Exam Notes: Univariate Data Summary

Univariate Data Summary Measures

Measures of Central Tendency

• Mean (Ungrouped Data): $\bar{x} = \frac{\sum x}{n}$
• Mean (Grouped Data - Frequency Tables): $\bar{x} = \frac{\sum (x \times f)}{\sum f}$
• Median: Middle number.
• Mode: Most common number.

Calculator Functions (Statistics Mode)

• Turning on Statistics Mode: MODE → 2: STAT → AC
• Inputting Data: SHIFT → 1 → 2: Data → Enter data (= after each entry) → AC
• Quartile 1 (Q1) and Quartile 3 (Q3): SHIFT → 1 → 5: MinMax → 3: Q1 or 5: Q3 → =
• Interquartile Range (IQR): $Q3 - Q1$
• Minimum and Maximum: SHIFT → 1 → 5: MinMax → 1: minX or 2: maxX → =
• Range: Maximum - Minimum
• Mean ($\bar{x}$): SHIFT → 1 → 4: Var → 2: $\bar{x}$ → =
• Median: SHIFT → 1 → 5: MinMax → 4: med → =
• Standard Deviation (SD): SHIFT → 1 → 4: Var → 3: $\sigma x$ (population) or 4: $s x$ (sample) → =

Outliers

• An outlier is significantly different from other data points.
• Lower Fence: $Q1 - 1.5 \times IQR$
• Upper Fence: $Q3 + 1.5 \times IQR$
• Values outside the fences are considered outliers.

Histograms

• Histograms display data ranges (intervals) along the horizontal axis.
• The x-axis shows data values/results.
• The y-axis shows the frequency of each result.
• Modal Class: The class with the highest frequency.

Box Plots

• A box plot is a graph of the five-number summary (min, Q1, median, Q3, max).
• Outliers are marked with an 'x'. The whisker extends to the next largest/smallest value within the fences.
• Parallel box plots compare statistics (median, range, IQR) across different datasets.

Stem and Leaf Plots

• Display numerical data using stems (leading digits) and leaves (trailing digits).
• Leaves are written in ascending order from left to right.
• Back-to-Back Stem and Leaf Plots: Compare two groups, with leaves branching outward from the stem.