Gazer's Digest

MEASURES OF SPREAD - RANGE & INTERQUARTILE RANGE

Range, Quartiles, and Interquartile range of data

March 16, 2021

The Range and the Inter-Quartile Range (IQR) are the measures that describe the spread of data.

EXAMPLE  2

The heights (mm) of a different variety of plants are as follows.

65, 32, 40, 27, 35, 49, 53, 33, 47, 56, 45, 30, 48, 67, 56, 37, 56, 41, 38, 52

Let’s arrange the data in ascending order.

27
30
32
33
35
37
38
40
41
45
47
48
49
52
53
56
56
56
65
67

 

RANGE

The range of a data set is the difference between the highest (maximum) and lowest (minimum) values.

Range = Maximum value - Minimum value

Range = 67 - 27 = 40 mm

 

QUARTILES

The 2nd Quartile (Q2) or the middle quartile is the median. It is the middle value that divides the data into two equal parts.

27
30
32
33
35
37
38
40
41
45
47
48
49
52
53
56
56
56
65
67
Median
(45 + 47) ÷ 2 = 46 mm

The 1st Quartile (Q1) or the lower quartile (QL) separates lower quarter of values from the rest of the values.This is the value at the middle point of the first half of the data

27
30
32
33
35
37
38
40
41
45
47
48
49
52
53
56
56
56
65
67
Lower Quartile (QL)
(35 + 37) ÷ 2 = 36 mm

The 3rd Quartile (Q3) or the upper quartile (QU) separates upper quarter of values from the rest of the values.This is the value at the middle point of the second half of the data

27
30
32
33
35
37
38
40
41
45
47
48
49
52
53
56
56
56
65
67
Upper quartile (QU)
(53 + 56) ÷ 2 = 54.5 mm

 

INTER QUARTILE RANGE (IQR)

It is the difference between the upper quartile (Q3 or QU) and the lower quartile (Q1 or QL)

IQR = QU - QL

IQR = 54.5 - 36 = 18.5 mm

 

 

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