Match List - I with List - II.List - I List - II (A) Coefficient of Dispersion (I) Standard deviation as a percentage of mean (B) Standard Deviation (II) Mean of squared deviations of individual scores from mean (C) Coefficient of variation (III) Variance in terms of mean (D) Variance (IV) Positive square root of variance
List I and List II Matching
This section explains the correct pairings between statistical measures in List I and their definitions/interpretations in List II.
Coefficient of Dispersion (A) Explained
Coefficient of Dispersion (List I - A) measures relative variability. Option (III) Variance in terms of mean represents a measure comparing variance to the mean, indicating relative dispersion.
Standard Deviation (B) Explained
Standard Deviation (List I - B) quantifies data dispersion around the mean. Option (IV) Positive square root of variance is its definition. The formula is $\sigma = \sqrt{\sigma^2}$.
Coefficient of Variation (C) Explained
Coefficient of Variation (List I - C) measures relative standard deviation, usually as a percentage. Option (I) Standard deviation as a percentage of mean correctly defines it. Formula: $CV = \frac{\sigma}{\mu} \times 100\%$.
Variance (D) Explained
Variance (List I - D) measures the spread of data points. Option (II) Mean of squared deviations of individual scores from mean is its definition. Formula: $\sigma^2 = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N}$.
Matching Summary
The established pairings are:
| List I Item | List II Item |
|---|---|
| (A) Coefficient of Dispersion | (III) Variance in terms of mean |
| (B) Standard Deviation | (IV) Positive square root of variance |
| (C) Coefficient of Variation | (I) Standard deviation as a percentage of mean |
| (D) Variance | (II) Mean of squared deviations of individual scores from mean |
Thus, the correct matching is (A)-(III), (B)-(IV), (C)-(I), (D)-(II).
Important Questions from Measures of Dispersion
If for a moderately symmetrical distribution mean deviation is 12, then the value of standard deviation is
Variance is independent of change of :
- Mean (M) and Standard Deviation (S) of different datasets are given in A-D below. Compute the coefficient of variation of each dataset and arrange in ascending order.
A. M = 60, S = 14
B. M = 70, S = 16
C. M = 80, S = 5
D. M = 90, S = 4
Choose the correct answer from the options given below: - Which of the following are methods of dispersion ?
A. Median
B. Mean
C. Mean deviation
D. Standard deviation
E. Range
Choose the correct answer from the options given below : - Mean (M) and coefficient of variation (CV expressed as a percentage) of different datasets are given in A-D below. Compute the standard deviation of each dataset and arrange in ascending order.
A. M = 60, CV = 70/3
B. M = 80, CV = 6.25
C. M = 70, CV = 160/7
D. M = 90, CV = 40/9
Choose the correct answer from the options given below:
