One dataset, three useful pictures

1 · Learn

A fictional class records ONE usual way of travelling per pupil. The frequency table is Walk 8, Bus 6, Cycle 4, Car 2: total 20. These are categories, not measurements. Walk is the modal category because it has the greatest frequency. There is no meaningful numerical mean of the words walk, bus, cycle and car.

A bar chart compares the category counts. Draw equal-width bars with gaps, label every category and use an evenly spaced frequency scale starting at zero. The supplied bars reach 8, 6, 4 and 2. Unequal widths or a hidden truncated baseline can make differences look misleading.

A pie chart shows shares of ONE whole. Calculate each angle as frequency/total × 360°. Walk uses 8/20 × 360° = 144°; Bus 108°; Cycle 72°; Car 36°. These sum to 360°. Use a protractor to draw sectors around the centre, and a key to connect sectors to categories. A pie chart's angles compare proportions, not totals from unrelated groups.

A pictogram replaces counts with symbols and needs a key. In the supplied picture, one circle means 2 pupils: Walk uses 4 circles, Bus 3, Cycle 2 and Car 1. If a category had 5 pupils under that key, it would need 2 whole circles and half a circle, not 5 circles. Keep symbols the same size.

2 · Worked example

Bus represents 6 of the 20 pupils. Its bar height is 6, pie angle is 108°, and pictogram has 3 circles with a key of 2 pupils per circle. These are three representations of the SAME count, not three different totals.

3 · Your turn

Use the supplied dataset. What fraction travel by cycle? What angle represents Car? How many pictogram circles represent Walk? Why must a category not be counted twice in this pie chart?

4 · Apply your learning

On paper draw your own frequency table, bar chart and pie chart for the four supplied categories. Check that the table totals 20 and the pie angles total 360°. Explain which picture makes comparing Walk and Bus easiest for you, and why.