Reading a Class Survey
A Grade 3 class surveys 24 students about their favourite fruit. The results are shown as counts: apples 6, bananas 9, grapes 5, oranges 4. The class makes a bar graph, but the bars are drawn with unequal widths and no scale on the vertical axis. One student reads the banana bar as "about 20" because it is the tallest. Another says apples and grapes together beat bananas. The teacher asks the class to rebuild the graph correctly and to answer questions from the data rather than from the picture.
1. Explain what is wrong with the first graph and describe how to fix it. Then state how many students chose bananas and how many chose apples and grapes together, and decide whether the second student's claim is correct.
Read the worked answer
Problems with the first graph:
- Bars have unequal widths, so taller-looking bars can mislead.
- There is no scale on the vertical axis, so a reader cannot tell what a bar height means.
- The student reading "about 20" for bananas is guessing from height, not from the data.
Fixes: give every bar the same width, label the vertical axis with a scale (for example, 0, 1, 2, 3 … up to 9 or 10), and title the graph.
From the counts:
- Bananas: 9 students.
- Apples + grapes: 6 + 5 = 11 students.
So the second student is correct: 11 is greater than 9. Apples and grapes together were chosen by more students than bananas alone.
Check the total: 6 + 9 + 5 + 4 = 24, which matches the 24 students surveyed.
2. The class wants to show the same data as a picture graph using one fruit symbol for every 2 students. Explain how many symbols each fruit needs and what to do about any leftover students. Then state which fruit is the most popular and by how many students it leads the next most popular.
Read the worked answer
With one symbol for every 2 students:
- Apples 6: 6 ÷ 2 = 3 symbols
- Bananas 9: 9 ÷ 2 = 4 symbols with 1 left over
- Grapes 5: 5 ÷ 2 = 2 symbols with 1 left over
- Oranges 4: 4 ÷ 2 = 2 symbols
Bananas and grapes do not divide evenly. A common solution is to use a half symbol for the leftover 1 student, so bananas show 4½ symbols and grapes show 2½ symbols. Another option is to use one symbol for every 1 student, which avoids halves but makes a longer graph.
Most popular: bananas with 9 students. Next most popular: apples with 6 students. Bananas lead apples by 9 − 6 = 3 students.