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
When Mean deviation is divided by the average used in finding out the mean deviation itself, the resulting quantity is described as_____________.
.- The distribution, which is skewed to the left, has one high point and has many high scores is called
- Which of the following are measures of dispersion?
A. Standard Deviation
B. Quartile Deviation
C. Mode
D. Variance
E. Range
Choose the correct answer from the options given below: - Two sets of data consisting of 10 and 20 observations have same mean 8 with standard deviations of 1 and 2, respectively. If the two data sets are combined, then the variance is
Two data set of sizes 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 respectively. The standard deviation of combined data set of size 15 is
