Grouped frequency table and relative frequency chart
MathematicsStatisticsAges 14–15
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Statistics
A data sample (student height, weight, or daily self-study time) is grouped into classes of a chosen width. The frequency table n_i, relative frequency f_i = n_i/n·100%, and the histogram update instantly as you drag the width slider; click a bar to see the values in that class, or click "New data" for a fresh sample. Two more screens: Frequency density (unequal class widths you can drag; bar height = frequency ÷ class width) and Cumulative frequency (read the median, quartiles, interquartile range and any percentile from the graph, with a box plot).
Lesson: Grouped frequency tables, grouped relative frequency, and histograms
What it shows
With equal classes [a; a + w) the simulation counts the frequency n_i and the relative frequency f_i = n_i/n · 100%. When classes have unequal widths, the bar height must be the frequency density = frequency ÷ class width, so that the area of each bar equals its frequency. The cumulative frequency graph shows how many values lie below each upper class boundary; reading across at n/4, n/2 and 3n/4 gives estimates of Q1, the median and Q3, which build a box plot. For box plots of raw data, see the sim "Summary statistics of a data set".
How to use
On Equal classes, drag the Class width slider and switch between Frequency and Relative frequency. On Frequency density, drag the ▲ handles to move the class boundaries, click a bar to see f ÷ w, and press Height = frequency (misleading) to compare. On Cumulative frequency, move the Percentile P slider, tap the graph to read how many values lie below x, and compare the graph estimates with the raw-data median and quartiles.
Parameters you can change
- Sample size n 20–200
- Class width 2–20
- Chart quantity Frequency n_i, Relative frequency f_i (%)
- Data set Height of Grade 9 students (cm), Weight of students (kg), Daily self-study time (minutes)
- Show frequency polygon
- Screen Equal classes, Frequency density (unequal classes), Cumulative frequency and box plot
- Percentile P (Cumulative frequency screen) 1–99
Questions to explore
- What do the relative frequencies in the table always add up to, whatever class width you choose?
- Which class width gives the clearest picture of the distribution for this data set, and why?
- Into which class does a value lying exactly on the boundary between two classes go?
