A data set is made up of these values. 3, 3, 4, 5, 6, 7, 10 Find the interquartile range. A. 3 - 3 = 0 B. 10 - 7 = 3 C. 7 - 3 = 4 D. 10 - 3 = 7

Question

asked Jul 15, 2022 161k views

1 Answer

Mark Stosberg · Answer 1 · 2022-07-20T17:02:54+0000

Answer:

C. 7 - 3 = 4

Explanation:

Given

Dataset: 3, 3, 4, 5, 6, 7, 10

Required

The IQR

The IQR is calculated using:

IQR = Q_3 - Q_1

Where:

$Q_3 \to$ Median of the upper
half

$Q_1 \to$ Median of the lower
half

The dataset has 7 values, so the median is: (7 + 1)/2 =8/2 = 4th position.

Split to two, we have:

$Lower \to 3, 3, 4$

$Median \to 5$

$Upper \to 6, 7, 10$

The lower half has 3 data; So, the median is the 2nd position.

Hence:

Q_1 = 3

The upper half has 3 data; So, the median is the 2nd position.

Hence:

Q_3 = 7

So, the IQR is:

IQR = Q_3 - Q_1

IQR = 7 - 3

IQR = 4