Very Short Answer on Measures of Dispersion Class 11 OP Malhotra Exe-21C ISC Maths Solutions Ch-21. In this article you would learn to solve hard 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 Very Short Answer ISC Maths Solutions Ch-21
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 11th |
| Chapter-21 | Measures of Dispersion |
| Writer | OP Malhotra |
| Exe-21(C) | Very Short Answer Type Questions. |
Very Short Answer on Measures of Dispersion
OP Malhotra ISC Class 11 Maths Solutions
Que-1: The mean deviation about the mean for 2, 4, 6, 8, 10 is ________.
Sol: Mean = (2 + 4 + 6 + 8 + 10)/5 = 6
Mean deviation = |2-6| + |4-6| + |6-6| + |8-6| + |10-6| / 5
= (4 + 2 + 0 + 2 + 4)/5
= 12/5 = 2.4
Que-2: The mean deviation about the median for 5, 7, 9, 11, 13 is ________.
Sol: Median = 9
Mean deviation = (4 + 2 + 0 + 2 + 4)/5
= 12/5 = 2.4
Que-3: If variance for a data is 49, then the standard deviation is ________.
Sol: We know: Standard Deviation (σ) = √Variance
σ = √49 = 7
Que-4: If σ is the standard deviation and x̄ the arithmetic mean, then the coefficient of variation is ________.
Sol: Coefficient of Variation (C.V.) = (σ / x̄) × 100
This measures relative variability of data.
Que-5: The mean deviation of a data is least when measured from the ________.
Sol: Mean deviation is minimum when calculated about the median.
This is a standard statistical property.
Que-6: The standard deviation of data 1, 3, 5, 7, 9 is ________.
Sol: x̄ = (1 + 3 + 5 + 7 + 9)/5
= 25/5 = 5
(1−5)² = 16,
(3−5)² = 4,
(5−5)² = 0,
(7−5)² = 4,
(9−5)² = 16
σ = √[(16+4+0+4+16)/5]
= √(40/5)
= √8 = 2√2 = 2.83.
Que-7: If for a given data, mean is y and mean deviation about the mean is x, then coefficient of mean deviation is ________.
Sol: Coefficient of Mean Deviation = Mean Deviation / Mean
= x / y
Que-8: Mean deviation for n observations x₁, x₂, … xₙ from their mean x̄ is given by ________.
Sol: Mean deviation = (Σ |xᵢ − x̄|) / n
Que-9: The mean of a data containing 10 observations is 12 and S.D = 5. Then, the sum of the squares of the observations is ________.
Sol: Using formula: σ² = (Σx² / n) − (x̄)²
25 = (Σx² / 10) − 144
Σx² / 10 = 169
⇒ Σx² = 1690
Que-10: The mean deviation about the mean for the data in the table
| x | 5 | 10 | 15 | 20 | 25 |
| f | 7 | 4 | 6 | 3 | 5 |
is ________.
Sol: First find mean:
Σf = 7 + 4 + 6 + 3 + 5 = 25
Σfx = (5×7 + 10×4 + 15×6 + 20×3 + 25×5)
= 35 + 40 + 90 + 60 + 125 = 350
Mean (x̄) = 350 / 25 = 14
Now find |x − x̄|:
|5−14|=9, |10−14|=4, |15−14|=1, |20−14|=6, |25−14|=11
Σf|x−x̄| = (7×9 + 4×4 + 6×1 + 3×6 + 5×11)
= 63 + 16 + 6 + 18 + 55 = 158
Mean deviation = 158 / 25 = 6.32
–: End Measures of Dispersion Class 11 OP Malhotra Exe-21C ISC Maths Ch-21 Solutions :–
Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
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