L3 · Bar Graphs and Dot Plots of Categorical Data

Learning goal

“I can read the frequencies in a bar graph and a dot plot, build either picture from a frequency table, and find the mode in both.”

Bar graph — a picture of frequencies using bars. Each category has its own bar, and the height of the bar shows that category's frequency.

Dot plot — a picture of frequencies using dots stacked above category labels. Each dot stands for one data point, so the number of dots is the frequency.

Axis — a line on a graph with numbers on it. On a bar graph, the frequency axis tells you how to read each bar's height.

Scale — the steps the axis numbers count by - by 1s, by 2s, by 5s, and so on. Always check the scale before reading a bar.

Worked example

A bar graph is titled "Favourite Sport to Watch." The frequency axis is marked 0, 1, 2, 3, ... up to 10. Reading the bars: the bar for Swimming rises to 8; the bar for Gymnastics rises to 5; the bar for Athletics rises to 6; the bar for Cycling rises to 3. Step 1: To read a bar, go to the TOP of the bar, then across to the number on the frequency axis. Swimming's top stops at 8, so Swimming's frequency is 8. Step 2: Read all four: Swimming 8, Gymnastics 5, Athletics 6, Cycling 3. Step 3: Use them like any frequency table: total = 8 + 5 + 6 + 3 = 22 students. The tallest bar is the mode: Swimming. Say it plainly: a bar graph is a frequency table wearing a picture. The numbers do not change - only the way they are shown.

Check yourself — explain it

Where do you look to find a bar's frequency?

Paired problem — example still visible

A dot plot shows ways to get to school: above the label Bus there are 6 dots; above Walk, 4 dots; above Car, 3 dots; above Bike, 5 dots. (a) How many students are shown? (b) What is the mode? -> (a) 18 (b) Bus (6 dots)

Faded completion — last step is yours

"A bar graph's axis is labelled 0, 2, 4, 6, 8, 10 - it counts by ___. The bars: Red rises to the line labelled 6; Blue rises to 10; Green rises to 4. Blue's frequency is ___, and the mode of the graph is ___." -> 2s (steps of 2); 10; Blue

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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