- 1. What Is Data? — Reading and Interpreting Raw Data
Define data, variable, and raw data; identify the variable and sample size (n) in any data set; and distinguish a raw data list from an organised or summarised representation.
- 2. Tally Marks and Frequency Tables — Organising Raw Data
Use tally marks to count values in a raw data set accurately and systematically, construct a complete three-column frequency distribution table, and verify any table using the rule $\Sigma f = n$.
- 3. Range — Measuring the Spread of Data
Define range as the difference between the highest and lowest values in a data set, calculate the range from raw ungrouped data, and read the range directly from a frequency distribution table.
- 4. Mode from Raw Data — Finding the Most Frequent Value
Define mode and correctly identify it as a value, not a frequency count; find the mode of a raw data set using two systematic methods; and classify a data set as unimodal, bimodal, or having no mode.
- 5. Mode from a Frequency Table — Reading the Dominant Value Directly
Locate the mode in a frequency distribution table by finding the row with the highest frequency, report the x value (never the f value) as the mode, and handle unimodal, bimodal, and multimodal cases.
- 6. Median from Raw Data — Finding the Exact Middle Value
Define the median and its role as a measure of central tendency; apply the position formula (n+1)/2 to locate the median for any odd-sized data set; and calculate the median by sorting and reading the middle value.
- 7. Mean of Ungrouped Raw Data — The Arithmetic Average
Define the arithmetic mean and apply Mean = Sum of values ÷ number of values, calculate the mean of any raw data set including fractions and decimals, and find the mean of data expressed in algebraic terms.
- 8. Mean from a Frequency Table — The Frequency-Weighted Formula
Extend a frequency table with an fx column and compute Σfx; apply Mean = Σfx ÷ Σf; and find an unknown frequency when the mean and the other frequencies are given.
- 9. Using the Mean — Finding Missing Values and Integrated Practice
Apply Mean × n = Σx to find missing values from a data set or frequency table when the mean is given; solve for unknown frequencies or data values algebraically; and combine range, mode, median, and mean in multi-part WAEC/JAMB problems.
