Multiple Choice Questions on Measures of Dispersion Class 11 OP Malhotra Exe-21D ISC Maths Solutions Ch-21. In this article you would learn to solve hard mcq problems on Measures of Dispersion. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11.
Measures of Dispersion Class 11 OP Malhotra Multiple Choice Questions ISC Maths Solutions Ch-21
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 11th |
| Chapter-21 | Measures of Dispersion |
| Writer | OP Malhotra |
| Exe-21(D) | Multiple Choice Questions. |
Multiple Choice Questions on Measures of Dispersion
OP Malhotra ISC Class 11 Maths Solutions
Que-1: The mean deviation of the set of observations −1, 0, 4 from the mean is
(a) 1 (b) 2 (c) 3 (d) 4
Answer: (b)
Sol: Mean = (−1 + 0 + 4) / 3 = 3 / 3 = 1
Mean deviation = [|−1−1| + |0−1| + |4−1|] / 3
= (2 + 1 + 3) / 3 = 6 / 3 = 2
Que-2: The scores of a batsman in 10 innings are 38, 70, 48, 24, 42, 55, 63, 46, 54, 44. Find the mean deviation about the median.
(a) 8 (b) 9.6 (c) 8.4 (d) 8.5
Answer: (b)
Sol: Arrange data: 24, 38, 42, 44, 46, 48, 54, 55, 63, 70
Median = (46 + 48)/2 = 47
Find deviations: |xi − 47|
= 23, 9, 5, 3, 1, 1, 7, 8, 16, 23
Sum = 96
Mean deviation = 96 / 10 = 9.6
Que-3: The variance of the data 2, 4, 6, 8, 10 is
(a) 6 (b) 7 (c) 8 (d) 9
Answer: (c)
Sol: Mean = (2+4+6+8+10)/5 = 6
Variance = [(2−6)² + (4−6)² + (6−6)² + (8−6)² + (10−6)²] / 5
= (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8
Que-4: The standard deviation for the data 6, 7, 8, 9, 10 is
(a) √10 (b) 2 (c) √2 (d) 10
Answer: (c)
Sol: Mean = (6+7+8+9+10)/5 = 8
Variance = [(6−8)² + (7−8)² + (8−8)² + (9−8)² + (10−8)²] / 5
= (4 + 1 + 0 + 1 + 4) / 5 = 10 / 5 = 2
Standard deviation = √2
Que-5: The following information relates to a sample of size 60, Σx² = 18000, and Σx = 960. Then, the variance is
(a) 6.63 (b) 16 (c) 22 (d) 44
Answer: (d)
Sol: n = 60, Σx = 960, Σx² = 18000
Mean (x̄) = Σx / n = 960 / 60 = 16
Variance = (Σx² / n) − (x̄)²
= (18000 / 60) − (16)²
= 300 − 256 = 44
Que-6: If the coefficients of variation of two distributions are 50, 60 and their arithmetic means are 30 and 25 respectively, then the difference of their standard deviation is
(a) 0 (b) 1 (c) 1.5 (d) 2.5
Answer: (a)
Sol: Coefficient of variation = (σ / mean) × 100.
σ₁ = (50/100) × 30 = 15
σ₂ = (60/100) × 25 = 15
Difference = 15 − 15 = 0
Que-7: Find the coefficient of variation of a series of 10 observations whose mean is 12 and the sum of squares of all the observations is 1530.
(a) 17% (b) 22% (c) 25% (d) 51%
Answer: (c)
Sol: Variance = (Σx² / n) − (mean)²
= (1530/10) − 12² = 153 − 144 = 9
σ = √9 = 3
C.V. = (3/12) × 100 = 25%
Que-8: The mean of a group of data is given as 27. Data is 39, 21, 18, x, y, 24. What could be the values of x and y, if both x and y are prime?
(a) x = 23, y = 29
(b) x = 29, y = 31
(c) x = 26, y = 24
(d) x = 12, y = 48
Answer: (b)
Sol: Mean = 27, total numbers = 6
Sum = 27 × 6 = 162
Sum of known values = 39 + 21 + 18 + 24 = 102
So, x + y = 162 − 102 = 60
Only primes satisfying this: 29 + 31 = 60
Que-9: If Σ(xᵢ − 5) = 9 and Σ(xᵢ − 5)² = 45, then the standard deviation of the 9 items x₁, x₂, … x₉ is
(a) 3 (b) 9 (c) 4 (d) 2
Answer: (d)
Sol: n = 9
Variance = [Σ(x−a)² / n] − [Σ(x−a)/n]²
= (45/9) − (9/9)² = 5 − 1 = 4
σ = √4 = 2
Que-10: If the mean of the data: 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is
(a) 2 (b) 7/8 (c) 9/8 (d) 1
Answer: (d)
Sol: Mean = 8, n = 8
Total sum = 8 × 8 = 64
Sum of known values = 7+8+9+7+8+7+8 = 54
λ = 64 − 54 = 10
Now compute variance → result = 1
Que-11: The variance of first 20 natural numbers is
(a) 309/2
(b) 379/12
(c) 133/4
(d) 133/2
Answer: (d)
Sol: Variance of first n natural numbers = (n² − 1)/12
For n = 20:
= (400 − 1)/12
= 399/12
= 133/2
Que-12: If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is
(a) 30 (b) 51 (c) 31 (d) 50
Answer: (c)
Sol: Formula: Mean = A + (Σd / n)
Here A = 30, Σd = 50, n = 50
Mean = 30 + (50/50)
= 30 + 1 = 31
–: End Measures of Dispersion Class 11 OP Malhotra Exe-21D ISC Maths Ch-21 Solutions :–
Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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