-Q1 = 20.25-3.75 = 16.5

Q1-1.5*IQR = 3.75-1.5*16.5 = -21

Q3+1.5*IQR = 20.25+1.5*16.5 = 45

No numbers are below -21, but 106 is above 45, so it can be considered an outlier.

Q: How do you find the outlier number?

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There cannot be an outlier in a dataset that comprises only one number!

An outlier is a number that is noticeably larger or smaller than the other numbers. Example- {3,4,5,6,7,8,9,50,3,2,5,6,7} the number 50 is the outlier. It is basically the one that does not belong.

Calculate the mean, median, and range with the outlier, and then again without the outlier. Then find the difference. Mode will be unaffected by an outlier.

An outlier is a number that is not around a group of number. ex. 4,5,6,7,8,100 see 100 is not near the other numbers so it is an outlier, but remember the outlier can more or less tan the others

Outliers are a number that are way out of the data range. They are pretty obvious to pick out; for example: 1,3,4,4,6,3,2,8,26,5,2,1 The outlier would be the number 26.

Related questions

i can not tell you need to space it out and to find outlier try using a box and whisker plot. and if it is just one number there is no outlier

It is the biggest or lowest number out of the set. The number would be way different than the rest. Example: 14 12 52 17 19 The outlier would be 52 because it is the biggest number. Example: 59, 42, 77, 65, 10 The outlier would be 10 because it is the lowest number.

There cannot be an outlier in a dataset that comprises only one number!

An outlier is a number that is noticeably larger or smaller than the other numbers. Example- {3,4,5,6,7,8,9,50,3,2,5,6,7} the number 50 is the outlier. It is basically the one that does not belong.

Calculate the mean, median, and range with the outlier, and then again without the outlier. Then find the difference. Mode will be unaffected by an outlier.

An outlier is a number that is not around a group of number. ex. 4,5,6,7,8,100 see 100 is not near the other numbers so it is an outlier, but remember the outlier can more or less tan the others

Outliers are a number that are way out of the data range. They are pretty obvious to pick out; for example: 1,3,4,4,6,3,2,8,26,5,2,1 The outlier would be the number 26.

An outlier

Yes, both of them will be outliers.

An outlier.

An outlier is a number completely different from the rest in a set of data.For example, in the set:13, 17, 22, 15, 19, 11, 342, 14342 is the outlier.

oulier means something that sticks out in math, like in the number 50, 51, 53, 54, & 100... 100 is the outlier