Vardaan
Class 7 Maths • Chapter 03

Data Handling

Vardaan Learning Institute • Detailed Notes with Practice Questions

📊 1. Key Terms

Term Definition Example
Data A collection of numbers/information gathered for a specific purpose Marks of 10 students
Raw Data Data collected in original form, not organised 52, 43, 76, 90, 43, 52, 76
Range Difference between highest and lowest values Range = Max − Min = 90 − 43 = 47
Frequency Number of times a value appears in data 52 appears twice → frequency = 2
Tally Marks Used to organise and count data quickly. Every 5th mark crosses the previous 4 (||||) |||| | = 6
Frequency Distribution Table A table showing values and their frequencies See example below
Class Interval Groups of values with equal width: e.g. 0-10, 10-20 Class width = 10
Example — Grouped Frequency Table:
Scores of 20 students: 55 60 65 70 45 80 75 50 65 70 72 55 65 80 48 72 60 75 50 70

Class Interval Tally Frequency
40 – 50 ||| 3
50 – 60 |||| 4
60 – 70 |||| | 6
70 – 80 |||| || 7
Total 20

📈 2. Mean, Median, Mode

Mean = Sum of all values ÷ Total number of values     ( x̄ = Σx/n )
Median = Middle value when data is arranged in ASCENDING order
Mode = Value that appears MOST frequently in the data
Example: Data = 4, 7, 3, 4, 8, 4, 7, 3
Arranged: 3, 3, 4, 4, 4, 7, 7, 8 (n=8)
Mean = (3+3+4+4+4+7+7+8) ÷ 8 = 40 ÷ 8 = 5
Median = average of 4th and 5th value = (4+4)/2 = 4
Mode = 4 (appears 3 times — most frequent)
🧠 When to use Mean, Median, Mode? • Mean: Best when data has no extreme values (no outliers). Use for exam averages.
• Median: Best when there are extreme values (e.g., salary data with very rich people). Middle value is fair.
• Mode: Best for finding the most popular item. E.g., most common shoe size, most popular subject.

📊 3. Bar Graph

A bar graph uses rectangular bars of equal width to represent data. The height of each bar = the frequency/value.

📊 Favourite Sports of 50 Students (Bar Graph)

🥧 4. Pie Chart (Circle Graph)

A pie chart shows data as parts of a whole circle. Each slice shows a category's share as a fraction/percentage of the total.

Angle for each category = (Value / Total) × 360°
🥧 Time Spent by Students Daily
📈 Double Bar — Sports by Gender

📉 5. Probability — Introduction

Probability of Event E = (Number of Favourable Outcomes) / (Total Possible Outcomes)
Key Points:
✏️ Practice Questions — Data Handling (28 Questions)

Section A — Definitions & Calculation Easy

Q1. Find Mean: 5, 8, 12, 3, 7
Q2. Find Median: 14, 9, 6, 21, 3
Q3. Find Mode: 2, 3, 5, 3, 2, 3, 7, 2, 3
Q4. Find Range: 18, 4, 30, 9, 21, 7
Q5. P(getting a tail when tossing a coin) = ?
Q6. P(getting 5 on rolling a die) = ?
Q7. Which average is most affected by extreme values?
Q8. Angle for category of 15 out of 60 in pie chart = ?

Section B — Data Interpretation Medium

Q9. Scores: 72, 68, 85, 90, 72, 85, 72, 60. Find Mean, Median, Mode.
Q10. If mean of 5 numbers is 12 and four of them are 8, 15, 10, 14, find the fifth number.
Q11. A bag has 4 red, 3 blue, 3 green balls. P(drawing a blue ball) = ?
Q12. Prepare a grouped frequency table for: 22, 34, 12, 55, 42, 34, 22, 55, 34, 12, 22, 42 (class width = 15, starting from 10)

Section C — Word Problems Medium

  1. Q13. Runs scored by Rohit in 6 matches: 45, 72, 60, 88, 55, 30. What is his average score?
  2. Q14. Mean of 8 observations is 25. One observation 15 is removed. Find the new mean of 7 observations.
  3. Q15. A die is rolled once. Find P(a) getting a number greater than 4, (b) getting an odd number, (c) getting a multiple of 3.
  4. Q16. A class of 40 students was asked their favourite colour. Red: 12, Blue: 10, Green: 8, Yellow: 10. Draw a pie chart (find angles for each).
  5. Q17. Monthly rainfall (cm) for 6 months: Jan 4, Feb 2, Mar 0, Apr 6, May 18, Jun 30. Find mean and range.

Section D — Challenge Problems Hard

  1. Q18. In a survey: liking for Mathematics — 45 students, Science — 30, Arts — 15, Sports — 30 (total 120). If this is a pie chart, find which subject gets exactly 90° angle.
  2. Q19. Mean of 10 numbers is 15. Mean of first 5 numbers is 12. What is the mean of the other 5?
  3. Q20. A bag has 5 red, x blue, and 3 green balls. Probability of red ball = 5/14. Find x.
  4. Q21. Median of 7 numbers in ascending order is the 4th number. If four numbers are 3, 7, 9, 15 and three others are all equal to 'k', and k is the mode, and the median is 9, find k.
  5. Q22. Two dice are rolled simultaneously. Find P(sum = 7).
  6. Q23. A class's marks are given. After the teacher adds 5 to every student's mark, how does mean/median/mode change?
  7. Q24. What is the probability that a randomly chosen 2-digit number is a perfect square? List all 2-digit perfect squares first.
  8. Q25. In 30 spins of the wheel, red came 12 times, blue 8 times, green 10 times. Compare the experimental probability vs theoretical (equal chances) for each colour.
✅ Key Answers: Q1: 7 | Q2: 9 | Q3: 3 | Q4: 26 | Q5: 1/2 | Q6: 1/6 | Q8: 90° | Q13: 58.33 | Q24: 6/90 = 1/15 (16,25,36,49,64,81 are 2-digit perfect squares) | Q22: 6/36 = 1/6

📝 Quick Revision

  1. Mean = Sum ÷ Count. Best for balanced datasets without extreme values
  2. Median = Middle value (sorted). If even count, average the two middle values
  3. Mode = Most frequent value. A dataset can have no mode, one mode, or multiple modes
  4. Range = Maximum − Minimum
  5. Pie chart angle = (Value/Total) × 360°
  6. Probability = Favourable Outcomes / Total Outcomes. Always between 0 and 1