Data Handling and Presentation · Lesson 2 of 7
Reading and Making Pictographs
“Read picture symbols through their key, then choose a key that represents the data clearly.”
• Explain what a pictograph represents and read its key before counting. • Use whole and partial symbols to calculate and compare frequencies. • Construct a pictograph from a frequency table with a suitable key. • Explain when a chosen key saves space and when it makes accurate drawing difficult. • Make supported comparisons and totals from a pictograph.
Pictures can stand for counts
A pictograph places symbols beside categories so that we can compare counts at a glance. A travel chart might show one small figure for each student who walks, cycles, or takes a bus. We can see the longest row quickly, but to find exact numbers we first need the chart’s key.
A display that uses pictures or symbols to show the frequencies of categories.
The statement telling us how many objects or people one full symbol represents.
If one symbol means one student, eight symbols mean eight students. If one means ten students, eight symbols mean eighty. A half symbol then means five. The picture itself is not enough: always read the key, and check what a fraction of the symbol means before calculating.
| Response about at least nine hours of sleep | Whole symbols | Half symbols | Children when one whole symbol means 10 |
|---|---|---|---|
| Always | 5 | 0 | 50 |
| Sometimes | 2 | 1 | 25 |
| Never | 4 | 0 | 40 |
Problem
A sleep pictograph shows two whole symbols and one half symbol for “Sometimes”; one whole symbol represents 10 children. What is the frequency?
- 1.The two whole symbols represent 2 × 10 = 20 children.
- 2.The half symbol represents half of 10, which is 5 children.
- 3.Together they show 20 + 5 = 25 children. Count children, not 2½ as if it were the final frequency.
Choose and explain a useful key
For classes with 3, 5, 4, 2, 0, 1, 5, and 7 absent students, using one symbol per student is simple. For attendance counts of 30 or 35 students, one symbol each would make a long, crowded picture. A key of 5 students per symbol reduces the drawing; a key of 10 may require half symbols for 25 and 35. Decide on a key by looking at all the values before drawing.
| Class | I | II | III | IV | V | VI | VII | VIII |
|---|---|---|---|---|---|---|---|---|
| Students present | 30 | 35 | 20 | 25 | 30 | 25 | 30 | 20 |
| Symbols with key = 5 | 6 | 7 | 4 | 5 | 6 | 5 | 6 | 4 |
Problem
Represent 35 students with a key of 5 students per symbol, then with a key of 10.
- 1.With a key of 5, calculate 35 ÷ 5 = 7 whole symbols.
- 2.With a key of 10, three whole symbols represent 30 and a half symbol represents 5.
- 3.Both displays represent 35. The second is shorter, but its half symbol must be clearly drawn and explained in the key.
A key of 10 can show 35 with three and a half symbols, but 33 would require a symbol for three children. If the chosen design cannot show that amount clearly, choose another key or another form of display. Never quietly round 33 to 30 or 35.
Draw and interpret pictographs
Start with a frequency table. Write each category in its own row or column. Put the key where a reader will notice it, then draw the correct number of equally sized symbols for each category. Rows may be horizontal or vertical. Finally count back from the completed pictograph to check every category, including any category with zero.
| Shopkeeper | Chaman | Rani | Rukhsana | Jasmeet | Jetha Lal | Poonam Ben |
|---|---|---|---|---|---|---|
| Kites purchased | 250 | 300 | 100 | 450 | 250 | 700 |
Problem
One kite symbol stands for 100 kites. How should 250 and 450 kites appear?
- 1.Two symbols represent 200 kites; half a symbol represents 50. Use 2½ symbols for 250.
- 2.Four symbols represent 400 kites; add half a symbol for 50. Use 4½ symbols for 450.
- 3.For 700, use seven full symbols. Since 700 > 2 × 300, Poonam Ben bought more than twice Rani’s 300 kites.
A different dataset may suggest a different key. Village counts of Mudhol Hounds are 18, 36, 12, 48, 18, and 24. All are multiples of six, so a six-dog key gives 3, 6, 2, 8, 3, and 4 whole symbols. Villages B and D together have 84 dogs; the other four together have 72. This is a comparison of the given village counts, not a claim about all dogs in the region.
In the weekly library-books pictograph, Thursday has the fewest, Saturday has the most, and the six days total 24 books. The reason for Saturday’s larger count is only a possible explanation. In the tractors pictograph, compare villages by converting symbols to tractors before subtracting. In the girls-by-class pictograph, a whole symbol means four girls and a half means two: adding two girls can change a final half symbol into a full one. Class 7 shows 12 girls. These are reasons to include every part of the key in the drawing.
Quiz
A chart has a key of one picture = 10 students. Four pictures represent…
With one full picture = 10, two full pictures and a half picture represent…
Which key represents 18, 36, and 48 with only whole symbols?
A class has 35 present students. With one full symbol = 10, which drawing is accurate?
Why might a key of 10 be awkward for a count of 33?
One picture = 4 girls and a class shows 2½ pictures. How many girls are shown?
Practice Problems
- Draw a pictograph for class absences 3, 5, 4, 2, 0, 1, 5, 7 using one symbol per student; show the class with zero clearly.
- Draw a second pictograph for present students 30, 35, 20, 25, 30, 25, 30, 20 using a five-student key. Verify the first two categories by counting your symbols.
- Use a 100-kite key to represent 250, 300, 100, 450, 250, and 700 kites. Explain your half symbols.
- Choose a key for Mudhol Hound counts 18, 36, 12, 48, 18, 24. Draw the symbols and compare B + D with all other villages.
- A pictograph shows 3½ symbols for one category with a key of 4. Find its frequency and explain what the half symbol means.
- Compare keys of 5 and 10 for a count of 27. Which makes an exact, easy-to-read pictograph? Explain the limitation of each choice.
Key Takeaways
• A pictograph displays category frequencies through symbols. • Read its key before translating whole or partial symbols into numbers. • Choose a key that saves space while still representing every value accurately. • Check the completed symbols against the original frequency table.