Question

the data set represents the number of snails that each person counted on a walk after a rainstorm. 12, 13, 22, 16, 6, 10, 13, 14, 12 what is the outlier of the data? 6 11 15 22

Explanation:

Step1: Order the data set

First, we order the given data set: \(6, 10, 12, 12, 13, 13, 14, 16, 22\)

Step2: Find the median (Q2)

The number of data points \(n = 9\) (odd). The median (Q2) is the middle value, which is the 5th value. So, \(Q2 = 13\)

Step3: Find Q1 (median of lower half)

The lower half of the data (values below Q2) is \(6, 10, 12, 12\). The number of values here is \(4\) (even). The median (Q1) is the average of the 2nd and 3rd values: \(\frac{10 + 12}{2}=\frac{22}{2} = 11\)

Step4: Find Q3 (median of upper half)

The upper half of the data (values above Q2) is \(13, 14, 16, 22\). The number of values here is \(4\) (even). The median (Q3) is the average of the 2nd and 3rd values: \(\frac{14+ 16}{2}=\frac{30}{2}=15\)

Step5: Calculate the interquartile range (IQR)

\(IQR=Q3 - Q1=15 - 11 = 4\)

Step6: Determine the outlier boundaries

Lower bound: \(Q1-1.5\times IQR=11 - 1.5\times4=11 - 6 = 5\)
Upper bound: \(Q3 + 1.5\times IQR=15+1.5\times4=15 + 6 = 21\)

Step7: Identify the outlier

We check each value:

• \(6\): \(5<6<21\), not an outlier.
• \(11\): \(5<11<21\), not an outlier.
• \(15\): \(5<15<21\), not an outlier.
• \(22\): \(22>21\), so \(22\) is an outlier.

Answer:

D. 22