Class 11 Mathematics

1. Range of a given set of observations is defined as:

• A. Maximum value - Minimum value
• B. Maximum value + Minimum value
• C. (Maximum value - Minimum value) / 2
• D. Sum of observations / Total number

2. The mean deviation about mean for ungrouped data is given by:

• A. (1/n) Σ |xᵢ - x̄|
• B. (1/n) Σ (xᵢ - x̄)²
• C. Σ |xᵢ - x̄|
• D. √[(1/n) Σ (xᵢ - x̄)²]

3. Find the range of the data: 6, 7, 10, 12, 13, 4, 8, 12.

• A. 9
• B. 8
• C. 7
• D. 10

4. Mean deviation about median is minimum compared to mean deviation about any other value. This statement is:

• A. True
• B. False
• C. True only for symmetric data
• D. Cannot be determined

5. Variance (σ²) of n observations x₁, x₂, ..., xₙ is given by:

• A. (1/n) Σ (xᵢ - x̄)²
• B. (1/n) Σ |xᵢ - x̄|
• C. √[(1/n) Σ (xᵢ - x̄)²]
• D. Σ (xᵢ - x̄)²

6. Standard Deviation (σ) is equal to:

• A. Square root of Variance
• B. Square of Variance
• C. Mean Deviation
• D. Half of Variance

7. The formula for Coefficient of Variation (C.V.) is:

• A. (σ / x̄) × 100
• B. (x̄ / σ) × 100
• C. (σ² / x̄) × 100
• D. (Mean Deviation / Mean) × 100

8. Between two series, the series with greater Coefficient of Variation is:

• A. More variable (less consistent)
• B. Less variable (more consistent)
• C. More consistent
• D. Has higher mean

9. Variance of first n natural numbers is given by:

• A. (n² - 1) / 12
• B. (n² + 1) / 12
• C. (n - 1) / 6
• D. n² / 12

10. Standard deviation of first n natural numbers is:

• A. √[(n² - 1) / 12]
• B. (n² - 1) / 12
• C. √[(n² + 1) / 12]
• D. (n + 1) / 2

11. If each observation is multiplied by a constant k, then the new standard deviation becomes:

• A. |k| × original σ
• B. k² × original σ
• C. original σ
• D. original σ + k

12. If each observation is multiplied by a constant k, the new variance becomes:

• A. k² × original variance
• B. k × original variance
• C. original variance
• D. original variance + k²

13. If a constant k is added to each observation, the new standard deviation is:

• A. Same as original σ
• B. original σ + k
• C. k × original σ
• D. original σ - k

14. Find mean deviation about mean for data: 4, 7, 8, 9, 10, 12, 13, 17.

• A. 3
• B. 3.25
• C. 4
• D. 2.5

15. Sum of deviations of observations from their actual mean is always:

• A. 0
• B. 1
• C. Positive
• D. Negative

16. Calculate variance for data: 6, 7, 10, 12, 13, 4, 8, 12.

• A. 9.25
• B. 8.5
• C. 10
• D. 9.75

17. Standard deviation of 5 observations is 4. If each observation is increased by 2, new S.D. is:

• A. 4
• B. 6
• C. 2
• D. 8

18. Standard deviation of 5 observations is 3. If each observation is multiplied by 2, new S.D. is:

• A. 6
• B. 3
• C. 12
• D. 9

19. Variance of 10 observations is 5. If each observation is multiplied by 3, new variance is:

• A. 45
• B. 15
• C. 25
• D. 135

20. If mean of a distribution is 25 and standard deviation is 5, its Coefficient of Variation is:

• A. 20%
• B. 5%
• C. 25%
• D. 125%

21. Find median of data: 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12.

• A. 13
• B. 14
• C. 12
• D. 13.5

22. Variance of constant sequence 5, 5, 5, 5, 5 is:

• A. 0
• B. 5
• C. 25
• D. 1

23. For grouped discrete frequency distribution, variance is given by:

• A. (1/N) Σ fᵢ(xᵢ - x̄)²
• B. (1/N) Σ fᵢ|xᵢ - x̄|
• C. Σ fᵢxᵢ² / N
• D. (1/N) Σ (xᵢ - x̄)²

24. Variance of first 5 natural numbers (1, 2, 3, 4, 5) is:

• A. 2
• B. 2.5
• C. 3
• D. 1.5

25. Which of the following is NOT a measure of dispersion?

• A. Mean
• B. Range
• C. Standard Deviation
• D. Variance

26. If C.V. of a distribution is 60% and standard deviation is 21, then mean is:

• A. 35
• B. 30
• C. 40
• D. 25

27. Sum of squares of deviations of 10 observations from their mean 15 is 250. Variance is:

• A. 25
• B. 250
• C. 5
• D. 15

28. Two series with means x̄₁ and x̄₂ have same S.D. σ. Which series is more consistent?

• A. Series with greater mean
• B. Series with smaller mean
• C. Both are equally consistent
• D. Cannot be determined

29. Shortcut formula for calculating variance with step-deviation yᵢ = (xᵢ - A)/h is:

• A. h² / N² × [N Σ fᵢyᵢ² - (Σ fᵢyᵢ)²]
• B. h / N × [N Σ fᵢyᵢ² - (Σ fᵢyᵢ)²]
• C. h² / N × [Σ fᵢyᵢ² - Σ fᵢyᵢ]
• D. [Σ fᵢyᵢ² - (Σ fᵢyᵢ)²] / N²

30. Mean deviation about mean is always:

• A. Less than or equal to Standard Deviation
• B. Greater than Standard Deviation
• C. Equal to Variance
• D. Double of Standard Deviation