Question

Why might the range not be the best estimate of variability?

Answer 1

it may be because the range isn't actually considered an average, it's shown using a box and whiskers diagram, Mode is the most common number. Mean is all the numbers added up and divided by the amount of values there are in the adding up process. so overall the range is less useful to show variability as it only shows the lowest and highest number in the data, and not the different individual numbers variety amongst the results 

Answer 2

Range does not measure the spread of the majority of values in a data set.

Explanation:

We are asked to tell why the range might not be the best estimate of variability.

We know that range is the difference between the upper data and lower data point of a data set.

We know that variability determines the spread of a data.

When a data set has large values data outliers, then it will affect the spread.

Let us take an example of the following data set.

`1,2,2,2,5,5,5,6,6,6,7,7,7,8,8,201`

The range of the data would be
`201-1=200`, while all the data points except 201 are 1 away from each other.

Since range does not measure the spread of the majority of values in a data set, therefore, the range is not the best estimate of variability.