Grouped data and histograms: heights in our class
Group the heights of a class into 10 cm classes, draw the histogram, and estimate the mean, the modal class and the median class.
Core concept
For grouped data the mean is estimated as Σfx ÷ Σf using mid-values; cumulative frequency finds the median class
Topic: Grouped data
The heights of 40 students are measured and grouped into classes of 10 cm: 130–140, 140–150, and so on. The number in each class is its frequency f. A histogram shows each class as a bar with no gaps, because height is continuous. We no longer know each exact height, so we use the mid-value x of each class: the mean is estimated as Σfx ÷ Σf. The modal class has the highest frequency. Adding the frequencies one class at a time gives the cumulative frequency cf, and the median class is the one that contains the (N ÷ 2)th student.
What you will learn
- Draw a histogram from a grouped frequency table.
- Estimate the mean of grouped data using mid-values.
- Find the modal class and the median class using cumulative frequency.
Before you start
- Mean, median and mode of ungrouped data.
Materials
- A measuring tape fixed to a wall
Equipment
- Graph paper
Procedure
- Tap − or + on each bar to change how many students are in that class.
- Read the table: f, mid-value x, fx and cf.
- Record the class survey of 40 students, then make the data symmetric with a mean of exactly 155 cm.
- Make 160–170 the modal class, and make the median class 140–150, recording each.
How this simulation is simplified
- Each class includes its lower limit and not its upper limit (for example 150 ≤ height < 160).