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. 41 51 35 43 41 37 39 46 43 37 34 54 43 36 15 53 39 50 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. 41 51 35 43 41 37 39 46 43 37 34 54 43 36 15 53 39 50 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, 34, 35, 36, 37, 37, 39, 39, 39, 41, 41, 43, 43, 43, 43, 46, 50, 51, 53, 54

Step2: Find the median (Q2)

There are (n = 21) data - points. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{21+1}{2}=11) - th value. So (Q_{2}=41).

Step3: Find Q1

The lower half of the data set is 15, 30, 34, 35, 36, 37, 37, 39, 39, 39. There are (n_1 = 10) data - points. The median of the lower half is the average of the (\frac{10}{2})-th and (\left(\frac{10}{2}+1\right))-th values. The 5 - th value is 36 and the 6 - th value is 37. So (Q_{1}=\frac{36 + 37}{2}=36.5).

Step4: Find Q3

The upper half of the data set is 43, 43, 43, 43, 46, 50, 51, 53, 54. There are (n_2 = 10) data - points. The median of the upper half is the average of the (\frac{10}{2})-th and (\left(\frac{10}{2}+1\right))-th values. The 5 - th value is 46 and the 6 - th value is 50. So (Q_{3}=\frac{46+50}{2}=48).

Step5: Calculate the inter - quartile range (IQR)

(IQR=Q_{3}-Q_{1}=48 - 36.5 = 11.5).

Step6: Identify outliers

The lower fence is (Q_{1}-1.5\times IQR=36.5-1.5\times11.5=36.5 - 17.25 = 19.25). The upper fence is (Q_{3}+1.5\times IQR=48+1.5\times11.5=48 + 17.25 = 65.25). The value 15 is an outlier since (15<19.25).

Answer:

a. (Q_{1}=36.5), (Q_{2}=41), (Q_{3}=48) b. (IQR = 11.5) c. The outlier is 15.