Q.1 Which of the following is NOT a measure of dispersion?
Range
Mean Deviation
Standard Deviation
Arithmetic Mean
Explanation - Arithmetic mean is a measure of central tendency, not dispersion. Dispersion deals with the spread of data.
Correct answer is: Arithmetic Mean
Q.2 Range is calculated as:
Maximum value - Minimum value
Sum of values / Number of values
Square root of variance
Median of data
Explanation - Range is the difference between the highest and lowest values in a dataset.
Correct answer is: Maximum value - Minimum value
Q.3 Which measure of dispersion is most affected by extreme values?
Standard Deviation
Range
Mean Deviation
Interquartile Range
Explanation - Range depends only on the maximum and minimum values, so it is highly affected by outliers.
Correct answer is: Range
Q.4 Variance is always:
Positive
Negative
Zero or positive
Equal to standard deviation
Explanation - Variance is the average of squared deviations, so it cannot be negative. It can be zero if all values are equal.
Correct answer is: Zero or positive
Q.5 The square root of variance is called:
Mean deviation
Standard deviation
Range
Quartile deviation
Explanation - By definition, the standard deviation is the square root of variance.
Correct answer is: Standard deviation
Q.6 If all observations in a dataset are the same, the standard deviation is:
1
0
Undefined
Equal to variance
Explanation - There is no spread when all values are equal, hence variance and standard deviation are zero.
Correct answer is: 0
Q.7 Which measure of dispersion uses the middle 50% of data?
Range
Interquartile Range
Variance
Standard Deviation
Explanation - Interquartile Range is the difference between Q3 and Q1, representing the middle 50% of data.
Correct answer is: Interquartile Range
Q.8 Mean deviation is calculated using:
Squares of deviations
Absolute deviations
Maximum and minimum values
Quartiles
Explanation - Mean deviation is the average of absolute deviations from a measure of central tendency.
Correct answer is: Absolute deviations
Q.9 Standard deviation is preferred over range because:
It is easier to calculate
It considers all data values
It is not affected by extreme values
It is always larger
Explanation - Standard deviation incorporates all data points, making it a more reliable measure of dispersion.
Correct answer is: It considers all data values
Q.10 Which of the following is a relative measure of dispersion?
Standard Deviation
Range
Coefficient of Variation
Mean Deviation
Explanation - The coefficient of variation expresses standard deviation as a percentage of the mean, making it relative.
Correct answer is: Coefficient of Variation
Q.11 Variance is expressed in:
Same units as mean
Square of the units of data
No units
Percentage form
Explanation - Since variance involves squaring deviations, its unit is the square of the data's unit.
Correct answer is: Square of the units of data
Q.12 Which measure of dispersion is least reliable?
Standard Deviation
Mean Deviation
Range
Interquartile Range
Explanation - Range depends only on extreme values, making it less reliable compared to other measures.
Correct answer is: Range
Q.13 Quartile Deviation is also known as:
Semi-Interquartile Range
Mean Deviation
Variance
Standard Deviation
Explanation - Quartile deviation is half of the interquartile range, so it is also called the semi-interquartile range.
Correct answer is: Semi-Interquartile Range
Q.14 In a normal distribution, about 68% of data lies within:
1 standard deviation
2 standard deviations
3 standard deviations
Half standard deviation
Explanation - According to the empirical rule, 68% of observations lie within 1 standard deviation from the mean in a normal distribution.
Correct answer is: 1 standard deviation
Q.15 Which is NOT a property of standard deviation?
Always positive
Affected by extreme values
Based on all observations
Expressed as a percentage
Explanation - Standard deviation is in the same unit as data, not in percentage. Coefficient of variation uses percentage.
Correct answer is: Expressed as a percentage
Q.16 Coefficient of Variation (CV) is defined as:
Variance / Mean × 100
Standard Deviation / Mean × 100
Mean / Standard Deviation × 100
Range / Mean × 100
Explanation - CV is the ratio of standard deviation to mean expressed as a percentage.
Correct answer is: Standard Deviation / Mean × 100
Q.17 If variance of a dataset is 0, it implies:
All values are equal
Data is skewed
Mean is 0
Standard deviation is 1
Explanation - Zero variance means there is no variability; hence all values must be the same.
Correct answer is: All values are equal
Q.18 Which measure of dispersion can never be negative?
Range
Variance
Standard Deviation
All of the above
Explanation - All measures of dispersion are non-negative since they represent spread.
Correct answer is: All of the above
Q.19 The square of standard deviation is:
Variance
Range
Coefficient of Variation
Quartile Deviation
Explanation - By definition, variance is the square of standard deviation.
Correct answer is: Variance
Q.20 Which of the following best measures the spread when data has outliers?
Range
Standard Deviation
Interquartile Range
Mean Deviation
Explanation - IQR focuses on the middle 50% of data, minimizing the effect of extreme values.
Correct answer is: Interquartile Range
Q.21 If the range of a dataset is 0, what does it imply?
Variance is maximum
All values are equal
Mean is zero
There is one observation
Explanation - Range 0 means maximum and minimum are equal, hence all values are identical.
Correct answer is: All values are equal
Q.22 Which of the following is measured in the same units as the original data?
Variance
Standard Deviation
Coefficient of Variation
Quartile Deviation
Explanation - Standard deviation is in the same units as the original data, unlike variance.
Correct answer is: Standard Deviation
Q.23 The interquartile range is calculated as:
Q3 - Q1
Q2 - Q1
Q4 - Q2
Mean - Median
Explanation - IQR is the difference between the third and first quartile.
Correct answer is: Q3 - Q1
Q.24 Mean deviation is minimum when deviations are taken from:
Mean
Median
Mode
Range
Explanation - Mean deviation is minimum when calculated from the median.
Correct answer is: Median
Q.25 If standard deviation = 0, then coefficient of variation (CV) is:
0
1
100
Undefined
Explanation - When standard deviation is 0, CV also becomes 0, indicating no variability.
Correct answer is: 0