Tables compress data but preserve structure
Grouped data replace individual observations with intervals and frequencies. Every later formula depends on reading these columns precisely.
Learning goals
- Identify and calculate class limits, boundaries, width and class marks.
- Distinguish ordinary and cumulative frequency.
- Choose and interpret mean, median or mode for a stated purpose.
Concept lesson
Observation and frequency
An observation is a recorded value or class; its frequency is the number of occurrences. Total frequency N is the sum of all frequencies.
Anatomy of a class interval
For limits a-b, class mark=(a+b)/2. Class width uses continuous boundaries; inclusive intervals may need boundary adjustment before median or mode work.
Frequency versus cumulative frequency
Ordinary frequency belongs to one class. Less-than cumulative frequency is a running total through that class; it never decreases and ends at N.
Which centre answers the question?
Use mean for an arithmetic balance point, median for the middle ordered position and mode for the most frequent value or class. State the context meaning, not only the name.
Label each interval quantity
For exclusive and inclusive interval tables, identify lower/upper limits, boundaries, width and midpoint, checking that midpoint is equidistant from both boundaries.
Build and check a running total
Add each new class frequency to the previous cumulative total; verify monotonicity and confirm the final cumulative frequency equals N.
Interpretation sorter
Match real-life statements to balance point, middle position or most frequent outcome and explain why the other measures answer different questions.
Prepare one table for three measures
Annotate a grouped table with class marks for mean, ordinary-frequency peak for mode and cumulative frequencies for median, then explain each column's role.
One-mark vocabulary precision
Name the requested class quantity exactly: modal class uses largest ordinary frequency; median class uses N/2 and cumulative frequency; class mark is the midpoint.
Grouped-data structure mastery
Label interval anatomy, construct cumulative frequency, identify the modal and median classes, and choose a suitable central measure for a context.