Question

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?

Answer 1

The correct option regarding the outliers of the data-set is given by:

The greatest value, 78, is the only outlier.

How to use the quartiles of a data-set to identitfy outliers?

• The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

• The first quartile is the median of the first half of the data-set.

• The third quartile is the median of the second half of the data-set.

• The interquartile range is the difference of the third quartile with the first quartile.

• Measures that are more than 1.5 IQR from Q1 and Q3 are considered outliers.

The IQR for this problem is:

IQR = 37 - 13 = 24.

Hence the bounds for outliers are:

• Less than 13 - 1.5 x 24 = -23.

• Greater than 37 + 1.5 x 24 = 73,

The options are:

• No outliers.

• Only 1 is an outlier.

• Only 78 is an outlier.

• Both 1 and 78 are outliers.

Hence the correct option is that only 78 is an outlier.

More can be learned about outliers of a data-set at https://brainly.com/question/17083142

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