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Anvisha [2.4K]
3 years ago
8

The five number summary of a dataset is given as

Mathematics
1 answer:
lord [1]3 years ago
7 0

Given:

The five number summary of two data sets are given as:

a) 0, 4, 12, 14, 20

b) 2, 8, 14, 18, 20

To find:

The range for the outliers.

Solution:

We know that,

An observation is considered an outlier if it is below Q_1-1.5(IQR)

An observation is considered an outlier if it is above Q_3+1.5(IQR)

Where, IQR is the interquartile range and IQR=Q_3-Q_1.

The five number summary of two data sets are given as:

0, 4, 12, 14, 20

Here, Q_1=4 and Q_3=14.

Now,

IQR=14-4

IQR=10

The range for the outliers is:

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-1.5(10),14+1.5(10)]

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[4-15,14+15]

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-11,29]

An observation is considered an outlier if it is below -11.

An observation is considered an outlier if it is above 29.

The five number summary of two data sets are given as:

2, 8, 14, 18, 20

Here, Q_1=8 and Q_3=18.

Now,

IQR=18-8

IQR=10

The range for the outliers is:

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-1.5(10),18+1.5(10)]

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[8-15,18+15]

[Q_1-1.5(IQR),Q_3+1.5(IQR)]=[-7,33]

An observation is considered an outlier if it is below -7.

An observation is considered an outlier if it is above 33.

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