Question

Use the standard deviation to identify any outliers in the given data set.
{35, 31, 29, 34, 6, 31, 32, 30}

Answer 1

Considering the standard deviation, the data-set has no outliers.

What are the mean and the standard deviation of a data-set?

• The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.

• The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

For the given data-set, the mean is:

(35+31+29+34+6+31+32+30)/8 = 28.5.

Hence the standard deviation is:

$S = \sqrt{\frac{(35-28.5)^2+(31-28.5)^2+(29-28.5)^2+(34-28.5)^2+(6-28.5)^2+(31-28.5)^2+(32-28.5)^2+(30-28.5)^2}{8}} = 8.7$

A measure is said to be an outlier if it is more than 3 standard deviations for the mean. Hence the thresholds are:

• Less than 28.5 - 3 x 8.7 = 2.4.

• More than 28.5 + 3 x 8.7 = 54.6.

Since all values are between 2.4 and 54.6, the data-set has no outliers.

More can be learned about the standard deviation of a data-set at https://brainly.com/question/24754716

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