Question

The inter-quartile range 10 19 25 7 29 14 21 28 13 15 11 15 22 9 23 12 29 17 8 29

Answer 1

To find the interquartile range (IQR), follow these steps:

Step 1: Arrange the data in ascending order:

7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 17, 19, 21, 22, 23, 25, 28, 28, 29, 29

Step 2: Find the first quartile (Q1):

Q1 = (n + 1) / 4

Q1 = (20 + 1) / 4

Q1 = 5.25

Since the position is not an integer, we take the average of the 5th and 6th values:

Q1 = (11 + 12) / 2

Q1 = 11.5

Step 3: Find the third quartile (Q3):

Q3 = 3(n + 1) / 4

Q3 = 3(20 + 1) / 4

Q3 = 15.75

Again, take the average of the 15th and 16th values:

Q3 = (25 + 28) / 2

Q3 = 26.5

Step 4: Calculate the IQR:

IQR = Q3 - Q1

IQR = 26.5 - 11.5

IQR = 15

The interquartile range (IQR) for the given data set is 15.

Answer 2

IQR = 12.5

Explanation:

• Arrange the data in ascending order.

10 19 25 7 29 14 21 28 13 15 11 15 22 9 23 12 29 17 8 29 =

7 8 9 10 11 12 13 14 15 15 17 19 21 22 23 25 28 29 29 29

• Divide the data in two halves. The median of the first half is your Q1, while the median of the second half is your Q3.

1st half : 7 8 9 10|11 12| 13 14 15 15

Q1 (median of 1st half) = 11 + 12 = 11.5

2

2nd half : 17 19 21 22|23 25| 28 29 29 29

Q3 (median of 2nd half) = 23 + 25 = 24

2

• To get the inter-quartile (IQL) range, subtract Q1 from Q3

IQL = Q3 - Q1 = 24 - 11.5 = 12.5