Chapter 15: Statistics

NCERT Solutions for CBSE Class 10 Mathematics — 11 solved questions with detailed explanations.

Questions

Topics

Solved Questions

Q1. The mean deviation about the mean of data 2, 4, 6, 8, 10 is:

Difficulty: Easy-Medium · Topic: Mean Deviation

Solution

Mean = 30/5 = 6. Deviations: |2-6|+|4-6|+|6-6|+|8-6|+|10-6| = 4+2+0+2+4 = 12. Mean deviation = 12/5 = 2.4.

Q2. The variance of the data 1, 2, 3, 4, 5 is:

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean = 3. Variance = [(1-3)²+(2-3)²+(3-3)²+(4-3)²+(5-3)²]/5 = [4+1+0+1+4]/5 = 10/5 = 2.

Q3. Standard deviation is the square root of

mode
variance
mean
median

Difficulty: Easy-Medium · Topic: Statistics

Solution

variance.

Q4. For a normal distribution, approximately 68% data lies within

μ ± 3σ
μ ± σ
μ ± 2σ
μ ± 0.5σ

Difficulty: Easy-Medium · Topic: Statistics

Solution

μ ± σ.

Q5. Coefficient of variation =

(σ²/mean)×100
σ×mean
(σ/mean)×100
mean/σ

Difficulty: Easy-Medium · Topic: Statistics

Solution

(σ/mean)×100.

Q6. Range of a dataset is

max - min
Q3 - Q1
max + min
mean - median

Difficulty: Easy-Medium · Topic: Statistics

Solution

max - min.

Q7. Variance of (1, 2, 3, 4, 5):

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean=3.0. Var=Σ(xi-mean)²/n=2.0.

Q8. Variance of (2, 4, 6, 8, 10):

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean=6.0. Var=Σ(xi-mean)²/n=8.0.

Q9. Variance of (1, 3, 5, 7, 9):

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean=5.0. Var=Σ(xi-mean)²/n=8.0.

Q10. Variance of (10, 20, 30, 40, 50):

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean=30.0. Var=Σ(xi-mean)²/n=200.0.

Q11. Variance of (5, 5, 5, 5, 5):

Difficulty: Easy-Medium · Topic: Variance

Solution

Mean=5.0. Var=Σ(xi-mean)²/n=0.0.

Other Chapters in Mathematics

Ch 1: Sets Ch 2: Relations & Functions Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 16: Probability

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