use the accompanying data set to complete the following actions. a. find the quartiles. b. find the…

use the accompanying data set to complete the following actions. a. find the quartiles. b. find the interquartile range. c. identify any outliers. 56 61 65 62 58 61 62 57 57 59 55 65 62 54 74 a. find the quartiles. the first quartile, q1, is . the second quartile, q2, is . the third quartile, q3, is . (type integers or decimals.)

use the accompanying data set to complete the following actions. a. find the quartiles. b. find the interquartile range. c. identify any outliers. 56 61 65 62 58 61 62 57 57 59 55 65 62 54 74 a. find the quartiles. the first quartile, q1, is . the second quartile, q2, is . the third quartile, q3, is . (type integers or decimals.)

Answer

Explanation:

Step1: Sort the data set

$54,55,56,57,57,58,59,61,61,62,62,62,62,65,65,74$

Step2: Find the median (Q2)

There are $n = 16$ data - points. The median is the average of the 8th and 9th ordered values. So, $Q_2=\frac{61 + 61}{2}=61$.

Step3: Find Q1

The lower half of the data set is $54,55,56,57,57,58,59,61$. There are $n = 8$ data - points. The median of the lower half is the average of the 4th and 5th ordered values. So, $Q_1=\frac{57+57}{2}=57$.

Step4: Find Q3

The upper half of the data set is $61,62,62,62,62,65,65,74$. There are $n = 8$ data - points. The median of the upper half is the average of the 4th and 5th ordered values. So, $Q_3=\frac{62 + 62}{2}=62$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=62 - 57 = 5$.

Step6: Identify outliers

The lower fence is $Q_1-1.5\times IQR=57-1.5\times5=57 - 7.5 = 49.5$. The upper fence is $Q_3 + 1.5\times IQR=62+1.5\times5=62 + 7.5 = 69.5$. Since $74>69.5$, the outlier is $74$.

Answer:

a. $Q_1 = 57$, $Q_2 = 61$, $Q_3 = 62$ b. $IQR = 5$ c. Outlier: $74$