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. 40 52 36 44 40 36 39 46 43 37 36 55 44 34 15 52 39 50 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.) b. find the interquartile range. the interquartile range (iqr) is . (type an integer or a decimal.) c. identify any outliers. choose the correct choice below. a. there exists at least one outlier in the data set at 15. (use a comma to separate answers as needed.) b. there are no outliers in the data set.

use the accompanying data set to complete the following actions. a. find the quartiles. b. find the interquartile range. c. identify any outliers. 40 52 36 44 40 36 39 46 43 37 36 55 44 34 15 52 39 50 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.) b. find the interquartile range. the interquartile range (iqr) is . (type an integer or a decimal.) c. identify any outliers. choose the correct choice below. a. there exists at least one outlier in the data set at 15. (use a comma to separate answers as needed.) b. there are no outliers in the data set.

Answer

Explanation:

Step1: Sort the data set

15, 30, 30, 34, 36, 36, 36, 37, 39, 39, 40, 40, 43, 44, 44, 46, 50, 52, 52, 55

Step2: Find the median (Q2)

There are (n = 20) data - points. The median is the average of the 10th and 11th ordered values. (\text{Q}_2=\frac{39 + 40}{2}=39.5)

Step3: Find Q1

The lower half of the data set is the first 10 values. The median of the lower half is the average of the 5th and 6th ordered values. (\text{Q}_1=\frac{36+36}{2}=36)

Step4: Find Q3

The upper half of the data set is the last 10 values. The median of the upper half is the average of the 15th and 16th ordered values. (\text{Q}_3=\frac{44 + 46}{2}=45)

Step5: Calculate the inter - quartile range (IQR)

(\text{IQR}=\text{Q}_3-\text{Q}_1=45 - 36=9)

Step6: Identify outliers

The lower fence is (\text{Q}_1-1.5\times\text{IQR}=36-1.5\times9=36 - 13.5 = 22.5) The upper fence is (\text{Q}_3 + 1.5\times\text{IQR}=45+1.5\times9=45 + 13.5=58.5) The value 15 is less than 22.5, so 15 is an outlier.

Answer:

a. The first quartile, Q1, is 36. The second quartile, Q2, is 39.5. The third quartile, Q3, is 45. b. The interquartile range (IQR) is 9. c. A. There exists at least one outlier in the data set at 15.