Statistics
Class 11 · Mathematics
4 ideas in Class 11 Mathematics, explained in plain words, with games and quizzes to practise.
Mean Median and Mode
Part of: Central Tendency and Mean Deviation
Mean averages all; median middles sorted data; mode repeats most; odd counts pick centre, even average pair; grouped data use class marks.
Why it matters. Centres summarise data. Each suits lopsided cases.
Formulas
- Mean = sum of observations / number of observations
- Median of n sorted items sits at position (n + 1) / 2
Key words
- Arithmetic mean
- : The average found by dividing the total by the count.
- Median
- : The middle value of data arranged in order.
- Mode
- : The value occurring most often in the data.
- Class mark
- : The midpoint of a class, used as its representative value.
Try it in two minutes
- Sort the data.
- Average, middle, repeat.
- Pick the fitting centre.
Try at home. Find mean height of friends.
Range and Mean Deviation
Part of: Central Tendency and Mean Deviation
Range spans max-minus-min; mean deviation averages absolute gaps from mean or median; grouped data weight by frequency; median-based deviations minimise.
Why it matters. Spread gauges consistency. Absolute gaps avoid cancellation.
Formulas
- Range = largest value - smallest value
- Mean deviation = sum|x - centre| / n
Key words
- Range
- : The gap between the largest and smallest observation.
- Mean deviation
- : Average distance of observations from a central value.
- Absolute deviation
- : Distance without sign, so opposite gaps never cancel.
- Frequency
- : How many times an observation occurs in grouped data.
Try it in two minutes
- Span max to min.
- Gap from centre.
- Average absolute gaps.
Try at home. Compare spread of two quiz scores.
Variance and Standard Deviation
Part of: Variance and Comparison
Variance averages squared gaps from mean; shortcut subtracts squared-mean from mean-squares; standard deviation roots variance; shifting ignores spread, scaling squares it.
Why it matters. Variance weights big strays. Roots restore units.
Formulas
- Variance = sum(x - mean)^2 / n
- SD = root(variance)
- Variance = (mean of squares) - (square of mean)
Key words
- Variance
- : The average of squared gaps from the mean.
- Standard deviation
- : The square root of variance, in the same units as data.
- Sigma square
- : Greek letter marking variance in symbols.
- Shortcut method
- : Computing variance via assumed mean to keep numbers small.
Try it in two minutes
- Square each gap.
- Average the squares.
- Root for units.
Try at home. Compare SD of two classes.
Coefficient of Variation
Part of: Variance and Comparison
CV percents SD over mean; lower CV means steadier; different units compare only via CV; means shift with origin but CV needs nonzero mean.
Why it matters. CV crowns consistency. Percentages level units.
Formulas
- CV = (SD / Mean) x 100
- Lower CV means steadier data
Key words
- Coefficient of variation
- : SD as a percent of mean, for comparing spreads.
- Consistency
- : How steady a data set is; higher steadiness means lower spread.
- Unit-free measure
- : A comparison number free from units of measurement.
Try it in two minutes
- Divide SD by mean.
- Percent it.
- Crown the lowest.
Try at home. Compare two batsmen CVs.
What your child will practise
- Coefficient of Variation: Desert Puzzle (Clue Puzzle)
- Coefficient of Variation: Desert Quick Fire (Quick Fire)
- Mean Median and Mode: Space Puzzle (Clue Puzzle)
- Range and Mean Deviation: Ocean Quest (Flip and Match)
- Variance and Standard Deviation: Jungle Quick Fire (Quick Fire)
- Quiz: Coefficient of Variation (8 questions)
- Quiz: Mean Median and Mode (8 questions)
- Quiz: Range and Mean Deviation (8 questions)
- Quiz: Variance and Standard Deviation (8 questions)