follow the steps to identify any potential outliers in the data set.\n11, 13, 13, 15, 16, 21, 24, 29, 31…

follow the steps to identify any potential outliers in the data set.\n11, 13, 13, 15, 16, 21, 24, 29, 31, 31, 35, 36, 37, 39, 43, 43, 52, 66, 84, 123, 152\n\na. find the five - number summary.\nminimum = \nq1 = \nq2 = \nq3 = \nmaximum = \nb. find the interquartile range.\niqr = \nc. find the lower limit and the upper limit of the data.\nlower limit = \nupper limit = \nd. identify any potential outliers. use a comma to separate answers as needed.

follow the steps to identify any potential outliers in the data set.\n11, 13, 13, 15, 16, 21, 24, 29, 31, 31, 35, 36, 37, 39, 43, 43, 52, 66, 84, 123, 152\n\na. find the five - number summary.\nminimum = \nq1 = \nq2 = \nq3 = \nmaximum = \nb. find the interquartile range.\niqr = \nc. find the lower limit and the upper limit of the data.\nlower limit = \nupper limit = \nd. identify any potential outliers. use a comma to separate answers as needed.

Answer

Explanation:

Step1: Sort the data

The data set is already sorted: 11, 13, 13, 15, 16, 21, 24, 29, 31, 31, 35, 36, 37, 39, 43, 43, 52, 66, 84, 123, 152.

Step2: Find the minimum and maximum

Minimum is the first - value, Minimum = 11. Maximum is the last - value, Maximum = 152.

Step3: Find Q2 (median)

There are (n = 21) data points. The median (Q2) is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{21+1}{2}=11) - th value. So Q2 = 35.

Step4: Find Q1

The lower half of the data is 11, 13, 13, 15, 16, 21, 24, 29, 31, 31. There are (n_1 = 10) data points. The median of the lower half (Q1) is the average of the (\frac{n_1}{2})-th and (\left(\frac{n_1}{2}+1\right))-th values. (\frac{10}{2}=5) and (\frac{10}{2}+1 = 6). So (Q1=\frac{16 + 21}{2}=18.5).

Step5: Find Q3

The upper half of the data is 36, 37, 39, 43, 43, 52, 66, 84, 123, 152. There are (n_2 = 10) data points. The median of the upper half (Q3) is the average of the (\frac{n_2}{2})-th and (\left(\frac{n_2}{2}+1\right))-th values. (\frac{10}{2}=5) and (\frac{10}{2}+1 = 6). So (Q3=\frac{43+52}{2}=47.5).

Step6: Calculate the inter - quartile range (IQR)

(IQR=Q3 - Q1=47.5−18.5 = 29).

Step7: Calculate the lower and upper limits

Lower limit (=Q1-1.5\times IQR=18.5−1.5\times29=18.5 - 43.5=-25). Upper limit (=Q3 + 1.5\times IQR=47.5+1.5\times29=47.5 + 43.5 = 91).

Step8: Identify potential outliers

Values less than the lower limit or greater than the upper limit are potential outliers. The potential outliers are 123, 152.

Answer:

a. Minimum = 11, Q1 = 18.5, Q2 = 35, Q3 = 47.5, Maximum = 152 b. IQR = 29 c. Lower limit=-25, Upper limit = 91 d. 123, 152