What could be the problems faced in preparing such a pictograph, if the total number of students present in a class is 33 or 27?

Question

Homi · Accepted Answer

Understand the Question

In a pictograph, a single symbol represents a fixed number of items (a scale factor, such as $5$ or $10$ students).
When the total number of students ( $33$ or $27$ ) is not an exact multiple of the scale, we are left with a remainder.
Representing these remainders requires drawing fractional or partial symbols (like $\dfrac{3}{5}$ or $\dfrac{7}{10}$ ), which creates practical difficulties in drawing and reading the pictograph.

Step 1 · Evaluate Scale of 5 Students per Symbol

If $1\text{ symbol} = 5\text{ students}$ : Diagram 1

For $33$ students: $33 \div 5 = 6 \text{ with a leftover of } 3$ This requires $6$ full symbols and $\dfrac{3}{5}$ of a symbol.

For $27$ students: $27 \div 5 = 5 \text{ with a leftover of } 2$ This requires $5$ full symbols and $\dfrac{2}{5}$ of a symbol.

Drawing accurate fractions like $\dfrac{3}{5}$ or $\dfrac{2}{5}$ of a symbol is very difficult.

Step 2 · Evaluate Scale of 10 Students per Symbol

If $1\text{ symbol} = 10\text{ students}$ :

For $33$ students: $33 \div 10 = 3 \text{ with a leftover of } 3$ This requires $3$ full symbols and $\dfrac{3}{10}$ of a symbol.

For $27$ students: $27 \div 10 = 2 \text{ with a leftover of } 7$ This requires $2$ full symbols and $\dfrac{7}{10}$ of a symbol.

Drawing fractions like $\dfrac{3}{10}$ or $\dfrac{7}{10}$ of a symbol makes the scale uneven and visually messy.

Step 3 · Identify Key Difficulties

Using partial symbols creates the following main issues:

Difficulty in Drawing: Precisely sketching fractions like $\dfrac{3}{5}$ , $\dfrac{2}{5}$ , $\dfrac{3}{10}$ , or $\dfrac{7}{10}$ of a symbol is nearly impossible by hand.
Visual Confusion & Misinterpretation: A viewer cannot easily guess the exact numerical value of a partial symbol, making quick and accurate reading difficult.

Answer

The main problems are:

Difficulty in Drawing: Drawing fractional symbols like $\dfrac{3}{5}$ , $\dfrac{2}{5}$ , $\dfrac{3}{10}$ , or $\dfrac{7}{10}$ accurately is difficult.
Visual Confusion: Viewers cannot easily interpret or count partial symbols, leading to incorrect estimation of data.

Common Mistakes

Ignoring the Remainder: Rounding off or omitting the leftover students ( $3$ or $7$ ) instead of accounting for them, which gives an incorrect total.
Assuming Partial Symbols are Clear: Assuming readers can accurately distinguish between fine fractions like $\dfrac{3}{10}$ and $\dfrac{2}{5}$ purely by visual inspection.

Question 4