Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Pictograph.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
A pictograph (or picture graph) displays data using pictures or symbols, where each picture represents a specific quantity. For example, if 🍎 = 5 apples, then 🍎🍎🍎 means 15 apples. A key (legend) always tells you what each symbol represents.
Instead of boring bars, pictographs use fun pictures to show data. If each smiley face means 2 students, and you see 5 smiley faces, that's 10 students! It makes data feel more real.
Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea:Pictograph organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to pictograph but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
A pictograph shows fruits with key 1 symbol = 8. Apples: 5 symbols. Bananas: 2.5 symbols. How many bananas?
Answer
20
First step
1
2.5×8=20.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A pictograph uses 1 symbol = 6 books. To minimize the number of total symbols across three rows of 30, 42, and 54 books, the key is set so each row uses whole symbols. What is the largest such key that works?
Example 3
medium
A pictograph shows two categories. Row A: 3 symbols = 24 items. What is the key value (items per symbol)?
Example 4
challenge
A pictograph compares two months. May has 6 symbols, June has 9 symbols. June's total is 24 more than May's. What is the key value (items per symbol)?
Example 5
easy
A pictograph shows the number of books read by four students. Each book symbol represents 2 books. Amy has 3 symbols, Ben has 5 symbols, Cara has 2 symbols, and Dan has 4 symbols. How many books did each student read?
Example 6
medium
A pictograph uses a star symbol where each star represents 5 stickers. If one row shows 3 full stars and a half star, how many stickers does that represent? Explain what a half symbol means.
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A pictograph key says 1 symbol = 2 apples. A row has 4 symbols. How many apples?
Example 2
easy
If 1 symbol = 5 and a row shows 3 symbols, how many items?
Example 3
easy
A pictograph uses 1 symbol = 10. A category has 6 symbols. How many items?
Example 4
easy
With 1 symbol = 4, how many symbols represent 12 items?
Example 5
easy
Two rows show 5 and 3 symbols with 1 symbol = 2. How many more items in the first row?Key: 1 symbol = 2. Row 1 has 5 symbols (10 items), Row 2 has 3 symbols (6 items). How many more in Row 1?
Example 6
easy
A pictograph must always include a key. If a graph has 5 symbols but no key, can you find the exact count? Answer 1 for yes, 0 for no.
Example 7
easy
With 1 symbol = 3, a row of 7 symbols shows how many items?
Example 8
easy
A pictograph row has 2 symbols, each = 6. What does the row total?
Example 9
medium
A pictograph row shows 4 full symbols and 1 half symbol with 1 symbol = 8. What is the row total?
Example 10
medium
To show 45 items with 1 symbol = 10, how many full symbols and what fraction extra? Give the fraction part.
Example 11
medium
A pictograph shows categories with 3, 5, and 2 symbols where 1 symbol = 4. What is the grand total of items?Key: 1 symbol = 4. Categories show 3, 5, and 2 symbols. What is the grand total of all items?
Example 12
medium
With 1 symbol = 6, category A shows 5 symbols and category B shows 8 symbols. How many items combined?Key: 1 symbol = 6. Category A has 5 symbols (30 items), B has 8 symbols (48 items). How many combined?
Example 13
medium
A pictograph row totals 28 items using 1 symbol = 4. How many symbols are drawn?
Example 14
medium
Two pictograph rows use different keys by mistake: row A has 4 symbols at 5 each, row B has 4 symbols at 3 each. What is the true difference in items?Row A: 4 symbols × key 5 = 20. Row B: 4 symbols × key 3 = 12. What is the true difference?
Example 15
challenge
A pictograph must show 90 items. Using 1 symbol = 12, how many full symbols are drawn and what fraction extra? Give the fraction part simplified.
Example 16
challenge
A pictograph shows category X with 6 symbols and category Y with twice as many items as X. With 1 symbol = 5, how many symbols does Y need?
Example 17
challenge
A pictograph uses 1 symbol = 8. Category A has 3.5 symbols and category B has 2.5 symbols. How many more items are in A than B?Key: 1 symbol = 8. A has 3.5 symbols (28 items), B has 2.5 symbols (20 items). How many more in A?
Example 18
medium
A pictograph row totals 36 items using 1 symbol = 9. How many symbols are drawn?
Example 19
medium
With 1 symbol = 7, category A shows 6 symbols and B shows 4 symbols. How many items combined?Key: 1 symbol = 7. A has 6 symbols (42 items), B has 4 symbols (28 items). How many items combined?
Example 20
medium
A pictograph row shows 3 full symbols and 1 half symbol with 1 symbol = 10. What is the row total?
Example 21
easy
A pictograph key says 1 symbol = 4 apples. A row has 6 symbols. How many apples?
Example 22
easy
If 1 symbol = 7 and a row shows 4 symbols, how many items?
Example 23
easy
A pictograph uses 1 symbol = 20. A category has 4 symbols. How many items?
Example 24
easy
With 1 symbol = 6, how many symbols represent 30 items?
Example 25
easy
Two rows show 6 and 4 symbols with 1 symbol = 3. How many more items in the first row?
Example 26
easy
With 1 symbol = 9, a row of 4 symbols shows how many items?
Example 27
easy
A pictograph row has 3 symbols, each = 7. What does the row total?
Example 28
medium
A pictograph row shows 5 full symbols and 1 half symbol with 1 symbol = 10. What is the row total?
Example 29
medium
To show 27 items with 1 symbol = 6, what fractional part of a symbol is needed beyond the full symbols? Give the fraction.
Example 30
medium
A pictograph shows categories with 4, 6, and 3 symbols where 1 symbol = 5. What is the grand total of items?
Example 31
medium
With 1 symbol = 12, category A shows 7 symbols and category B shows 5 symbols. How many more items in A than B?
Example 32
medium
A pictograph key is 1 symbol = 15. A row shows 84 items. How many full symbols plus what fraction? Give the fraction part.
Example 33
medium
A pictograph uses 1 symbol = 10. Class 5A has 3 symbols and Class 5B has 4.5 symbols. What is the combined total?
Example 34
hard
A pictograph uses 1 symbol = 4. Category A shows 7 symbols, B shows 4 symbols, C shows 6.5 symbols. What is the mean count per category?
Example 35
hard
A pictograph designer wants the smallest key value k that lets categories with counts 16, 24, and 40 each use a whole number of symbols. What is k?
Example 36
hard
A pictograph row needs to show 99 items. The key value is 1 symbol = 11. How many symbols are drawn (whole only, no fractions)?
Example 37
medium
A pictograph uses 1 symbol = 4. To show 14 items with whole-and-half symbols, how many symbols (use half-symbols if needed) are drawn? Give as a decimal.
Example 38
challenge
A pictograph uses 1 symbol = k for an unknown k. Three rows show 5, 8, and 11 symbols with totals 30, 48, and 66 respectively. Find k.
Example 39
medium
A pictograph shows the number of goals scored by four teams. Each football symbol = 3 goals. Team W: 6 symbols, Team X: 4 symbols, Team Y: 7 symbols, Team Z: 5.5 symbols (half symbol included). How many more goals did Team Y score than Team Z?
Example 40
hard
You need to create a pictograph for this data: Red 18, Blue 27, Green 12, Yellow 9. Choose an appropriate key value and determine how many symbols each category needs.