Quartiles from an ogive
The marks of 40 students are grouped into classes 10 marks wide. Draw the cumulative frequency curve, read the lower quartile, the median and the upper quartile, and check each one with the formula.
Core concept
For continuous data, Q₁, the median and Q₃ are the values at positions N/4, N/2 and 3N/4 of the cumulative frequency; in the class holding the position, quartile = L + (position − c.f.) ÷ f × h
Topic: Statistics
The marks of 40 students are grouped in classes 0–10, 10–20, 20–30, 30–40 and 40–50 with frequencies 5, 8, 12, 10 and 5. Adding them up class by class gives the cumulative frequency (c.f.): 5, 13, 25, 35 and 40 students scored less than 10, 20, 30, 40 and 50. Plotting these against the upper class limits and joining them gives a less-than ogive. Quartiles split the data into four equal parts. The lower quartile Q₁ is at position N/4, the median Q₂ at N/2 and the upper quartile Q₃ at 3N/4. Find the class whose c.f. first reaches the position, then use Q = L + (position − c.f.) ÷ f × h, where L is the lower limit of that class, c.f. the cumulative frequency before it, f its frequency and h its width.
What you will learn
- Make a cumulative frequency table and draw a less-than ogive.
- Find the positions of Q₁, the median and Q₃.
- Calculate quartiles of continuous data with the formula.
- Find the quartile deviation, (Q₃ − Q₁) ÷ 2.
Before you start
- Know class intervals, frequency and the median of discrete data.
Materials
- Graph paper and a pencil
Equipment
- A calculator
Procedure
- Read the median and record it.
- Change to the lower quartile and record.
- Change to the upper quartile and record.
How this simulation is simplified
- The marks in each class are spread evenly across it.