5. name a measure of variability and how it is calculated.

Explanation:

Step1: Choose a measure

We choose the standard - deviation as a measure of variability.

Step2: Define the formula for population standard - deviation

For a population of data values (x_1,x_2,\cdots,x_N) with population mean (\mu), the population standard - deviation (\sigma) is calculated as (\sigma=\sqrt{\frac{\sum_{i = 1}^{N}(x_i-\mu)^2}{N}}).

Step3: Define the formula for sample standard - deviation

For a sample of data values (x_1,x_2,\cdots,x_n) with sample mean (\bar{x}), the sample standard - deviation (s) is calculated as (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}}).

Answer:

One measure of variability is the standard - deviation. For a population, (\sigma=\sqrt{\frac{\sum_{i = 1}^{N}(x_i-\mu)^2}{N}}), and for a sample, (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}}).