Study Notes
Cumulative frequency is used to find the total of frequencies up to a certain value and is helpful in estimating medians and quartiles from grouped data.
- Cumulative Frequency — the running total of frequencies up to each upper class boundary. Example: If you have frequency data for age groups, cumulative frequency shows the total number of people up to each age group.
- Median — the middle value of a data set when arranged in order. Example: In a cumulative frequency curve, the median is found at 50% of the total frequency.
- Quartiles — values that divide the data into four equal parts. Example: Q1 is the 25th percentile, Q2 is the median, and Q3 is the 75th percentile.
- Interquartile Range (IQR) — the difference between the upper quartile (Q3) and the lower quartile (Q1). Example: If Q3 is 3.8 and Q1 is 2.4, then IQR is 1.4.
Exam Tips
Key Definitions to Remember
- Cumulative Frequency: The running total of frequencies up to each upper class boundary.
- Median: The middle value of a data set.
- Quartiles: Values dividing the data into four equal parts.
- Interquartile Range (IQR): Difference between Q3 and Q1.
Common Confusions
- Confusing cumulative frequency with simple frequency.
- Misidentifying the median on a cumulative frequency curve.
Typical Exam Questions
- How do you calculate the cumulative frequency? Add each frequency to the sum of its predecessors.
- How do you find the median from a cumulative frequency curve? Locate the 50% mark on the y-axis and draw a line to the curve, then down to the x-axis.
- What is the interquartile range? The difference between the 75th percentile (Q3) and the 25th percentile (Q1).
What Examiners Usually Test
- Ability to construct and interpret cumulative frequency tables and curves.
- Estimating medians and quartiles from cumulative frequency diagrams.