Measures of variability

Compute the missing values in the table below. Round all values to 3 decimal places.

data mean IQR MAD variance standard deviation
{1, 2, 3}
{4, 5, 6}
{2, 4, 6}
{0, 5, 10}

Formulas for measures of variability:
(recall: $$d_i =$$ each data point, $$n =$$ number of data, $$\mu =$$ mean)

• range = maximum - minimum
• IQR (interquartile range) = $$Q_3 - Q_1$$
• MAD (mean absolute deviation) = $$\dfrac{|d_1 - \mu| + |d_2 - \mu| + \ldots + |d_n - \mu|}{n}$$
• variance ($$\sigma^2$$) = $$\dfrac{(d_1 - \mu)^2 + (d_2 - \mu)^2 + \ldots + (d_n - \mu)^2}{n}$$
• standard deviation ($$\sigma$$) = $$\sqrt{\text{variance}}$$

Discussion questions

1. Which data set is most spread out? How can you tell?

2. The second data set is +3 of the first data set. What measures changed and why?

3. The third data set is twice (×2) the first data set. What measures changed and why?