Question

use the accompanying data set to complete the following actions. a. find the quartiles. b. find the interquartile range. c. identify any outliers. 41 53 37 45 41 37 40 48 44 39 34 54 44 34 15 53 39 49 30 29 a. find the quartiles. the first quartile, q1, is the second quartile, q2, is the third quartile, q3, is (type integers or decimals.)

Explanation:

Step1: Sort the data set

15 29 30 34 34 37 37 39 39 40 41 41 44 44 45 48 49 53 53 54

Step2: Calculate the position of Q2

There are $n = 20$ data - points. The position of $Q_2$ (the median) is $\frac{n + 1}{2}=\frac{20+1}{2}=10.5$. So, $Q_2=\frac{40 + 41}{2}=40.5$.

Step3: Calculate the position of Q1

The lower - half of the data set has $n_1 = 10$ data - points. The position of $Q_1$ is $\frac{10 + 1}{2}=5.5$. So, $Q_1=\frac{34+37}{2}=35.5$.

Step4: Calculate the position of Q3

The upper - half of the data set has $n_2 = 10$ data - points. The position of $Q_3$ is $\frac{10 + 1}{2}=5.5$. So, $Q_3=\frac{44+48}{2}=46$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=46 - 35.5 = 10.5$.

Step6: Find the lower and upper bounds for outliers

Lower bound $=Q_1-1.5\times IQR=35.5-1.5\times10.5=35.5 - 15.75 = 19.75$.
Upper bound $=Q_3 + 1.5\times IQR=46+1.5\times10.5=46 + 15.75 = 61.75$.
The outlier is 15 since it is less than 19.75.

Answer:

a. The first quartile, $Q_1$, is $35.5$.
The second quartile, $Q_2$, is $40.5$.
The third quartile, $Q_3$, is $46$.
b. The inter - quartile range is $10.5$.
c. The outlier is 15.