Question

A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements are outliers.

a.65

b.21

c.72

d.98

Short answer

(a) Not an outlier

(b) Outlier

(c) Not an outlier

(d) Outlier

Step-by-step solution

Determining whether 65 is an outlier

We will use the z- score method$$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{65-57}{11} \\ =\frac{8}{11} \\ =0.727 \end{gathered}$$

As the z score < 3, 65 is not an outlier.

Finding whether 21 is an outlier

$$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{21-57}{11} \\ =\frac{-36}{11} \\ =-3.27 \end{gathered}$$

21 is an outlier

Calculating whether 72 is an outlier

$$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{72-57}{11} \\ =\frac{15}{11} \\ =1.36 \end{gathered}$$

72 is not an outlier.

Calculating whether 98 is an outlier

$$\begin{gathered} z=\frac{Value-Mean}{Standarddeviation} \\ =\frac{98-57}{11} \\ =\frac{41}{11} \\ =3.727 \end{gathered}$$

98 is an outlier.