About Graphical Representation — Class 10 ICSE

Plot and interpret histograms, frequency polygons, and cumulative frequency curves. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 10-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Graphical Representation — solved examples for Class 10 ICSE

Practice questions on Graphical Representation

1. Q1.easy

   In a histogram, the area of each bar is proportional to:

   1. A)The class width
   2. B)The frequency of that class
   3. C)The cumulative frequency
   4. D)The class mark
   Show answer

   Answer: The frequency of that class

   Hint: Area = width × height. For equal class widths, height alone represents frequency.

2. Q2.easy

   A frequency polygon is drawn by plotting:

   1. A)Frequencies against upper class boundaries
   2. B)Frequencies against class marks (mid-values)
   3. C)Cumulative frequencies against upper boundaries
   4. D)Frequencies against lower class boundaries
   Show answer

   Answer: Frequencies against class marks (mid-values)

   Hint: The frequency polygon connects the midpoints of the tops of histogram bars.

3. Q3.easy

   The class mark of the interval $20 - 30$ is:

   1. A)$20$
   2. B)$30$
   3. C)$25$
   4. D)$50$
   Show answer

   Answer: $25$

   Hint: Class mark = (Lower limit + Upper limit) / 2.

4. Q4.medium

   A 'less than' ogive passes through the points $(10, 5)$, $(20, 15)$, $(30, 30)$, $(40, 42)$, $(50, 50)$. What is the frequency of the class $20-30$?

   1. A)$15$
   2. B)$30$
   3. C)$10$
   4. D)$12$
   Show answer

   Answer: $15$

   Hint: The frequency of a class = cf at its upper boundary minus cf at its lower boundary.

5. Q5.medium

   From the following ogive data, estimate the median.
   
   | Less than | $10$ | $20$ | $30$ | $40$ | $50$ | $60$ |
   |---|---|---|---|---|---|---|
   | cf | $5$ | $13$ | $28$ | $42$ | $48$ | $50$ |

   1. A)$28$
   2. B)$30$
   3. C)$25.67$
   4. D)$27.33$
   Show answer

   Answer: $27.33$

   Hint: n = 50, n/2 = 25. Median class is where cf first reaches 25. Interpolate.

6. Q6.medium

   Convert the following inclusive classes to exclusive classes: $1-10, 11-20, 21-30, 31-40$. The adjusted first class is:

   1. A)$0.5-10.5$
   2. B)$1-10$
   3. C)$0-11$
   4. D)$0.5-9.5$
   Show answer

   Answer: $0.5-10.5$

   Hint: Adjustment factor = (11-10)/2 = 0.5. Subtract from lower, add to upper.

7. Q7.hard

   A histogram has unequal class widths as shown. Find the adjusted height (frequency density) for the class $20-50$ with frequency $30$.
   
   Minimum class width in the distribution = $10$.

   1. A)$30$
   2. B)$10$
   3. C)$15$
   4. D)$3$
   Show answer

   Answer: $10$

   Hint: Frequency density = frequency / class width. Or adjust: height = frequency × (minimum width / class width).

8. Q8.hard

   The following data gives the distribution of wages. Draw a histogram and estimate the mode graphically.
   
   | Wages | $800-840$ | $840-880$ | $880-920$ | $920-960$ | $960-1000$ |
   |---|---|---|---|---|---|
   | Workers | $14$ | $20$ | $30$ | $22$ | $14$ |
   
   The mode estimated from the histogram is approximately:

   1. A)$892$
   2. B)$896$
   3. C)$900$
   4. D)$888$
   Show answer

   Answer: $896$

   Hint: Draw diagonals from the top corners of the modal class bar to adjacent bars and find the intersection.

9. Q9.hard

   From the following data, construct both ogives and find the median graphically.
   
   | Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
   |---|---|---|---|---|---|
   | $f$ | $5$ | $15$ | $20$ | $12$ | $8$ |
   
   The intersection of the two ogives occurs at approximately which x-value?

   1. A)$22$
   2. B)$24$
   3. C)$25$
   4. D)$23.5$
   Show answer

   Answer: $25$

   Hint: The intersection gives the median. Verify using the median formula.

These are 9 of the 60 questions available for Graphical Representation. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.