Calculating measures of spread

• Calculate various statistical measures of spread, including the range, quartiles, interquartile range (IQR), percentiles, interpercentile range, interdecile range, and standard deviation.
• Determine specified interpercentile bounds (e.g., 10th to 90th percentile) when the mathematical bounds do not align perfectly with existing data values, understanding acceptable estimation methodologies (e.g., averaging values straddling the median).
• Apply standard deviation formulas to grouped frequency distributions:

$\text{Standard deviation}=\sqrt{\frac{\sum f(x-\bar{x}{)}^2}{\sum f}}\text{ or }\sqrt{\frac{\sum f{x}^2}{\sum f}-{(\frac{\sum }{}}^{}}$