Range

In statistics, a range shows how spread a set of data is. The bigger the range, the more spread out the data. If the range is small, the data is closer together or more consistent.

The range of a set of numbers is the largest value, subtract the smallest value.

range = largest~number - smallest~number

7 babies are weighed and weigh the following amounts:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Find the range of the weights of the babies.

\text{Range} = \text{biggest number} - \text{smallest number} = 4.1 - 2.5 = 1.6

The range of weights is 1.6 kg.

Interquartile range - Higher

The interquartile range shows the range in values of the central 50% of the data.

To find the interquartile range, subtract the value of the lower quartile ( \frac{1}{4} or 25%) from the value of the upper quartile ( \frac{3}{4} or 75%).

\text{Interquartile range} = \text{upper quartile} - \text{lower quartile}

7 babies are weighed and weigh the following amounts:

2.5 kg, 3.1 kg, 3.4 kg, 3.5 kg, 3.5 kg, 4 kg, 4.1 kg

Find the interquartile range of the weights of the babies.

To find the median value, or the value that is half way along the list, the method is to count the number of numbers, add one and divide by 2.

To find the lower quartile or the value that is one quarter of the way along the list, count how many numbers there are, add 1 and divide by 4.

Lower quartile = \frac{7 + 1}{4} = \frac{8}{4}, which is the second value in the list.

\begin{array}{ccccccc} 2.5~\text{kg}, & 3.1~\text{kg}, & 3.4~\text{kg}, & 3.5~\text{kg}, & 3.5~\text{kg}, & 4~\text{kg}, & 4.1~\text{kg} \\ & \text{lower quartile} && \text{median} &&& \end{array}

To find the value of the upper quartile, multiply the lower quartile by 3 as \frac{1}{4} \times 3 = \frac{3}{4}.

The lower quartile was the 2nd number in the list, so the upper quartile must be the 6th number in the list ( 2 \times 3 = 6).

\begin{array}{ccccccc} 2.5~\text{kg}, & 3.1~\text{kg}, & 3.4~\text{kg}, & 3.5~\text{kg}, & 3.5~\text{kg}, & 4~\text{kg}, & 4.1~\text{kg} \\ & \text{lower quartile} &&&& \text{upper quartile} & \end{array}

\text{Interquartile range} = \text{upper quartile} - \text{lower quartile} = 4 - 3.1 = 0.9

The interquartile range of the weights of these babies is 0.9 kg.