CBSE 10th Board Maths : Statistics, Probability, and Mensuration

The home stretch of your CBSE Class 10 Maths journey is here! This article focuses on the last three chapters: statistics, probability, and mensuration (Surface Area & Volume). We’ll explore key concepts with examples, explanations, and questions to help you solidify your understanding.

Chapter 14: Statistics

Statistics helps us make sense of data. Here’s a breakdown of central tendency measures:

• Mean: The “average” of a set of values.
  • Example: Your scores in 4 Maths tests are 75, 82, 90, and 88. Find the mean.
    • Explanation: Mean = (75 + 82 + 90 + 88) / 4 = 83.75.
• Median: The “middle” value when data is arranged in order (ascending or descending).
  • Example: Your project marks are 95, 87, 78, 92, and 100. Find the median.
    • Explanation: Arrange the marks: 78, 87, 92, 95, 100. The median is 92.
• Mode: The value that appears most frequently.
  • Example: You surveyed 10 friends about their favourite color. 4 chose blue, 3 chose red, and the others chose different colors. Find the mode.
    • Explanation: Blue appears most often (4 times), so it’s the mode.

Questions

1. Calculate the mean, median, and mode for the following set of numbers: 12, 15, 18, 12, 10. (Explain how you arrived at each answer.)
2. A class has 25 students. If the median score is 75, what can you say about the distribution of scores? (Explain your reasoning.)
3. In a survey, 30 people preferred apples, 25 preferred oranges, and the rest preferred other fruits. Is there a mode? Why or why not?
4. What is the difference between mean and median? When might you use one over the other?
5. How can measures of central tendency help us understand a data set?

Chapter 15: Probability

Probability deals with the likelihood of events happening. Here are the two main approaches:

• Theoretical Probability: Calculated based on possible outcomes (n(S)) and favorable outcomes (n(E)). P(E) = n(E) / n(S).
  • Example: A bag has 3 red marbles and 2 blue marbles. What’s the probability of picking a red marble?
    • Explanation: n(S) = total outcomes (picking any marble) = 3 (red) + 2 (blue) = 5. n(E) = favorable outcome (picking red) = 3. P(red) = 3/5.
• Empirical Probability: Based on observations or experiments.
  • Example: You roll a die 100 times and observe a 6 appearing 16 times. Find the empirical probability of getting a 6.
    • Explanation: Empirical Probability = Favorable outcomes (number of 6s) / Total outcomes (number of rolls) = 16/100.

Questions

1. A coin has two sides: heads and tails. What is the probability of getting heads when you toss it once? (Explain how you reached the answer.)
2. You draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a heart (considering suit only)? (Explain your reasoning.)
3. Is theoretical probability always more accurate than empirical probability? Why or why not?
4. Describe a situation where you might use theoretical probability and another where you might use empirical probability.
5. How can the concept of probability be helpful in everyday life?

Chapter 13: Mensuration (Surface Area & Volume)

This chapter deals with calculating areas and volumes of 3D shapes. Here are some key formulas and an example:

• Cube: Surface Area (SA) = 6a² (a = side length); Volume (V) = a³.
  • Example: A cube has a side length of 4 cm. Find its surface area and volume.
    • Explanation: SA = 6 * 4² = 96 cm²; V = 4³ = 64 cm³.

Mensuration (Surface Area & Volume) – (Questions)

1. A cuboid has a length of 8 cm, a breadth of 5 cm, and a height of 3 cm. Calculate its surface area and volume. (Explain how you used the formula to arrive at the answers.)
2. A cuboid has a square base with a side of 6 cm. If the total surface area is 156 cm², find the height of the cuboid. (Set up an equation and explain how you solved for the height.)
3. A sphere has a radius of 7 cm. Find its surface area and volume (use 4/3π for pie). (Introduce the formula for sphere and explain each variable.)
4. Compare the surface areas of two cubes with side lengths of 4 cm and 6 cm. How much larger is the surface area of the bigger cube? (Calculate the surface areas of both cubes and find the difference.)
5. A cylindrical pencil has a radius of 0.5 cm and a height of 7 cm. Calculate the curved surface area of the pencil (excluding the top and bottom). (Introduce the formula for curved surface area of a cylinder and explain each variable.)