Statistics — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Statistics, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Statistics in one look
how spread out the data really is, measured four different ways
What dispersion measures
- the mean alone hides how spread out data is. Two datasets can share the same mean and look completely different
- dispersion measures answer one question: how far, on average, do the observations sit from some central value
- the four measures here, range, mean deviation, variance and standard deviation, each answer that question a different way
Range
- biggest value minus smallest value in the dataset
R=x_max-x_min
Four measures, four levels of detail
- Range: uses only the two extreme values, ignores everything in between
- Mean deviation: uses every value's absolute distance from the mean
- Variance: uses every value's SQUARED distance from the mean
- Standard deviation: the square root of variance, back in the original units
Mean deviation about the mean
- ungrouped data, n observations
MD=1/nΣ_i=1^n|x_i-x| - grouped data, N=Σ f_i
MD=1/NΣ f_i|x_i-x|
Mean deviation about the median
- the same idea, but measured from the median M instead of the mean: MD=1/nΣ|x_i-M|
- mean deviation about the median is always the SMALLEST possible mean deviation from any single value, a property unique to the median
- mean deviation is rarely asked for grouped data with a shortcut method. Direct substitution into the formula above is usually fastest
Worked: mean deviation about the mean
Q. find the mean deviation about the mean for the data 2,4,6,8,10
- mean: x=2+4+6+8+10/5=30/5=6
- absolute deviations from 6: |2-6|=4, |4-6|=2, |6-6|=0, |8-6|=2, |10-6|=4
- sum of absolute deviations: 4+2+0+2+4=12
- MD=12/5=2.4
Answer: mean deviation about the mean is 2.4
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Statistics sheet covers
- What dispersion measures
- Range
- biggest value minus smallest value in the dataset
- Four measures, four levels of detail
- Mean deviation
- Variance
- Standard deviation
- Mean deviation about the mean
- ungrouped data, n observations
- grouped data, N=Σ f_i
- Mean deviation about the median
- Worked: mean deviation about the mean
- Variance and standard deviation
- variance, ungrouped data
- standard deviation, the positive square root
- a useful shortcut identity
- Spread, pictured
- Worked: variance and standard deviation
- Variance for a frequency distribution
- the matching shortcut identity
- Coefficient of variation, comparing two datasets
- CV, expressed as a percentage
- Which measure of dispersion to reach for
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Statistics the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.