Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 15 Data Representation and Prediction

Count above a mark from a histogram with an unequal class

Answer: 24 students

💡 What it's asking: When the bars of a histogram have different widths, the AREA of a bar (not just its height) tells you how many students are in it. Find the frequency of each bar above 30 and add them.

1. 1Spot the standard (usual) class width and notice the 30-50 bar is twice as wide.
2. 2For a double-width bar, frequency = height × 2 = 6 × 2 = 12.
3. 3The 50-60 bar has the standard width, so its frequency is just its height: 12.
4. 4Add the bars above 30 marks: 12 + 12 = 24 students.

✅ All the bars together give 8 + 4 + 10 + 12 + 12 = 46, which is the total number of students, so the readings are right.

Fraction above a mark from a histogram with unequal classes

Answer: 7/12

💡 What it's asking: We need the fraction of students who scored more than 40. Two bars are twice the standard width, so their frequencies are double their heights.

1. 1Read the bar heights: 20, 80, 60 and 10. The standard width is 10 marks.
2. 2The 40-60 and 60-80 bars are 20 marks wide (double), so their frequencies are 2 × 60 = 120 and 2 × 10 = 20.
3. 3Total students = 20 + 80 + 120 + 20 = 240.
4. 4Above 40 marks = 120 + 20 = 140.
5. 5Fraction = 140/240 = 7/12.

✅ 7/12 is a bit more than a half, and the two right-hand bars do cover more area than the left two, so it makes sense.

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