Question

a modified box - and - whisker plot is a box - and - whisker plot that uses symbols to identify outliers. the horizontal line of a modified box - and - whisker plot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. (a) identify any outliers and (b) draw a modified box - and - whisker plot that represents the data - set
13 12 10 13 8 10 11 13
11 25 1 15 15 11 8
(a) identify any outliers. select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the outlier(s) is(are)
(type an integer or decimal. use a comma to separate answers as needed)
b. there are no outliers
(b) choose the correct modified box - and - whisker plot below

Explanation:

Step1: Sort the data

First, sort the data set: \(1,8,8,10,10,11,11,11,12,13,13,13,15,15,25\)

Step2: Find the median (\(Q_2\))

Since there are \(n = 15\) data points, \(Q_2\) is the \(\frac{n + 1}{2}=8^{th}\) data point. So \(Q_2=11\)

Step3: Find \(Q_1\) and \(Q_3\)

The lower half of the data is \(1,8,8,10,10,11,11\). There are \(n_1=7\) data points. \(Q_1\) is the \(\frac{n_1 + 1}{2}=4^{th}\) data point. So \(Q_1 = 10\)
The upper half of the data is \(12,13,13,13,15,15,25\). There are \(n_2 = 7\) data points. \(Q_3\) is the \(\frac{n_2+1}{2}=4^{th}\) data point. So \(Q_3=13\)

Step4: Calculate the inter - quartile range (IQR)

\(IQR=Q_3 - Q_1=13 - 10 = 3\)

Step5: Find the lower and upper bounds for outliers

Lower bound \(=Q_1-1.5\times IQR=10-1.5\times3=10 - 4.5 = 5.5\)
Upper bound \(=Q_3 + 1.5\times IQR=13+1.5\times3=13 + 4.5=17.5\)

Step6: Identify outliers

Data points less than \(5.5\) or greater than \(17.5\) are outliers. The data point \(1\) is less than \(5.5\) and \(25\) is greater than \(17.5\)

Answer:

A. The outlier(s) is(are) \(1,25\)