What is range in statistics, with examples

What is range ?

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

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

Therefore the range is 9 − 3 = 6.

It is that simple!

The Range Can Be Misleading

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

Example: In {4, 10, 15, 19, 17, 16, 3620}:

the lowest value is 4,

and the highest is 3620,

So the range is 3620 − 4 = 3616.

The single value of 3620 makes the range large, but most values are around 15.

Example:  Mohan took 7 math tests in one marking period. What is the range of his test scores?

98,  83,  74,  81,  77,  78,  84

Solution: Ordering the test scores in Ascending order, we get:

74,  77,  77,  81,  83,  94,  98

highest - lowest = 98 - 73 = 25

Answer: The range of these test scores is 25

Definition: The range of a set of data is the difference between the highest and least values in the set.

In the example above, the set of data consists of seven test scores. We ordered the data in ascending order (from least to greatest) before finding the range. We recommend that you do this, too. This is very important with a large group of data. Let's look at some more examples.

Example 1: The Sharma family drove through 6 midwestern states on their summer vacation. Petrol prices varied from state to state. What is the range of Petrol prices?

80,  83,  76,  86,  79,  82

Solution: Ordering the data from Ascending order (least to greatest), we get:

76, 79, 80, 82, 83, 86

highest - lowest = 86 - 76 = 10

Answer: The range of Petrol prices is 10

Example 2: Ms. Rita listed 9 integers on the blackboard. What is the range of these integers?

18,  -14,  20,  0,  -6,  -8,  14,  -10,  8

Solution: Ordering the data in Ascending order ( from least to greatest),  we get:

-14,  -10,  -8,  -6,  0,  8,  14,  18,  20

highest - lowest = 20 - (-14)

 = 20 +14 = +34

Answer: The range of these integers is +34.

Example 3: A race was completed by 5 contestants. What is the range of times given in the hours below?

2.6 hr,  8.4 hr,  3.6 hr,  5.2 hr,  4.8 hr

Solution: Ordering the data in Ascending order ( from least to greatest), we get:

2.6,  3.6,  4.8,  5.2,  8.4

highest - lowest = 8.4 hr - 2.6 hr = 5.8 hr

Answer: The range of swim times is 5.8 hr.

Summary: The range of a group of data is the difference between the highest and least values in the group. To find the range, first, order the data in Ascending (from least to greatest). Then subtract the least value from the largest value in the group.

Watch Video below for explanation in hindi.