Question

1. check each data set for outliers.

a. 16, 18, 22, 19, 3, 21, 17, 20
b. 24, 32, 54, 31, 16, 18, 19, 14, 17, 20
c. 321, 343, 350, 327, 200

1. check each data set for outliers.

a. 88, 72, 97, 84, 86, 85, 100
b. 145, 119, 122, 118, 125, 116
c. 14, 16, 27, 18, 13, 19, 36, 15, 20

Explanation:

Step1: Sort the data set

For part a of 29: Sorting 16, 18, 22, 19, 3, 21, 17, 20 gives 3, 16, 17, 18, 19, 20, 21, 22.

Step2: Calculate the quartiles

First, find the median (Q2). Since there are 8 data - points, Q2 is the average of the 4th and 5th ordered values. Q2=$\frac{18 + 19}{2}=18.5$.
The lower half is 3, 16, 17, 18. The median of the lower half (Q1) is $\frac{16+17}{2}=16.5$.
The upper half is 19, 20, 21, 22. The median of the upper half (Q3) is $\frac{20 + 21}{2}=20.5$.

Step3: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 20.5 - 16.5 = 4.

Step4: Determine the outlier boundaries

Lower boundary = Q1-1.5IQR = 16.5-1.54 = 10.5.
Upper boundary = Q3 + 1.5IQR = 20.5+1.54 = 26.5.
The value 3 is an outlier.

For part b of 29: Sorting 24, 32, 54, 31, 16, 18, 19, 14, 17, 20 gives 14, 16, 17, 18, 19, 20, 24, 31, 32, 54.
There are 10 data - points. Q2=$\frac{19 + 20}{2}=19.5$.
The lower half is 14, 16, 17, 18, 19. Q1 = 17.
The upper half is 20, 24, 31, 32, 54. Q3 = 31.
IQR = Q3 - Q1 = 31 - 17 = 14.
Lower boundary = Q1-1.5IQR = 17-1.514 = -4.
Upper boundary = Q3 + 1.5IQR = 31+1.514 = 52.
The value 54 is an outlier.

For part c of 29: Sorting 321, 343, 350, 327, 200 gives 200, 321, 327, 343, 350.
There are 5 data - points. Q2 = 327.
The lower half is 200, 321. Q1 = 260.5.
The upper half is 343, 350. Q3 = 346.5.
IQR = Q3 - Q1 = 346.5 - 260.5 = 86.
Lower boundary = Q1-1.5IQR = 260.5-1.586 = 131.5.
Upper boundary = Q3 + 1.5IQR = 346.5+1.586 = 475.5.
The value 200 is not an outlier.

For part a of 30: Sorting 88, 72, 97, 84, 86, 85, 100 gives 72, 84, 85, 86, 88, 97, 100.
There are 7 data - points. Q2 = 86.
The lower half is 72, 84, 85. Q1 = 84.
The upper half is 88, 97, 100. Q3 = 97.
IQR = Q3 - Q1 = 97 - 84 = 13.
Lower boundary = Q1-1.5IQR = 84-1.513 = 64.5.
Upper boundary = Q3 + 1.5IQR = 97+1.513 = 116.5.
No outliers.

For part b of 30: Sorting 145, 119, 122, 118, 125, 116 gives 116, 118, 119, 122, 125, 145.
There are 6 data - points. Q2=$\frac{119 + 122}{2}=120.5$.
The lower half is 116, 118, 119. Q1 = 118.
The upper half is 122, 125, 145. Q3 = 125.
IQR = Q3 - Q1 = 125 - 118 = 7.
Lower boundary = Q1-1.5IQR = 118-1.57 = 107.5.
Upper boundary = Q3 + 1.5IQR = 125+1.57 = 135.5.
The value 145 is an outlier.

For part c of 30: Sorting 14, 16, 27, 18, 13, 19, 36, 15, 20 gives 13, 14, 15, 16, 18, 19, 20, 27, 36.
There are 9 data - points. Q2 = 18.
The lower half is 13, 14, 15, 16. Q1=$\frac{14 + 15}{2}=14.5$.
The upper half is 19, 20, 27, 36. Q3=$\frac{20 + 27}{2}=23.5$.
IQR = Q3 - Q1 = 23.5 - 14.5 = 9.
Lower boundary = Q1-1.5IQR = 14.5-1.59 = 1.
Upper boundary = Q3 + 1.5IQR = 23.5+1.59 = 37.
No outliers.

Answer:

a. of 29: 3 is an outlier.
b. of 29: 54 is an outlier.
c. of 29: No outliers.
a. of 30: No outliers.
b. of 30: 145 is an outlier.
c. of 30: No outliers.