Descriptive statistics

Practicing Statistics Interview Questions in R

Zuzanna Chmielewska

Actuary

Descriptive statistics

Descriptive statistics

Descriptive statistics

• central tendency measures
• variability measures

Descriptive statistics

• central tendency measures
• variability measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Central tendency measures

Descriptive statistics

• central tendency
• variability

Variability

Variability

Variability

Variability measures

• variance
• standard deviation
• range

Variability measures

• variance $$\sigma^2 = \frac{\sum(x_i - \mu)^2}{n}$$

Variance - numerical example

$ x_1 = 2, x_2 = 5, x_3=11 $

$ \mu = \frac{\sum_{i=1}^{n} x_i}{n} = \frac{2+5+11}{3} = 6$

$ (x_1 - \mu)^2 = (2 - 6)^2 = (-4)^2 = 16 $

$ (x_2 - \mu)^2 = (5 - 6)^2 = (-1)^2 = 1 $

$ (x_3 - \mu)^2 = (11 - 6)^2 = (5)^2 = 25 $

$\sum_{i=1}^{n} (x_i - \mu)^2 = 16 + 1 + 25 = 42$

$\frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n} = \frac{42}{3} = 14$

Variability measures

• variance $$\sigma^2 = \frac{\sum(x_i - \mu)^2}{n}$$
• standard deviation $$\sigma = \sqrt{\sigma^2}$$

Variability measures

• variance $$\sigma^2 = \frac{\sum(x_i - \mu)^2}{n}$$
• standard deviation $$\sigma = \sqrt{\sigma^2}$$
• range $$\text{range}{} = \text{max} - \text{min}$$

Summary

• central tendency measures
  • mean
  • median
  • mode
• skewness
• variability measures
  • variance
  • standard deviation
  • range

Let's practice!

Practicing Statistics Interview Questions in R