Q.1 Which of the following is NOT a measure of dispersion?
Range
Variance
Mean
Standard Deviation
Explanation - Mean is a measure of central tendency, not dispersion. Dispersion refers to the spread of data values.
Correct answer is: Mean
Q.2 The difference between the highest and lowest values in a dataset is called:
Variance
Mean Deviation
Range
Standard Deviation
Explanation - Range is calculated as the maximum value minus the minimum value of the dataset.
Correct answer is: Range
Q.3 Which measure of dispersion is always non-negative?
Variance
Standard Deviation
Mean Deviation
All of the above
Explanation - Dispersion measures describe spread and are non-negative because spread cannot be negative.
Correct answer is: All of the above
Q.4 If the range of a dataset is zero, it means:
All values are equal
Values are very large
Data is skewed
Variance is high
Explanation - When range is zero, the maximum and minimum are equal, meaning all values are the same.
Correct answer is: All values are equal
Q.5 Which of these is the square root of variance?
Standard Deviation
Range
Mean Deviation
Quartile Deviation
Explanation - Standard deviation is defined as the positive square root of variance.
Correct answer is: Standard Deviation
Q.6 The formula for variance of ungrouped data is:
Σ(xi - x̄)/n
Σ(xi - x̄)²/n
Σ(xi)/n
Σfi/n
Explanation - Variance is the average of squared deviations from the mean.
Correct answer is: Σ(xi - x̄)²/n
Q.7 Standard deviation is preferred over range because:
It uses only two values
It considers all data points
It is always zero
It is easier to calculate
Explanation - Unlike range, standard deviation incorporates deviations of all observations from the mean.
Correct answer is: It considers all data points
Q.8 The interquartile range is defined as:
Q3 - Q1
Q2 - Q1
Q4 - Q1
Q3 - Q2
Explanation - Interquartile range measures the spread of the middle 50% of data as Q3 minus Q1.
Correct answer is: Q3 - Q1
Q.9 If variance is 0, what is the standard deviation?
1
0
Cannot be determined
Infinity
Explanation - Since standard deviation is the square root of variance, SD = √0 = 0.
Correct answer is: 0
Q.10 Which measure of dispersion is most affected by extreme values?
Range
Interquartile Range
Standard Deviation
Mean Deviation
Explanation - Range depends only on maximum and minimum values, making it highly sensitive to outliers.
Correct answer is: Range
Q.11 For the data 2, 2, 2, 2, the variance is:
2
0
4
1
Explanation - All values are identical, so deviations from the mean are 0, hence variance is 0.
Correct answer is: 0
Q.12 The measure of dispersion that divides data into four equal parts is:
Range
Variance
Quartile Deviation
Standard Deviation
Explanation - Quartile deviation is based on the spread between the first and third quartile.
Correct answer is: Quartile Deviation
Q.13 What is the square of standard deviation called?
Range
Variance
Quartile Deviation
Mean
Explanation - By definition, variance is the square of the standard deviation.
Correct answer is: Variance
Q.14 If the variance of data is 25, the standard deviation is:
25
5
12.5
50
Explanation - Standard deviation = √Variance = √25 = 5.
Correct answer is: 5
Q.15 Which measure of dispersion is expressed in the same units as the original data?
Variance
Standard Deviation
Coefficient of Variation
Quartile Deviation
Explanation - Standard deviation retains the same units as the data, unlike variance which is squared.
Correct answer is: Standard Deviation
Q.16 Mean deviation is calculated as:
Average of squared deviations
Average of absolute deviations from mean or median
Range of data
Difference between quartiles
Explanation - Mean deviation takes absolute deviations to avoid cancellation of positive and negative differences.
Correct answer is: Average of absolute deviations from mean or median
Q.17 If a dataset is multiplied by 3, the variance becomes:
Multiplied by 3
Divided by 3
Multiplied by 9
Unchanged
Explanation - Variance scales with the square of the constant, so multiplying data by 3 multiplies variance by 9.
Correct answer is: Multiplied by 9
Q.18 Coefficient of variation (CV) is defined as:
Variance / Mean
Standard Deviation / Mean × 100
Range / Mean
Median / Mean
Explanation - CV is a relative measure of dispersion, expressing standard deviation as a percentage of the mean.
Correct answer is: Standard Deviation / Mean × 100
Q.19 Which of the following is the most reliable measure of dispersion?
Range
Standard Deviation
Quartile Deviation
Mean Deviation
Explanation - Standard deviation considers all data values and is less affected by sampling fluctuations.
Correct answer is: Standard Deviation
Q.20 In a normal distribution, about 68% of data lies within:
±1 Standard Deviation
±2 Standard Deviations
±3 Standard Deviations
No fixed range
Explanation - Empirical rule states that about 68% of values lie within 1 standard deviation of the mean.
Correct answer is: ±1 Standard Deviation
Q.21 What is the range of numbers 5, 7, 9, 12, 15?
10
15
20
12
Explanation - Range = Maximum - Minimum = 15 - 5 = 10.
Correct answer is: 10
Q.22 If all data points are shifted by a constant value, variance:
Increases
Decreases
Remains unchanged
Becomes zero
Explanation - Variance depends on spread, not absolute position of data. Shifting does not affect variance.
Correct answer is: Remains unchanged
Q.23 Which measure is also called semi-interquartile range?
Variance
Quartile Deviation
Standard Deviation
Mean Deviation
Explanation - Quartile deviation is half of the interquartile range (Q3 - Q1)/2.
Correct answer is: Quartile Deviation
Q.24 In a highly skewed distribution, which measure of dispersion is most reliable?
Range
Variance
Standard Deviation
Quartile Deviation
Explanation - Quartile deviation is less influenced by extreme values, making it reliable for skewed data.
Correct answer is: Quartile Deviation
Q.25 The measure of dispersion best used for comparing two datasets with different means is:
Variance
Coefficient of Variation
Range
Quartile Deviation
Explanation - Coefficient of variation adjusts for differences in mean, allowing fair comparison between datasets.
Correct answer is: Coefficient of Variation