Histograms: grouping a class's marks
Thirty students got marks out of 50 in a maths test. Group the marks into classes 5, 10 or 25 marks wide, draw a histogram, and see which class width shows the pattern best and where the modal class is.
Core concept
Grouped data are counted in class intervals and shown as a histogram, whose bars touch because the classes follow on without gaps; the tallest bar is the modal class, and the class width decides how much of the pattern you can see
Topic: Statistics
When there are many values, we group them. The marks of 30 students, from 0 to 50, can be counted in class intervals such as 0–10, 10–20, 20–30, 30–40 and 40–50. A mark of 30 goes in 30–40, not 20–30: each class includes its lower end. The number of marks in a class is its frequency. A histogram shows the frequencies as bars that touch each other, because the classes follow on with no gaps, unlike a bar diagram whose bars stand apart. The class with the tallest bar is the modal class. Very narrow classes make a bumpy picture, and very wide ones hide the shape.
What you will learn
- Group data into class intervals and make a frequency table.
- Draw a histogram and explain why its bars touch.
- Find the modal class from a histogram.
- Choose a sensible class width.
Before you start
- Know how to make a tally and a bar diagram.
Materials
- A list of test marks (with names removed) and graph paper
Equipment
- A ruler and coloured pencils
Procedure
- Record the histogram with classes 10 marks wide.
- Change to classes 5 marks wide and record.
- Change to classes 25 marks wide and record.
How this simulation is simplified
- Each class includes its lower end but not its upper end: a mark of 30 is in 30–40.