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. 42 53 35 44 40 38 39 48 44 38 34 55 42 35 15 53 38 49 30 30 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. 42 53 35 44 40 38 39 48 44 38 34 55 42 35 15 53 38 49 30 30 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

15, 30, 30, 34, 35, 35, 38, 38, 39, 40, 42, 42, 44, 44, 48, 49, 53, 53, 55

Step2: Find the median (Q2)

There are $n = 19$ data - points. The median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{19+1}{2}=10$ - th value. So, $Q_2=40$.

Step3: Find the lower half and Q1

The lower half of the data set is 15, 30, 30, 34, 35, 35, 38, 38, 39. There are $n_1 = 9$ data - points. The median of the lower half is the $\left(\frac{9 + 1}{2}\right)$-th value. $\frac{9+1}{2}=5$ - th value. So, $Q_1 = 35$.

Step4: Find the upper half and Q3

The upper half of the data set is 42, 42, 44, 44, 48, 49, 53, 53, 55. There are $n_2 = 9$ data - points. The median of the upper half is the $\left(\frac{9+1}{2}\right)$-th value. $\frac{9 + 1}{2}=5$ - th value. So, $Q_3=48$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=48 - 35=13$.

Step6: Find the lower and upper bounds for outliers

Lower bound: $Q_1-1.5\times IQR=35-1.5\times13=35 - 19.5 = 15.5$. Upper bound: $Q_3+1.5\times IQR=48+1.5\times13=48 + 19.5 = 67.5$. The value 15 is an outlier since it is less than 15.5.

Answer:

a. $Q_1 = 35$, $Q_2=40$, $Q_3 = 48$ b. $IQR = 13$ c. Outlier: 15