- 1. Building Grouped Frequency Distributions — Class Intervals, Boundaries, and Marks
Construct a five-column grouped frequency distribution table from raw data; calculate class limits, class boundaries, class width, and class marks; and identify the modal class.
- 2. Cumulative Frequency Tables — Running Totals and Ogive Foundations
Construct a cumulative frequency column as a running total, express each cumulative frequency as a "less than its upper class boundary" statement, and identify the anchor point and all (UCB, CF) coordinate pairs for the ogive.
- 3. Bar Charts and Pie Charts — Construction, Sector Angles, and Reading
Construct a labelled bar chart; calculate sector angles and construct a pie chart; read frequencies, probabilities, and percentages from bar and pie charts.
- 4. Histograms — Class Boundaries, Touching Bars, and the Modal Class
Draw a histogram with class boundaries on the x-axis and bars that touch, identify the modal class as the tallest bar, and estimate the mode geometrically using the diagonal intersection method.
- 5. Ogives — Constructing and Reading Cumulative Frequency Curves
Construct an ogive by plotting (UCB, CF) pairs plus the anchor point and joining with a smooth S-curve; read the median at the N/2 level using the horizontal-then-vertical method; read Q1 at N/4 and Q3 at 3N/4.
- 6. Range and Mode of Grouped Data — The Interpolation Formula
Calculate the range from extreme class limits, identify the modal class and extract its components, and apply the mode interpolation formula for grouped data.
- 7. Median of Grouped Data — Identifying the Median Class and the Interpolation Formula
Identify the median class using the N/2 criterion; extract the components $L_1$, $cf_m$, $f_m$, $C$, and $N$; apply the interpolation formula $\text{Median} = L_1 + \frac{N/2 - cf_m}{f_m} \times C$; and verify the result against the ogive.
- 8. Mean of Grouped Data — Class Mark Method and Assumed Mean Method
Calculate the mean of a grouped frequency distribution using the class mark method and the assumed mean method, and confirm that the two methods are algebraically equivalent.
- 9. Mean Deviation and Variance of Grouped Data — Extended Tables
Calculate the mean deviation $MD = \frac{\Sigma f|x_m - \bar{x}|}{\Sigma f}$, the variance with the long method $S^2 = \frac{\Sigma f(x_m - \bar{x})^2}{\Sigma f}$, and the variance with the shortcut $S^2 = \frac{\Sigma f x_m^2}{\Sigma f} - (\bar{x})^2$, confirming both methods agree.
- 10. Standard Deviation and Integrated Statistical Analysis
Calculate standard deviation as the square root of variance; construct the complete master table combining all unit outputs from one distribution; and execute a full integrated analysis (range, mode, median, mean, variance, standard deviation) in WAEC Paper 2 format.
