Measures of Dispersion
Class 11 · Economics
4 ideas in Class 11 Economics, explained in plain words, with games and quizzes to practise.
Range and Quartile Deviation
Part of: Range and Quartiles
Range spans extremes; quartile deviation halves Q3-minus-Q1; coefficient ratios scale; simple but outlier-sensitive.
Why it matters. Spans sketch spread. Quartiles resist extremes.
Formulas
- Range = maximum - minimum
- Coefficient of range = (Max - Min) / (Max + Min)
- Quartile deviation = (Q3 - Q1) / 2
- Interquartile range covers the middle 50 percent
Key words
- Range
- : Gap between the largest and smallest values.
- Interquartile range
- : Middle-half span between quartiles one and three.
- Quartile deviation
- : Half of the interquartile span.
- Coefficient of range
- : Range scaled by the sum of extremes.
- Coefficient of QD
- : QD scaled by the mean of the quartiles.
Try it in two minutes
- Span max-min.
- Quarter the data.
- Halve the gap.
Try at home. Range your marks.
Mean Deviation
Part of: Range and Quartiles
Absolute gaps from mean or median average out; median-based minimises; grouped data weights frequencies; coefficients ratio to centre.
Why it matters. Gaps gauge typical stray. Weights handle groups.
Formulas
- MD = sum |x - centre| / n
- Coefficient of MD = MD / centre
Key words
- Mean deviation
- : Average of absolute gaps from a centre.
- Absolute deviations
- : Gaps counted without sign so they cannot cancel.
- Median choice
- : Centre giving the smallest mean deviation.
- Grouped MD
- : Frequency-weighted gaps for grouped data.
- Coefficient of MD
- : MD scaled by its centre for comparison.
Try it in two minutes
- Gap from centre.
- Absolute each.
- Average all.
Try at home. MD of family ages.
Standard Deviation
Part of: Standard Deviation and Lorenz
Variance averages squared gaps from mean; SD roots it; step shortcuts shift origins; discrete weights frequencies; CV percents SD over mean.
Why it matters. Squares weight big strays. Roots restore units.
Formulas
- Variance = sum (x - mean)^2 / n
- SD = sqrt(variance)
- CV = SD x 100 / mean
- Shifting data leaves SD unchanged; scaling scales SD equally
Key words
- Variance
- : Average of squared gaps from the mean.
- Standard deviation
- : Root of variance, in the same units as data.
- Coefficient of variation
- : SD as a percent of the mean for comparison.
- Step deviation
- : Origin shift shortcut for grouped computation.
- Discrete weighting
- : Frequency-weighted gaps for discrete series.
Try it in two minutes
- Square the gaps.
- Average squares.
- Root the total.
Try at home. SD of siblings heights.
Lorenz Curve
Part of: Standard Deviation and Lorenz
Cumulative income shares plot against people shares; diagonal marks perfect equality; wider bows mean deeper inequality; Gini ratios size the gap.
Why it matters. Pictures reveal inequality. Bows compare nations.
Formulas
- Gini near 0 = near equality, near 1 = extreme inequality
Key words
- Lorenz curve
- : Plot of income shares against people shares.
- Equality line
- : Diagonal marking perfectly equal shares.
- Bow of inequality
- : Wider bow showing deeper income gaps.
- Gini ratio
- : Single number sizing the gap from equality.
- Fair comparison
- : Curves compared only on matching axes and scales.
Try it in two minutes
- Cumulate both shares.
- Plot against diagonal.
- Read the bow.
Try at home. Lorenz pocket money.
What your child will practise
- Lorenz Curve: Candy Puzzle (Clue Puzzle)
- Lorenz Curve: Candy Quick Fire (Quick Fire)
- Mean Deviation: Desert Puzzle (Clue Puzzle)
- Range and Quartile Deviation: Jungle Quest (Flip and Match)
- Standard Deviation: Ocean Quick Fire (Quick Fire)
- Quiz: Lorenz Curve (8 questions)
- Quiz: Mean Deviation (8 questions)
- Quiz: Range and Quartile Deviation (8 questions)
- Quiz: Standard Deviation (8 questions)