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1.2 Measures of Dispersion — Test 1
Q1. The range of a data set is calculated as:✓ Highest value − lowest value
Q2. The variance of a data set is:✓ The average of the squared deviations from the mean
Q3. The standard deviation is:✓ The square root of the variance
Q4. The square of the standard deviation is the:✓ Variance
Q5. The coefficient of variation (CV) is calculated as:✓ (Standard deviation ÷ mean) × 100
Q6. The coefficient of variation is especially useful for:✓ Comparing the variability of two data sets with different units or means
Q7. The standard deviation is preferred over the range because the standard deviation:✓ Uses all observations, not just the two extremes
Q8. The quartile deviation (semi-interquartile range) is calculated as:✓ (Q3 − Q1) ÷ 2
Q9. The standard error of the mean is given by:✓ Standard deviation ÷ √n
Q10. A measure of dispersion describes the:✓ Spread or variability of the data around a central value
Q11. A key limitation of the range as a measure of dispersion is that it:✓ Is greatly affected by extreme values and ignores the rest
Q12. The units of variance, compared with the units of the original data, are:✓ Squared (e.g. cm becomes cm²)
Q13. The standard deviation has the same units as the data, which makes it:✓ Easier to interpret than the variance
Q14. Between two data sets with the same mean, the one with the smaller standard deviation is:✓ More consistent (less variable)
Q15. The coefficient of variation is expressed as:✓ A percentage (and is therefore unit-free)
Q16. The interquartile range (IQR) is defined as:✓ Q3 − Q1
Q17. Variance can never be negative because it is based on:✓ Squared deviations, which are always non-negative
Q18. Absolute measures of dispersion (like SD) differ from relative measures (like CV) in that absolute measures:✓ Are expressed in the units of the data
Q19. A standard deviation of zero for a data set indicates that:✓ All values are identical (no variability)
Q20. Match each measure of dispersion with its description and select the correct option.✓ A-ii, B-i, C-iv, D-iii