Overview
This lecture covers basic statistics concepts essential for the Digital SAT Math exam, focusing on mean, median, sample size, interpreting data sets, handling outliers, and understanding measures of spread.
Sample Size and Notation
- Sample size is denoted as lowercase n, representing the number of data values or participants.
- For grouped data, n is the sum of all frequencies.
Calculating Mean and Median
- Mean (average) = sum of data values / n.
- Median position = (n + 1) / 2; arrange the data in order before finding the median.
- For even n, median is the average of the two middle values.
Working with Data Sets
- Always order data when finding the median.
- For frequency tables/histograms, multiply each value by its frequency when computing the sum for mean.
- n for grouped data is the total sum of frequencies.
Interpreting Graphical Data
- Histogram: x-axis = value, y-axis = frequency. Use "include left, exclude right" for bins.
- Frequency table: columns for values and their frequencies; same computation as histogram.
- Bar chart: represents categorical data (use values, not frequencies, on axes).
- Box plot: minimum, maximum, median, and quartiles are displayed; each segment is 25% of data.
Large Data Sets and Combining Data
- Means are not additive; recalculate mean after combining data sets using total sum / total n.
- Sums and sample sizes are additive when merging data sets.
Range and Standard Deviation
- Range = largest value - smallest value.
- Standard deviation indicates average distance from the mean; larger spread means higher standard deviation.
- Compare standard deviations by visually assessing data spread.
Modifying Data Sets
- Adding/subtracting a number to all values shifts mean/median but does not affect spread or range.
- Multiplying data increases or decreases both spread and mean/median.
- Shifting numbers on either side of the median increases spread but keeps the center unchanged.
Outliers
- Outlier: value significantly different from the others.
- Adding or removing outliers greatly affects the mean and range, but median is less affected.
Box Plots
- Middle line = median; ends = min/max; inner lines = quartiles (Q1, Q3).
- Each segment represents 25% of data.
- Box plots do not show mean or standard deviation.
Key Terms & Definitions
- Mean — average; sum of values divided by n.
- Median — middle value in ordered data set.
- Range — difference between the largest and smallest values.
- Standard deviation — measure of spread; average distance from the mean.
- Histogram — graph showing frequency of values.
- Box plot — graph showing min, Q1, median, Q3, and max.
- Frequency table — table listing data values and their frequencies.
- Outlier — value far from the rest of the data.
Action Items / Next Steps
- Download and complete the final review worksheet linked in the video description.
- Practice calculating mean and median for lists, frequency tables, histograms, and bar charts.
- Prepare questions for further review and clarification.