median {3,14,28,22,5,9} q3 q1 iqr median {8,11,32,29,9,34} q3 q1 iqr edian {2,12,52,33,8,14} q3 q1 iqr

Answer:

For the set {3,14,28,22,5,9}:

Median: 11.5 Q1: 6 Q3: 22 IQR: 16

For the set {8,11,32,29,9,34}:

Median: 20 Q1: 9.5 Q3: 31 IQR: 21.5

For the set {2,12,52,33,8,14}:

Median: 13 Q1: 8 Q3: 33 IQR: 25

Explanation:

For the set {3,14,28,22,5,9}:

Step1: Sort the data

3, 5, 9, 14, 22, 28

Step2: Calculate the median

Since there are 6 numbers, median=$\frac{9 + 14}{2}=11.5$

Step3: Find Q1

The lower - half is 3, 5, 9. Q1 = 5+$\frac{9 - 5}{2}=6$

Step4: Find Q3

The upper - half is 14, 22, 28. Q3 = 22

Step5: Calculate IQR

IQR=Q3 - Q1=22 - 6 = 16

For the set {8,11,32,29,9,34}:

Step1: Sort the data

8, 9, 11, 29, 32, 34

Step2: Calculate the median

Since there are 6 numbers, median=$\frac{11+29}{2}=20$

Step3: Find Q1

The lower - half is 8, 9, 11. Q1=$\frac{9 + 10}{2}=9.5$

Step4: Find Q3

The upper - half is 29, 32, 34. Q3=$\frac{32+34}{2}=31$

Step5: Calculate IQR

IQR=Q3 - Q1=31 - 9.5 = 21.5

For the set {2,12,52,33,8,14}:

Step1: Sort the data

2, 8, 12, 14, 33, 52

Step2: Calculate the median

Since there are 6 numbers, median=$\frac{12 + 14}{2}=13$

Step3: Find Q1

The lower - half is 2, 8, 12. Q1 = 8

Step4: Find Q3

The upper - half is 14, 33, 52. Q3 = 33

Step5: Calculate IQR

IQR=Q3 - Q1=33 - 8 = 25