Question

use the accompanying data set to complete the following actions. a. find the quartiles. b. find the interquartile range. c. identify any outliers. 63 61 56 65 57 65 60 56 57 60 65 63 60 54 80 a. find the quartiles. the first quartile, q1, is 57. the second quartile, q2, is 61. the third quartile, q3, is 65. (type integers or decimals.)

Explanation:

Step1: Sort the data set

54, 56, 56, 57, 57, 60, 60, 60, 61, 63, 63, 65, 65, 65, 80

Step2: Find the median (Q2)

There are 15 data - points. The median is the 8th value. So, $Q_2 = 60$.

Step3: Find Q1

The lower half of the data is 54, 56, 56, 57, 57, 60, 60. There are 7 data - points. The median of the lower half (Q1) is the 4th value, so $Q_1 = 57$.

Step4: Find Q3

The upper half of the data is 61, 63, 63, 65, 65, 65, 80. There are 7 data - points. The median of the upper half (Q3) is the 4th value, so $Q_3 = 65$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=65 - 57 = 8$.

Step6: Identify outliers

Lower fence: $Q_1-1.5\times IQR=57-1.5\times8 = 57 - 12=45$.
Upper fence: $Q_3 + 1.5\times IQR=65+1.5\times8 = 65 + 12 = 77$.
The value 80 is greater than 77, so 80 is an outlier.

Answer:

a. $Q_1 = 57$, $Q_2 = 60$, $Q_3 = 65$
b. $IQR = 8$
c. Outlier: 80