use the accompanying data set to complete the following actions.\na. find the quartiles.\nb. find the…

Explanation:

Step1: Sort the data set

First, sort the data set in ascending order: 15, 29, 30, 36, 36, 36, 36, 36, 37, 39, 39, 40, 42, 43, 44, 44, 48, 50, 50, 50, 55.

Step2: Calculate the position of Q2 (median)

There are $n = 21$ data - points. The position of the median $Q_2$ is $\frac{n + 1}{2}=\frac{21+1}{2}=11$. So, $Q_2$ is the 11th value in the sorted data set, and $Q_2 = 39$.

Step3: Calculate the position of Q1

The lower - half of the data set consists of the first 10 values. The position of $Q_1$ is $\frac{10 + 1}{2}=5.5$. So, $Q_1=\frac{36+36}{2}=36$.

Step4: Calculate the position of Q3

The upper - half of the data set consists of the last 10 values. The position of $Q_3$ is $\frac{10 + 1}{2}=5.5$. So, $Q_3=\frac{44+44}{2}=44$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=44 - 36 = 8$.

Step6: Identify outliers

The lower fence for outliers is $Q_1-1.5\times IQR=36-1.5\times8=36 - 12 = 24$. The upper fence for outliers is $Q_3 + 1.5\times IQR=44+1.5\times8=44 + 12 = 56$. The value 15 is less than 24, so 15 is an outlier.

Answer:

a. The first quartile, $Q_1$, is 36 The second quartile, $Q_2$, is 39 The third quartile, $Q_3$, is 44 b. The inter - quartile range is 8 c. The outlier is 15