A bar graph uses a scale where each unit on the vertical axis represents 5 students. A bar reaches up to position 4 on the axis. How many students does this bar represent?
A4 — that is the number where the bar ends
B9 — because 4 + 5 = 9
C20 — because 4 units × 5 students per unit = 20
D5 — because the scale is 5
When a graph has a scale, you multiply: graph position × scale factor = actual value. The bar reaches position 4, and each unit represents 5 students, so 4 × 5 = 20. Option A is exactly the misconception being tested — reading the axis position as the actual count without applying the scale factor. This mistake makes the answer five times too small.
Question 2 Multiple Choice
Two bars in a scaled graph (scale factor = 10) reach axis positions '3' and '6'. How many MORE students does the second category have than the first?
A3 — the difference in axis positions
B30 — apply scale to the difference: (6 − 3) × 10
C6 — the axis position of the second bar
D60 — the scaled value of the second bar alone
Apply the scale before comparing. Bar 1 = 3 × 10 = 30; Bar 2 = 6 × 10 = 60. Difference = 60 − 30 = 30. Equivalently, the difference in axis positions is 3 units, and 3 × 10 = 30. Option A is the error of comparing axis positions without scaling — it gives an answer 10 times too small. Option D correctly scales one bar but doesn't find the difference.
Question 3 True / False
The first step before reading any value from a scaled graph is to identify the scale factor.
TTrue
FFalse
Answer: True
Without knowing the scale, you cannot interpret any bar height or data point correctly. The scale is found by examining the axis: find two consecutive labeled values and note the difference — that is the scale factor. Every read after that is: axis position × scale factor = actual value. Skipping this step produces systematically wrong answers.
Question 4 True / False
On a graph where each unit represents 5, a bar reaching '8' on the axis means there are 8 items in that category.
TTrue
FFalse
Answer: False
With a scale factor of 5, each unit on the axis represents 5 real items. A bar at position 8 means 8 × 5 = 40 items — not 8. Reading 8 as the actual count ignores the scale entirely. This is the most common and consequential error with scaled graphs: treating the axis position as a direct count rather than a scaled position.
Question 5 Short Answer
A graph's vertical axis shows the values 0, 2, 4, 6, 8, 10. A bar reaches the mark labeled '6'. How do you find the actual count, and what error would a student who ignores the scale make?
Think about your answer, then reveal below.
Model answer: First identify the scale: consecutive values differ by 2, so each unit represents 2. The bar at position 6 means 6 × 2 = 12 actual items. A student who ignores the scale reads 6 as the answer, getting half the real value.
This problem illustrates why checking the scale is non-negotiable. A scale of 2 is subtle — the axis looks like it counts by ones if you're not paying attention. The habit of reading the scale before reading any data value is what separates reliable graph readers from those who get caught by unfamiliar scales.