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About Data Handling — Class 6 Olympiad

Organize data, create and interpret bar graphs and pictographs, and solve statistics-based reasoning problems. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 10). On this page you can practice 48 questions across three difficulty levels — 10 easy, 20 medium, and 18 hard — each with a visual step-by-step solution, plus a timed 33-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Data Handling — solved examples for Class 6 Olympiad

Example 1easy

In a survey of favorite fruits, 5 people chose Apple, 7 chose Banana, 4 chose Orange, and some chose Grapes. If the total number of people surveyed was 25, how many people chose Grapes?
  1. A)A. 7
  2. B)B. 8
  3. C)C. 9
  4. D)D. 10

Step-by-step solution

  1. The number of people who chose Apple, Banana, and Orange are 5, 7, and 4 respectively.
  2. Sum of people who chose these three fruits = 5 + 7 + 4 = 16 people.
  3. The total number of people surveyed was 25.
  4. Number of people who chose Grapes = Total people surveyed - (People who chose Apple + Banana + Orange) = 25 - 16 = 9 people.

Answer: C. 9

Example 2medium

A pictograph represents the number of trees planted in four different parks.
Park P: 🌳🌳🌳🌳
Park Q: 🌳🌳🌳🌳🌳🌳
Park R: 🌳🌳🌳
Park S: 🌳🌳🌳🌳🌳
Each symbol 🌳 represents an equal number of trees. The number of trees planted in Park R is 60% of the number of trees planted in Park S. If 240 trees were planted in Park P, what is the total number of trees planted in all four parks?
  1. A)1080
  2. B)1120
  3. C)1160
  4. D)1200

Step-by-step solution

  1. From the pictograph, Park P has 4 tree symbols. Given that 240 trees were planted in Park P, each tree symbol (🌳) represents 240 / 4 = 60 trees.
  2. Calculate trees for other parks:
    Park Q = 6 symbols × 60 trees/symbol = 360 trees.
    Park R = 3 symbols × 60 trees/symbol = 180 trees.
    Park S = 5 symbols × 60 trees/symbol = 300 trees.
  3. Verify the given condition: Park R (180 trees) is 60% of Park S (300 trees)? 0.60 × 300 = 180. The condition holds true.
  4. Total trees planted in all four parks = 240 (P) + 360 (Q) + 180 (R) + 300 (S) = 1080 trees.

Answer: 1080

Example 3hard

A school surveyed 120 students about their favourite colours: Red (R), Green (G), Blue (B), Yellow (Y). Each student chose exactly one colour. Green received twice as many votes as Red. Blue received 5 more votes than Green. Yellow received more votes than Red but fewer than Green. All vote counts are distinct positive integers. What is the maximum possible number of votes for Yellow?
  1. A)A) 28
  2. B)B) 29
  3. C)C) 30
  4. D)D) 31

Step-by-step solution

  1. Let the number of votes for Red be R. According to the conditions: Green (G) = 2R, Blue (B) = G + 5 = 2R + 5. Yellow (Y) must satisfy R < Y < G, which means R < Y < 2R.
  2. The total number of votes is 120: R + G + B + Y = 120. Substituting the expressions: R + 2R + (2R + 5) + Y = 120, which simplifies to 5R + 5 + Y = 120, so Y = 115 - 5R.
  3. Now, substitute Y into the inequality R < Y < 2R: R < 115 - 5R < 2R. This gives two inequalities: (1) R < 115 - 5R => 6R < 115 => R < 19.16... (2) 115 - 5R < 2R => 115 < 7R => R > 16.42...
  4. Since R must be an integer, 17 ≤ R ≤ 19. To maximize Y, we need to minimize R in Y = 115 - 5R. So, R = 17. If R = 17, then Y = 115 - 5(17) = 115 - 85 = 30. (R=17, G=34, B=39, Y=30; all distinct and satisfy R<Y<G).
    R=17  ⟹  Y=115−5(17)=30R = 17 \implies Y = 115 - 5(17) = 30

Answer: C) 30

Practice questions on Data Handling

  1. Q1.easy

    A pictograph shows the number of cars sold by a dealer. Each full car symbol (🚗) represents 10 cars. If half a car symbol ( आधा 🚗 ) represents 5 cars, and the pictograph shows 3 full symbols and 1 half symbol for Tuesday, and 4 full symbols for Wednesday, what is the total number of cars sold on both days?
    1. A)A. 65
    2. B)B. 75
    3. C)C. 85
    4. D)D. 95
    Show answer

    Answer: B. 75

    Hint: First, calculate the total number of cars sold on Tuesday and Wednesday separately. Then, add these two totals together.

  2. Q2.easy

    A bar graph shows the number of students who prefer different sports: Football (20 students), Cricket (40 students), Basketball (10 students), and Tennis (30 students). What percentage of the total students surveyed prefer Football?
    1. A)A. 20%
    2. B)B. 25%
    3. C)C. 30%
    4. D)D. 35%
    Show answer

    Answer: A. 20%

    Hint: First, find the total number of students surveyed by adding up all the preferences. Then, divide the number of students who prefer Football by this total and multiply by 100 to get the percentage.

  3. Q3.easy

    The average height of 5 students in a group is 140 cm. If a new student with a height of 146 cm joins the group, what will be the new average height of the 6 students?
    1. A)A. 141 cm
    2. B)B. 142 cm
    3. C)C. 143 cm
    4. D)D. 144 cm
    Show answer

    Answer: A. 141 cm

    Hint: First, calculate the total height of the initial 5 students. Then, add the new student's height to find the new total height, and divide by the new number of students.

  4. Q4.medium

    A survey was conducted among 200 students about their favorite fruits. The results were recorded in a frequency table, but some entries are missing or described by relations:
    | Fruit | Number of Students |
    | :--------- | :----------------- |
    | Apple | 2x |
    | Banana | 3x |
    | Cherry | x + 10 |
    | Date | y |
    | Elderberry | y - 10 |
    The number of students who like Banana is twice the number of students who like Cherry. How many students chose Date as their favorite fruit?
    1. A)30
    2. B)35
    3. C)40
    4. D)45
    Show answer

    Answer: 40

    Hint: First, use the relationship between Banana and Cherry to find the value of x. Then calculate the number of students for Apple, Banana, and Cherry. Finally, use the total number of students to find y.

  5. Q5.medium

    A bar graph shows the production of three types of toys (Cars, Dolls, Robots) in a factory over two months, January and February.
    Production in January: Cars = 300 units, Dolls = 200 units, Robots = 200 units.
    Production in February: Cars = 450 units, Dolls = 300 units, Robots = 350 units.
    What is the ratio of the total production of Dolls in both months to the total production of Robots in both months?
    1. A)10 : 11
    2. B)11 : 10
    3. C)5 : 6
    4. D)6 : 5
    Show answer

    Answer: 10 : 11

    Hint: Calculate the total production for Dolls across both months, then do the same for Robots. Finally, express these two totals as a simplified ratio.

  6. Q6.medium

    A student conducted a survey of 100 people about their favorite color among Red, Blue, Green, and Yellow. She presented her findings in a bar graph.
    She claimed:
    I. The number of people who like Red is twice the number who like Green.
    II. The number of people who like Blue is 20% less than those who like Red.
    III. The number of people who like Yellow is 15 more than those who like Green.
    IV. The total number of people surveyed was 100, but her graph shows the sum of people who like Red, Blue, Green, and Yellow as 105.
    Which statement indicates a fundamental error in the data collection or representation that cannot be reconciled?
    1. A)Statement I
    2. B)Statement II
    3. C)Statement III
    4. D)Statement IV
    Show answer

    Answer: Statement IV

    Hint: Consider which statement presents an impossibility or a direct contradiction with basic data handling principles, rather than just a complex relationship.

  7. Q7.hard

    A pictograph shows the number of cars sold by a dealer over three months: March, April, and May. Each car symbol (🚗) represents a certain number of cars. March had 4 🚗 symbols, April had 6 🚗 symbols, and May had 5 🚗 symbols. The total number of cars sold in April and May combined was 165. How many cars were sold in March?
    1. A)A) 45
    2. B)B) 60
    3. C)C) 75
    4. D)D) 80
    Show answer

    Answer: B) 60

    Hint: First, determine the value represented by one car symbol using the combined sales data for April and May. Then, use this scale to find sales for March.

  8. Q8.hard

    A bar graph was drawn to show the heights of five friends: Amit, Bala, Chitra, David, and Esha. The graph paper had a scale where 1 unit on the vertical axis represented 10 cm. Amit's bar reached 14 units, Bala's reached 12 units, Chitra's 15 units, David's 11 units, and Esha's 13 units. If the paper setter made an error and the correct scale should have been 1 unit representing 8 cm, what is the actual difference in height between the tallest and the shortest friend?
    1. A)A) 32 cm
    2. B)B) 30 cm
    3. C)C) 28 cm
    4. D)D) 24 cm
    Show answer

    Answer: A) 32 cm

    Hint: First, identify the friends who are tallest and shortest based on the number of units. Then, recalculate their actual heights using the corrected scale and find the difference.

  9. Q9.hard

    In a class of 50 students, a survey was conducted about their preference for two subjects: Mathematics and Science. 70% of the students liked Mathematics, and 60% liked Science. If 10% of the students liked neither subject, how many students liked both Mathematics and Science?
    1. A)A) 15
    2. B)B) 20
    3. C)C) 25
    4. D)D) 30
    Show answer

    Answer: D) 30

    Hint: Use the concept of percentages and sets. First, find the percentage of students who liked at least one subject. Then, apply the formula for the union of two sets to find the overlap.

These are 9 of the 48 questions available for Data Handling. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.