The Range between the Largest and Smallest Values of the Data Set

The Range
The range is the difference between the largest value and the smallest value. It gives us an indication of how big the span of the data is.
The range of a data set is the difference between the maximum and minimum values in the set.
The most straightforward measure of dispersion is the range. The range simply tells us how far apart the largest and smallest values in a data set are. The range is very sensitive to outliers.

The Range is a Measure of Spread, and tells you… well, how spread out the data is!
How to work out the Range:
1. Subtract the smallest data value away from the biggest data value!

Worked example: Range
QUESTION
Find the range of the following data set:

{1;4;5;8;6;7;5;6;7;4;10;9;10}

What would happen if we removed the first value from the set?
solution:
Step 1: Determine the range
The smallest value in the data set is 1 and the largest value is 10.
The range is 10-1=9

Step 2: Remove the first value
If the first value, 1, were to be removed from the set, the minimum value would be 4. This means that the range would change to 10-4=6. 1 is not typical of the other values. It is an outlier and has a big influence on the range.

More Related Examples

1. A group of 15 learners count the number of sweets they each have. This is the data they collect:

Calculate the range of values in the data set.
solution:
We first need to order the data set:
{4; 5; 5; 6; 7; 7; 7; 8; 10; 11; 12; 12; 13; 14; 14}

Next we find the maximum value in the data set:
maximum value=14

Then we find the minimum value in the data set:
minimum value=4

Finally, we calculate the range of the data set:
range = (maximum value) – (minimum value)
=(14)-(4)=10

2. A group of 10 learners count the number of playing cards they each have. This is the data they collect:


Calculate the range of values in the data set.
solution:
We first need to order the data set:
{1; 1; 1; 3; 3; 3; 4; 4; 5; 10}

Next we find the maximum value in the data set:
maximum value =10

Then we find the minimum value in the data set:
minimum value =1

Finally, we calculate the range of the data set:
range = (maximum value) – (minimum value)
=10-1=9

3. Find the range of the data set

{1; 2; 3; 4; 4; 4; 5; 6; 7; 8; 8; 9; 10; 10}

solution:
The data set is already ordered. Firstly, we find the maximum value in the data set:
maximum value : 10

Secondly, we find the minimum value in the data set:
minimum value :1

Finally, we calculate the range of the data set:
range = (maximum value) – (minimum value)
=10-1=9

4. A group of 20 learners count the number of marbles they each have. This is the data they collect:


Calculate the range of values in the data set.
solution:
We need to order the data set:

Now we find the maximum value in the data set:
maximum value =19

Next we find the minimum value in the data set:

minimum value =1

Finally, we calculate the range of the data set.
range = (maximum value) – (minimum value)
=19-1=18

5. A group of 15 learners count the number of sweets they each have. This is the data they collect:


Calculate the range of values in the data set.
solution:
We first need to order the data set:

Next we find the maximum value in the data set.
maximum value =15

Then we find the minimum value in the data set.
minimum value =1

Finally, we calculate the range of the data set.
range = (maximum value) – (minimum value)
=15-1=14

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