Questions: Simple Picture Graphs

Question 1

In a class picture graph about favorite colors, the 'blue' column has 4 pictures and the 'red' column has 6 pictures. What does this tell you?

• A. Blue is a better color than red
• B. 6 children chose red as their favorite color
• C. There are 6 red crayons in the class
• D. Blue was counted 4 times more than red

Answer: (B)

In a picture graph where each picture represents exactly one response, counting the pictures in a column tells you how many people made that choice. 6 pictures in the 'red' column means 6 children chose red as their favorite color. Picture graphs represent choices — they tell you how many people responded a certain way, not anything about the objects themselves.

Question 2

A student making a picture graph places her sticker in the 'apple' column, then adds another sticker later because she 'really likes apples.' Is this correct?

• A. Yes — she should be able to show how strongly she feels about her choice
• B. No — each person gets exactly one picture, so a second sticker breaks the one-to-one rule
• C. Yes — adding more pictures makes the graph more accurate
• D. No — she should erase the first sticker and start over

Answer: (B)

Each person gets exactly one picture — this is the one-to-one correspondence that makes the graph valid. If a student places two stickers, the graph shows 2 votes for that student instead of 1, which makes the count wrong. The graph only works because each picture stands for exactly one response. Adding a second sticker breaks the rule and makes the data inaccurate.

Question 3

If pictures in a graph are scattered randomly instead of organized in columns, the graph still works just as well — you just have to count more carefully.

• T. True
• F. False

Answer: False

Organization is what makes a picture graph work. When pictures are lined up in columns, you can count each column reliably and compare column heights at a glance. Scattered pictures are easy to miss, hard to count accurately, and impossible to compare visually. The whole point of a picture graph is to make data easy to read — randomness defeats that purpose.

Question 4

Each picture in a picture graph stands for exactly one person's response.

• T. True
• F. False

Answer: True

This one-to-one rule is the foundation of a picture graph. Every respondent contributes exactly one picture placed in the correct category column. This is the same one-to-one correspondence from counting applied to data display: one person, one picture, one category. When this rule holds, counting the pictures in a column tells you exactly how many people made that choice.

Question 5

What is the rule that makes a picture graph accurate, and why does it matter?

Model answer: Each picture must represent exactly one response — one person, one picture, placed in the right category column. This rule matters because the graph works by counting pictures to count responses. If someone gets two pictures, the count is wrong. If pictures land in the wrong column, the category count is wrong. The graph is only as accurate as the rule it follows.

This is the same one-to-one correspondence students learned for counting applied to data display. Graphs are useful because you trust them to represent reality accurately — and that trust depends entirely on following the one-to-one rule consistently for every respondent.