Question

(brainiest and 50 points)A data set is made up of these values.
1, 4, 5, 6, 6, 9, 11
Find the interquartile range.
A. 4 – 1 = 3

B. 11 – 9 = 2

C. 11 – 1 = 10

D. 9 – 4 = 5

Answer 1

Answer:

• D. 9 – 4 = 5

Step-by-step explanation:

Given data:

• 1, 4, 5, 6, 6, 9, 11

Q1

• The median of the lower half is 4

Q3

• The median of the upper half is 9

IQR is the difference of the above two numbers:

• IQR = Q3 - Q1 = 9 - 4 = 5

Correct choice s D

Answer 2

Answer:

D.  9 - 4 = 5

Step-by-step explanation:

Given data set:  1, 4, 5, 6, 6, 9, 11

To find the Interquartile Range (IQR):

Step 1

Place the data values in order from smallest to largest:

1, 4, 5, 6, 6, 9, 11

Step 2

To find the position of the lower quartile, count how many data values there are, add 1, and divide by 4:

$\implies \sf \textsf{Position of lower quartile}= \dfrac{7\:data\:values+1}{4}=2nd\:position$

Therefore, the lower quartile is 4.

Step 3

To find the position of the upper quartile, count how many data values there are, add 1, multiply by 3, and divide by 4:

$\implies \sf \textsf{Position of upper quartile}= \dfrac{(7\:data\:values+1) \times 3}{4}=6th\:position$

Therefore, the upper quartile is 9.

Step 4

$\begin{aligned}\textsf{Interquartile range (IQR)} & = \textsf{upper quartile} - \textsf{lower quartile}\\& = \sf 9-4\\& = \sf 5 \end{aligned}$