Overview
This lecture covers common summary statistics for quantitative data, focusing on measures of center, spread, and position, as well as sample size.
Measures of Center (Averages)
- Mean is the arithmetic average, best for normal data, acting as the balancing point.
- Median is the middle value when data is ordered and is most accurate for representing the center.
- Mode is the most frequently occurring value; a data set can have none, one, or multiple modes.
- Mid-range is calculated as (maximum + minimum) / 2; it's quick but less accurate than mean or median.
Measures of Spread (Variability)
- Standard deviation measures how far typical values are from the mean in normal data.
- Variance is the square of the standard deviation (sĀ²), also for normal data.
- Range is calculated as maximum minus minimum; easy but not the most informative about typical values.
- Interquartile range (IQR) is Q3 minus Q1 and is best for skewed or non-normal data.
Measures of Position
- Minimum is the smallest value in the data set.
- Maximum is the largest value in the data set.
- First quartile (Q1) is the value below which about 25% of data falls.
- Third quartile (Q3) is the value below which about 75% of data falls.
- Typical values in skewed data are often between Q1 and Q3.
Sample Size
- Sample size (n) is the total number of data points in the set.
- Knowing sample size is important for assessing reliability and detecting sampling bias.
Key Terms & Definitions
- Mean ā arithmetic average of a data set.
- Median ā middle value when data is ordered.
- Mode ā value that appears most frequently in a data set.
- Mid-range ā average of maximum and minimum values.
- Standard deviation ā typical distance of values from the mean.
- Variance ā square of the standard deviation.
- Range ā difference between maximum and minimum values.
- Interquartile range (IQR) ā difference between third and first quartile.
- Minimum ā smallest number in a data set.
- Maximum ā largest number in a data set.
- First quartile (Q1) ā 25th percentile of data.
- Third quartile (Q3) ā 75th percentile of data.
- Sample size (n) ā total number of observations in the data set.
Action Items / Next Steps
- Review section 1G in the textbook on summary statistics.
- Practice identifying and calculating each summary statistic for sample data sets.