YOU ARE LEARNING:

# The Range

### The Range

The range gives us an idea of the how spread out the data is, by finding the difference between the largest and smallest values.

Data can be analyzed by looking at the different measures of averages. However, we can also look at the **variance** of a set of data - in other words, how spread out the data is.

The **range** tell us how far apart the lowest value is from the highest value in the set of data, and it can be calculated by subtracting the smallest value from the biggest value in a data set.

A few friends take part in a 100m race. The following is a set of data which describes the times in which they finished. Let's find the range! $10.7s, \space 11.3s, \space12s, \space11.1s, \space14s$

What is the smallest value?

What is the largest value?

Smallest = $10.7$ and the largest = $14$

Find the difference between these values

$14-10.7=3.3$

Good work! 😎

The range is $3.3s$

The following shows the lengths of a family of blue whales. What is the range, to 3 significant figures? $12.7m,\space 24m, \space 25m, \space 26.5m, \space 23m, \space 22m, \space 21m$

The table shows the amount of boxers in each weight class at a boxing club

Finding the range in grouped intervals is very similar to finding the range with absolute values.

Identify the upper and lower bounds of the intervals

The **smallest** possible value in the dataset is the **lower bound** of the smallest interval. Similarly, the **largest** possible value is the **upper bound** of the largest interval.

What is the smallest possible value?

What is the largest possible value?

Now we can find the range

The lowest possible value is $60kg$ and the largest possible value is $91kg$. The range is the **difference** between these two values.

What is the range of weights at the boxing club?

The range of weights is $31kg$

$91-60=31$. Hopefully the boxers will only fight within their classes...