Center, Spread, and Shape of Distributions: Foundations

Measures of Center

Mean (Average)

Sum of all values divided by number of values

Median

Middle value when data is ordered (or average of two middle values)

Mode

Most frequently occurring value(s)

Example 1: Calculating Measures of Center

Find the mean, median, and mode for: 5, 7, 8, 8, 10, 12, 15

Try it!

Find the median of: 3, 9, 2, 7, 5, 1, 6

Measures of Spread

Range

Maximum value - Minimum value

Interquartile Range (IQR)

Q3 (75th percentile) - Q1 (25th percentile)

Standard Deviation

Measure of how far data points are from the mean

Example 2: Calculating Spread

For the data: 10, 12, 14, 15, 17, 18, 20

Practice: Find IQR

Calculate the IQR for: 5, 7, 8, 10, 12, 15, 18, 20

Shapes of Distributions

Symmetric

Skewed Left

Skewed Right

Example 3: Identifying Shape

Describe the shape of this distribution:

SAT Practice

A distribution has mean = 45 and median = 38. What is the most likely shape?