A picture graph has a key showing ★ = 5 students. The 'soccer' row has 6 stars. How many students chose soccer?
A6 — count the symbols in the row
B11 — add the symbol count (6) to the key value (5)
C30 — multiply the symbol count (6) by the key value (5)
D1 — divide the symbol count (6) by the key value (5), rounding down
When a key says each symbol represents N items, you must multiply the symbol count by N to recover the actual data value. 6 symbols × 5 students per symbol = 30 students. Reporting just the symbol count (6) is the most common reading error — it ignores the key entirely and gives an answer that is 5 times too small.
Question 2 Multiple Choice
A student is making a picture graph where the largest category has 40 data points. Which key value produces the most readable graph?
AEach symbol = 1 (shows exact counts with no multiplication required)
BEach symbol = 10 (at most 4 symbols per row — clean and easy to scan)
CEach symbol = 100 (fewer than 1 symbol for most categories)
DEach symbol = 3 (gives about 13 symbols for the largest row)
A key of 10 gives at most 4 symbols in the largest row, which is clean and easy to count at a glance. A key of 1 requires drawing 40 symbols in one row — cluttered and hard to count. A key of 100 would give less than 1 symbol for any category under 100, making the graph unreadable. A key of 3 gives ~13 symbols per row for the largest category, which is workable but busier than necessary. Choosing a key that keeps rows between 2–10 symbols is the standard design goal.
Question 3 True / False
To find the number of students who chose 'dogs' in a picture graph, you should count the symbols in that row and report that count as your answer.
TTrue
FFalse
Answer: False
This is only correct if the key says each symbol = 1. If the key says each symbol = 3 (or any number greater than 1), you must multiply the symbol count by the key value to get the actual data. Skipping the multiplication step is the most common picture-graph reading error — it produces an answer that is too small by a factor equal to the key value.
Question 4 True / False
When comparing two rows in a picture graph where each symbol = 3, you should multiply each row's symbol count by 3 before comparing, not compare the symbol counts directly.
TTrue
FFalse
Answer: True
Because the key applies equally to every row, comparing symbol counts directly gives the same relative ordering as comparing the actual values — the row with more symbols always has more data. So in practice, for simple 'which is more' comparisons, you don't have to multiply first. However, when asked 'how many more' or 'what is the total', you must apply the key. The habit of always applying the key before making any numerical comparison prevents errors on these calculation questions.
Question 5 Short Answer
Why do picture graphs sometimes use a key where each symbol represents more than one item, instead of drawing one symbol per item?
Think about your answer, then reveal below.
Model answer: A scaled key lets you represent large data values with far fewer symbols, making the graph easier to read at a glance. If one category has 40 items and you draw one symbol per item, that row contains 40 symbols — visually cluttered and tedious to count. With a key of 'each symbol = 10', you draw only 4 symbols, which is clean and instantly scannable. The cost is that readers must multiply when interpreting the graph, but the visual clarity gained is worth it for large data sets. Choosing the right key value is a design decision about how to represent information efficiently.
This question tests whether the student understands why the key exists at all — not just how to use it. The key is a compression device: it lets a small visual (a few symbols) represent a large quantity. Understanding this 'why' also explains why the key value matters: too small a value gives too many symbols (cluttered), too large a value gives too few symbols to compare meaningfully.