E ExamMaster

CBSE Class 11 · Mathematics

Statistics

Official NCERT chapter from Mathematics (book code kemh1). ExamMaster notes are original teaching at CBSE Class 11 depth.

This lesson follows the official chapter “Statistics” in Mathematics. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 11
  • Medium level
  • 8 concepts

1Measures of Dispersion

Dispersion is how spread out a list is — not the centre. Two lists can share a mean 10 and disagree in spread. A measure of dispersion is a number for that spread (range, mean deviation, variance/sd as taught). “They look mixed” is not a measure.

Using the mean as if it were the spread is the heading-steal.

Figure. Both lists share mean 5. The lower list is more spread out — that extra spread is what a measure of dispersion reports.

How it works

  1. See the list’s centre as already named or computedThe middle.
  2. Ask how far members sit from that middle or from each otherThe spread.
  3. Hang a named measureDispersion.

2Range

Range is largest minus smallest. For 4, 6, 6, 10 the range is 6. It uses only two members; a wild extra 100 would jump the range. Range is a first look, not the whole spread-story.

Calling 10 the range because it is the largest is a miss.

Figure. Range is one subtraction: largest observation minus smallest. Here 9 − 2 = 7. The middle mark 5 is not used.

How it works

  1. Find max and minThe ends.
  2. SubtractThe range.
  3. Note it ignores the middle pileA first look.

3Mean Deviation

Mean deviation about the mean (or median, as taught) is the average of |x_i − centre|. For 4, 6, 10 with mean 20/3, the absolute gaps average to a school MD. Bars, not signed gaps that cancel.

Averaging 4−mean without bars can cancel to a fake “no spread”.

Figure. Mean deviation is the average of the distances from the mean, not the signed leftovers. Distances 4, 0 and 4 give MD = 8/3.

How it works

  1. Compute the centre asked (mean or median)The centre.
  2. Take |x_i − centre| and averageThe MD.
  3. Keep the barsOtherwise signs cancel.

4Variance and Standard Deviation

Variance is the average of squared gaps from the mean (division by n or n−1 as the lesson chose). Standard deviation is its square-root — back in the data’s unit. For a tiny list 4, 6, 8, mean 6, squares 4+0+4=8, variance 8/3 if ÷n. SD is not the range.

Leaving variance in “squared rupees” when SD was asked is a unit-miss.

Figure. Variance is the mean of the squared deviations. For 2, 6 and 10 the squares are 16, 0 and 16, so variance is 32/3. Standard deviation is the positive square root of that.

How it works

  1. Find the meanThe centre.
  2. Average the squared gaps (as taught)Variance.
  3. Square-root for SDBack to the unit.

4, 6, 8

Mean, then variance using ÷n, then SD.

  • Mean6
  • Squares(−2)²+0+2²=8
  • Var and SD8/3 and √(8/3)

Pro tip. Squares first; SD returns to the list’s unit.

5A definition is a test you can run

Spread-measure is a test: range, MD, or variance/SD. If you only say “varied”, you have a heading.

A crowd-photo is not the test.

Figure. Range is not a picture of the list. It is a test you run: subtract the smallest observation from the largest. If that subtraction is not what you wrote, the name is wrong.

How it works

  1. Name the list and which measureThe object.
  2. Compute ends, bars, or squaresThe test.
  3. Then the word has contentThe definition ran.

6Name the given before the unknown

The given is the list. The unknown is the spread-number. Copy every member before you use only min and max for an SD.

Dropping the middle 6 because it “does not spread” is a silent given.

Figure. Write the list you were given before you name the measure you want. Here the given values are 4, 6 and 10; the unknown is whichever measure the question asked.

How it works

  1. Copy the listThe given.
  2. Name range, MD, or SDThe unknown.
  3. Then ends, bars, or squaresGiven first.

7One worked case is enough at this class

One tiny list is enough. A page of the same 4,6,8 clone does not add a new MD.

Ten twins of range 4 are still one idea.

Figure. One small list is enough at this class: 4, 7 and 10. Mean is 7. Range is 10 − 4 = 6. The same list is later reused for mean deviation.

How it works

  1. Run one range or one SDThe case.
  2. A second only as a checkOptional.
  3. StopThis class.

8A miss: swapping the school name for the picture

A crowd-photo is a setting. The maths is a list and a spread-number. Faces are not variance.

A stadium still is not σ.

Figure. An arithmetic progression is a list with a fixed step. This chapter is about how far values sit from a centre. A tidy +d picture is the wrong school name for dispersion.

How it works

  1. Keep the crowd as a storyA setting.
  2. Write the listThe maths.
  3. Then the measureDo not swap.
Range of 4, 6, 6, 10 is
  1. 6
  2. 10
  3. 4

Max minus min; not the largest alone.

Notes

  • The official chapter title is “Statistics”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • range = max−min
  • MD = average of |x−centre|
  • SD = √(variance)

Recap

Hold these pegs from the official chapter “Statistics”. The wording is ExamMaster’s teaching, not a textbook recap.

Measures of Dispersion
Dispersion is how spread out a list is — not the centre.
Range
Range is largest minus smallest. For 4, 6, 6, 10 the range is 6. It uses only two members; a wild extra 100 would jump the range. Range is a first look, not the whole spread-story.
Mean Deviation
Mean deviation about the mean (or median, as taught) is the average of |x_i − centre|.
Variance and Standard Deviation
Variance is the average of squared gaps from the mean (division by n or n−1 as the lesson chose).
A definition is a test you can run
Spread-measure is a test: range, MD, or variance/SD.
Name the given before the unknown
The given is the list. The unknown is the spread-number. Copy every member before you use only min and max for an SD.

Practise Statistics

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.