Bar Charts and Pie Charts

Both charts start from the same place: a frequency table counting how many observations fall into each category, or a relative frequency table showing what fraction each category makes up. A bar chart turns each category into a bar whose height equals its count or percent, with gaps between bars because the categories are separate, unordered groups, not points along a continuous scale. A pie chart instead slices a circle: each category gets a wedge whose angle equals its relative frequency times 360 degrees, since the whole circle represents 100% of the data.

The two charts answer slightly different questions. A pie chart is built to show parts of a whole, so it is good at saying 'red is 30% of all responses.' It is weaker at letting you compare two categories directly, because judging and comparing angles or slice areas by eye is hard. A bar chart lines up bars side by side at the same baseline, so your eye can directly compare heights, which is why differences between groups jump out in a bar chart far more than in a pie chart.

This sets up a caution that follows you through the rest of the unit: how a graph is drawn can shape what you see, independent of what the data actually say. A bar chart whose vertical axis starts at 40 instead of 0 stretches the visible gaps between bars, making small real differences look dramatic. Reading graphs carefully, always checking the axis, carries forward into every distribution and comparison you make for the rest of the course.