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. use open circles (∘) to plot any outliers. 56 67 38 46 58 61 62 18 31 47 54 48 46 97 42 48 1 26 (a) identify any possible 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.

Explanation:

Step1: Sort the data

First, we sort the given data set: \(1, 18, 26, 31, 38, 42, 46, 46, 47, 48, 48, 54, 56, 58, 61, 62, 67, 97\)

Step2: Find the median (Q2)

The number of data points \(n = 18\) (even), so the median \(Q2\) is the average of the 9th and 10th values.
9th value: \(47\), 10th value: \(48\)
\(Q2=\frac{47 + 48}{2}=47.5\)

Step3: Find Q1 (median of lower half)

Lower half data: \(1, 18, 26, 31, 38, 42, 46, 46, 47\) (9 values, odd), so \(Q1\) is the 5th value.
\(Q1 = 38\)

Step4: Find Q3 (median of upper half)

Upper half data: \(48, 48, 54, 56, 58, 61, 62, 67, 97\) (9 values, odd), so \(Q3\) is the 5th value.
\(Q3 = 58\)

Step5: Calculate the interquartile range (IQR)

\(IQR=Q3 - Q1=58 - 38 = 20\)

Step6: Determine the outlier boundaries

Lower bound: \(Q1-1.5\times IQR=38 - 1.5\times20=38 - 30 = 8\)
Upper bound: \(Q3 + 1.5\times IQR=58+1.5\times20=58 + 30 = 88\)

Step7: Identify outliers

Check each data point:

• \(1\): \(1<8\), so \(1\) is an outlier.
• \(97\): \(97>88\), so \(97\) is an outlier.

Answer:

A. The outlier(s) is(are) \(1, 97\)