Introduction to Statistics

Measures of Central Tendency

Mean (Average)

$\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$

Median

Middle value when data is ordered. For even count, average the two middle values.

Mode

Most frequently occurring value.

Example

Data: $5, 8, 3, 8, 12, 6, 8$

Ordered: $3, 5, 6, 8, 8, 8, 12$

• Mean: $\frac{3+5+6+8+8+8+12}{7} = \frac{50}{7} \approx 7.14$
• Median: $8$ (4th value out of 7)
• Mode: $8$ (appears 3 times)

Measures of Spread

• Range: $\text{Max} - \text{Min} = 12 - 3 = 9$
• IQR (Interquartile Range): $Q_3 - Q_1$

Box Plots

Show the five-number summary: Min, Q1, Median, Q3, Max

Stem-and-Leaf Plots

Show data values organized by their leading digits.

Data: 23, 25, 31, 34, 37, 42, 45

| Stem | Leaf | |------|------| | 2 | 3 5 | | 3 | 1 4 7 | | 4 | 2 5 |

Choosing the Right Display

| Data Type | Display | |-----------|---------| | Categorical | Bar graph, circle graph | | Numerical | Histogram, dot plot, box plot | | Comparing two groups | Double bar graph, side-by-side box plots |

Key idea: The mean is affected by outliers; the median is not. Choose the median for skewed data.