Question

what are 4 similarities between range and variance?

Answer 1

Ans:

Range is the difference between the minimum and the maximum value present in a data set while Variance is the mean of the squared differences of the data points from the sample mean of the data set.

Eg: If {X₁,X₂,...,X_n } be a set of random variables then

$\fn_cm \small range=(x_{max}-x_{min})$

$\fn_cm \small variance=\frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}$ , for sample

  $\fn_cm \small =\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}$ , for population

So,

1. Both are measures of dispersion.

2. Both are unaffected by change of origin but get affected by change of scale

3. Both need at least 2 points in the data set to get calculated/estimated

4.The interquartile range is used in boxplot to check the skewness of the data set and variance along with the 3rd central moment  is used to determine the skewness of a probability distribution.