QMT 181/ STA104-MEASURES OF DISPERSION (RANGE)

The Range (Statistics)

The Range is the difference between the lowest and highest values.

Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9.

So the range is 9-3 = 6.

It is that simple!

The Range Can Be Misleading

Misleading

The range can sometimes be misleading when there are extremely high or low values

Example: In {8, 11, 5, 9, 7, 6, 3616}:

 the lowest value is 5,and the highest is 3616,

So the range is 3616-5 = 3611.

The single value of 3616 makes the fk range large, but most values are around 10.

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What is the range for the following set of numbers?

15, 21, 57, 43, 11, 39, 56, 83, 77, 11, 64, 91, 18, 37

Help

What is the range for the following set of numbers?

57, -5, 11, 39, 56, 82, -2, 11, 64, 18, 37, 15, 68

Answer: 87

QUESTION:The frequency table shows the numbers of goals the Lakers scored in their last twenty matches.What was the range?



The range is the difference between the lowest and highest values.

The highest value was 7 (They scored 7 goals on 1 occasion)

The lowest value was 0 (They scored 0 goals on 2 occasions)

Therefore the range = 7 - 0 = 7

The children in a class did a survey of the number of siblings (brothers and sisters) each of them had. The results are recorded in the following table:

Range =highest value - lowest value

            = 9-0

            = 9

In case of grouped data, the range is the difference between the upper boundary of the highest class and the lower boundary of the lowest class.

Find the range of the weight of the students of a university.

Weights (Kg)	60−62	63−65	66−68	69−71	72−74
Number ofStudents	5	18	42	27	8

Calculate the range and coefficient of range.

Solution:
           

Weights (Kg)	Class Boundaries	Mid Value	No. ofStudents
60−62	59.5−62.5	61	5
63−65	62.5−65.5	64	18
66−68	65.5−68.5	67	42
69−71	68.5−71.5	70	27
72−74	71.5−74.5	73	8

            Here   xm= Upper class boundary of the highest class =74.5
                       x0= Lower class boundary of the lowest class =59.5
            Range =xm−x0=74.5−59.5=15 Kilogram

EXERCISES:

Following are the wages of 8 workers of a factory. Find the range and the coefficient of range. Wages in Dollars 1400, 1450, 1520, 1380, 1485, 1495, 1575, 1440.

Solution:

Here Largest value =xm=1575 and Smallest Value =x0=1380
            Range =xm−x0=1575−1380=195

The following distribution gives the numbersof houses and the number of persons per house.

Number ofPersons	1	2	3	4	5	6	7	8	9	10
Number of Houses	26	113	120	95	60	42	21	14	5	4

Calculate the range and coefficient of range.

Solution:
            Here Largest value =xm=10 and Smallest Value =x0=1
            Range =xm−x0=10−1=9

Reference: 

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