Unit 5: Descriptive Statistics — Class 11 Applied Maths 2026-27 | Boundless Maths
Unit 5 of 7 10 Marks CBSE 2026–27 Includes Regression Analysis

Unit 5: Descriptive
Statistics

CBSE Class 11 Applied Mathematics · Unit 5 · Free MCQs, Solved Examples & Case Studies

Unit 5 carries 10 marks in the CBSE Class 11 annual exam. Complete free resources: 20 MCQs + AR questions, 13 solved examples and 4 case studies. Covers Measures of Dispersion, Percentiles, Correlation (Karl Pearson & Spearman) and Regression Analysis — fully aligned to CBSE 2026-27.

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Case Studies

Class 11 Applied Maths Unit 5: Descriptive Statistics — Complete Free Resources (CBSE 2026-27)

This page covers all topics in Unit 5 of CBSE Class 11 Applied Mathematics — carrying 10 marks in the CBSE Class 11 annual exam. You'll find 15 MCQs and 5 Assertion-Reason questions with answers, 13 solved examples, and 4 case studies. Unit 5 covers four areas of statistics: Measures of Dispersion (Range, Mean Deviation, Variance, Standard Deviation, Coefficient of Variation), Percentiles (percentile rank calculation), Correlation (Karl Pearson's coefficient and Spearman's Rank Correlation), and Regression Analysis (regression lines, regression coefficients and their properties). Free CBSE 2026-27 aligned practice on standard deviation problems, percentile rank questions with solutions, correlation and regression numericals, and a step-by-step guide to coefficient of variation.

Measures of Dispersion Percentile Rank Correlation Regression 10 Marks
Unit 5 · 10 Marks

Topics & Key Formulas

Four topic areas examined across MCQs, short answers and case studies.

1. Measures of Dispersion

Quantify how spread out a data set is around its central value.

  • Range = Maximum − Minimum
  • Mean Deviation = Σ|xᵢ − x̄| / n
  • Variance σ² = Σ(xᵢ − x̄)² / n
  • Standard Deviation σ = √Variance
  • Coefficient of Variation CV = (σ/x̄) × 100
σ² = Σ(xᵢ−x̄)²/n  ·  CV = (σ/x̄)×100

2. Percentile & Quartile Rank

Position of a value relative to the rest of the data set.

  • Percentile Rank = (No. of values below + 0.5)/n × 100
  • Q₁ = 25th percentile  ·  Q₂ (Median) = 50th percentile  ·  Q₃ = 75th percentile
  • Quartile Deviation = (Q₃ − Q₁)/2
  • Higher percentile = better relative standing
Percentile Rank = (below + 0.5)/n × 100

3. Correlation

Measures strength and direction of the linear relationship between two variables.

  • Karl Pearson's r = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n·σX·σY)
  • −1 ≤ r ≤ +1 always  ·  r=0 → no linear relation
  • Spearman's ρ = 1 − 6Σd²/[n(n²−1)] for ranked data
  • Correlation does NOT imply causation
r ∈ [−1,+1]  ·  ρ = 1 − 6Σd²/n(n²−1)

4. Regression Analysis

Predicts the value of one variable from another using a fitted equation. Full deep-dive page →

  • Y on X: Y−Ȳ = bYX(X−X̄)  ·  X on Y: X−X̄ = bXY(Y−Ȳ)
  • bYX = r·(σY/σX)  ·  bXY = r·(σX/σY)
  • Both lines pass through (X̄, Ȳ)
  • r = ±√(bYX × bXY) — r is the geometric mean of the two coefficients
r = ±√(bYX × bXY)
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Interactive Practice

Practice MCQs — Unit 5: Descriptive Statistics

15 MCQs + 5 Assertion-Reason questions. Click Show Answer to see the full explanation.

Measures of Dispersion
Q1 Dispersion
Which of the following is NOT a measure of dispersion?
(a) Range
(b) Standard Deviation
(c) Median
(d) Quartile Deviation
Answer: (c) Median
Median is a measure of central tendency, not dispersion. Range, Standard Deviation and Quartile Deviation all measure the spread of data.
Q2 Range
A shopkeeper records the number of customers walking in each day for a week: 4, 7, 2, 15, 9, 11, and 3. What is the range of this data?
(a) 9
(b) 11
(c) 13
(d) 15
Answer: (c) 13
Range = Maximum − Minimum = 15 − 2 = 13.
Q3 Variance
A delivery rider logs the number of packages dropped off at five consecutive stops: 2, 4, 6, 8, and 10. What is the variance of these values?
(a) 6
(b) 8
(c) 10
(d) 12
Answer: (b) 8
Mean = 30/5 = 6. Σ(xᵢ−6)² = 16+4+0+4+16 = 40. Variance = 40/5 = 8.
Q4 Coefficient of Variation
Coefficient of Variation (CV) is defined as:
(a) (σ/x̄) × 100
(b) (x̄/σ) × 100
(c) (σ²/x̄) × 100
(d) σ × x̄
Answer: (a) (σ/x̄) × 100
CV is a relative, unit-free measure of dispersion. Lower CV = more consistency; higher CV = more variability.
Q5 Effect on SD
If 5 is added to every observation in a data set, the standard deviation:
(a) Increases by 5
(b) Decreases by 5
(c) Is multiplied by 5
(d) Remains unchanged
Answer: (d) Remains unchanged
Adding a constant shifts the mean equally, so deviations (xᵢ−x̄) stay the same. SD measures spread, not position.
Percentile & Quartile Rank
Q6 Percentile
A student scores at the 80th percentile. This means:
(a) The student scored 80 marks
(b) 80% of students scored above the student
(c) 80% of students scored at or below the student's score
(d) The student is in the bottom 20%
Answer: (c)
The pth percentile is a value at or below which p% of observations fall. 80th percentile → outperformed 80% of the group.
Q7 Quartiles
The second quartile (Q₂) is equivalent to which percentile?
(a) 25th percentile
(b) 50th percentile
(c) 75th percentile
(d) 90th percentile
Answer: (b) 50th percentile
Q₁=25th, Q₂=50th (Median), Q₃=75th percentile. Q₂ divides data into two equal halves.
Correlation
Q8 Pearson's r
Karl Pearson's coefficient of correlation (r) always lies between:
(a) 0 and 1
(b) −1 and 0
(c) −1 and +1
(d) −2 and +2
Answer: (c) −1 and +1
r=+1 → perfect positive; r=−1 → perfect negative; r=0 → no linear correlation.
Q9 Spearman's ρ
Two judges at a singing competition independently ranked the same 5 contestants. When their rankings were compared, the differences between corresponding ranks (d) worked out to 1, 0, −1, 2, and −2. What is Spearman's rank correlation coefficient ρ for this panel?
(a) 0.4
(b) 0.5
(c) 0.7
(d) 1.0
Answer: (b) 0.5
Σd²=1+0+1+4+4=10. n(n²−1)=5×24=120. ρ=1−60/120=0.5.
Q10 Interpreting r
If r = 0.85 between height and weight of students, the most appropriate conclusion is:
(a) Height causes weight to increase
(b) There is a strong positive linear relationship
(c) Height and weight are not related
(d) There is a weak negative relationship
Answer: (b)
r=0.85 close to +1 → strong positive correlation. Correlation does NOT imply causation, so (a) is wrong.
Regression Analysis
📌 New to Class 11 Syllabus

Regression is a recently added topic. See the dedicated Regression Analysis page for the full concept explanation, 6 properties, and 5 worked examples.

Q11 Regression Coefficients
A statistician calculates both regression coefficients for a dataset and finds bYX = 0.6 and bXY = 0.4. What is the value of the correlation coefficient r?
(a) 0.24
(b) 0.49
(c) 0.5
(d) 1.0
Answer: (b) 0.49
r = √(bYX × bXY) = √(0.6×0.4) = √0.24 ≈ 0.49.
Q12 Regression Lines
Both lines of regression (Y on X, and X on Y) always pass through:
(a) The origin (0,0)
(b) The point (X̄, Ȳ)
(c) The point (1,1)
(d) They never intersect
Answer: (b) The point (X̄, Ȳ)
Both regression lines pass through the means of X and Y — this is the key property linking them.
Q13 Validity Check
A student computes the two regression coefficients for a project dataset and reports bYX = 2.5 and bXY = 0.8. Could these actually be the regression coefficients of the same data set?
(a) Yes, both are valid
(b) No, since bYX × bXY > 1, giving r > 1
(c) Yes, but only if r = 0
(d) Cannot be determined
Answer: (b)
bYX×bXY = 2.5×0.8 = 2.0. Since r² = bYX×bXY must be ≤ 1, this is impossible — invalid coefficients.
Q14 Prediction
An analyst has fitted a regression line of Y on X for her dataset: Y = 3X + 20. If she now wants to predict Y for a new observation where X = 10, what value should she get?
(a) 23
(b) 30
(c) 50
(d) 60
Answer: (c) 50
Y = 3(10) + 20 = 30 + 20 = 50.
Q15 Correlation vs Regression
Which statement correctly distinguishes correlation from regression?
(a) Both give an equation for prediction
(b) Correlation gives one number; regression gives an equation for prediction
(c) Regression is symmetric; correlation is not
(d) There is no real difference between them
Answer: (b)
Correlation (r) measures strength/direction only. Regression provides an equation Y=a+bX that allows actual prediction.
Assertion-Reason Questions (AR 1–5)
AR 1 Dispersion
Assertion (A): Standard deviation is always greater than or equal to zero.

Reason (R): Standard deviation is the square root of variance, and variance is the mean of squared deviations, which is always non-negative.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
Variance ≥ 0 always (squared terms). SD = √Variance ≥ 0. R correctly and fully explains A.
AR 2 Spearman's ρ
Assertion (A): Spearman's rank correlation can be computed without knowing the actual data values.

Reason (R): Spearman's formula uses only rank differences (d) between paired observations.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
Both correct — ρ = 1 − 6Σd²/n(n²−1) needs only ranks, not the raw data, which is exactly why it works for ordinal data.
AR 3 Regression
Assertion (A): The two lines of regression (Y on X, and X on Y) are generally different lines.

Reason (R): Regression coefficients bYX and bXY are usually not equal, except when r = ±1.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (a)
Regression is not symmetric: bYX ≠ bXY generally. When r=±1, the two lines coincide. R correctly explains why A is true.
AR 4 Regression vs Correlation
Assertion (A): A strong correlation between two variables proves that one causes the other.

Reason (R): Correlation only measures the strength and direction of a linear association, not a cause-and-effect relationship.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (d)
A is false: correlation does NOT prove causation — two variables can be correlated due to a third factor or coincidence. R is true and correctly states the limitation, which is precisely why A is false.
AR 5 Percentile
Assertion (A): A student at the 90th percentile has scored 90 marks.

Reason (R): Percentile rank reflects relative standing in a group, not an absolute mark or score.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R does NOT explain A
(c) A is true, R is false
(d) A is false, R is true
Answer: (d)
A is false: 90th percentile means the student scored better than 90% of others — it says nothing about the actual mark obtained. R is true and explains why A is wrong.

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  • Karl Pearson's r, Spearman's ρ, regression coefficients
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Step-by-Step Solutions

Solved Examples

Click Show Solution to reveal complete working.

Measures of Dispersion
Q1 Mean Deviation
A small bakery records the number of cupcakes sold each day over 8 days: 6, 7, 10, 12, 13, 4, 8, and 20. Find the mean deviation of daily sales about the mean.
n = 8. Mean x̄ = (6+7+10+12+13+4+8+20)/8 = 80/8 = 10
|xᵢ−x̄|: 4, 3, 0, 2, 3, 6, 2, 10 → Σ|xᵢ−x̄| = 30
Mean Deviation = 30/8 = 3.75
✓ Mean Deviation about the Mean = 3.75
Q2 Variance & SD
A fitness tracker logs the number of minutes a runner spends jogging on 10 consecutive mornings: 4, 8, 11, 17, 12, 3, 14, 6, 8, and 7. Find the variance and standard deviation of this running time.
n = 10. Σxᵢ = 90, Mean x̄ = 9
Σ(xᵢ−9)² = 25+1+4+64+9+36+25+9+1+4 = 178
Variance σ² = 178/10 = 17.8
Standard Deviation σ = √17.8 ≈ 4.22
✓ Variance = 17.8  |  SD ≈ 4.22
Q3 Coefficient of Variation
Compare the consistency of two batsmen using coefficient of variation.
A: 25,85,40,80,120,10,60  |  B: 50,70,65,45,80,60,70
Batsman A: Mean = 420/7 = 60. σA = √(8750/7) ≈ 35.36. CVA = (35.36/60)×100 ≈ 58.9%
Batsman B: Mean ≈ 62.86. σB ≈ 11.30. CVB = (11.30/62.86)×100 ≈ 18.0%
Since CVB < CVA, Batsman B has lower relative variability
✓ Batsman B is more consistent (CV ≈ 18% vs ≈ 59%)
Q4 Quartile Deviation
A school analyses the marks scored by 50 students in a unit test. The first quartile (Q₁) of the marks works out to 28, and the third quartile (Q₃) works out to 52. Find: (i) the Interquartile Range, (ii) the Quartile Deviation, and (iii) the Coefficient of Quartile Deviation.
(i) IQR = Q₃−Q₁ = 52−28 = 24
(ii) QD = IQR/2 = 24/2 = 12
(iii) Coefficient of QD = (Q₃−Q₁)/(Q₃+Q₁) = 24/80 = 0.30
✓ (i) IQR=24  |  (ii) QD=12  |  (iii) Coeff. QD=0.30
Q5 Mean Deviation about Median
A wildlife survey team records the number of birds spotted at 11 different observation points in a forest: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, and 21. Find the mean deviation about the median for this data.
n=11. Ascending: 3,3,4,5,7,9,10,12,18,19,21. Median = 6th value = 9
|xᵢ−9|: 6,6,5,4,2,0,1,3,9,10,12 → Σ = 58
MD about Median = 58/11 ≈ 5.27
✓ Mean Deviation about Median ≈ 5.27
Percentile & Quartile Rank
Q6 Percentile Rank
In a class of 40 students, a student ranks 10th from the top. Find the percentile rank.
Students below = 40−10 = 30
Percentile Rank = (30+0.5)/40 × 100 = 76.25
✓ Percentile Rank ≈ 76 (better than ~76% of class)
Correlation — Karl Pearson's r
Q7 Pearson's r
A teacher wants to know how closely a student's attendance correlates with their class participation score. Over 5 weeks, the number of classes attended (X) was 1, 2, 3, 4, and 5, while the corresponding participation score out of 5 (Y) was 2, 4, 5, 4, and 5. Calculate Karl Pearson's coefficient of correlation r for this data.
n=5; x̄=3, ȳ=4
Σ(xᵢ−x̄)(yᵢ−ȳ) = 6; Σ(xᵢ−x̄)²=10; Σ(yᵢ−ȳ)²=6
r = (6/5)/(√2×√1.2) = 1.2/1.549 ≈ 0.775
✓ Karl Pearson's r ≈ 0.775 → Strong positive correlation
Q8 Interpreting r
Advertising spend (X, ₹000) vs Sales (Y, ₹ Lakhs) over 5 months gives r = 0.92. Interpret the result.
r = 0.92 is close to +1 → very strong positive linear correlation
As advertising spend increases, sales tend to increase substantially
Correlation does NOT prove causation — other factors may also affect sales
✓ r=0.92 → Very strong positive correlation between ad spend and sales
Correlation — Spearman's Rank Correlation
Q9 Spearman's ρ
At a regional dance competition, two judges were asked to independently rank 6 performers from best (rank 1) to worst (rank 6). Judge A's rankings were 1, 2, 3, 4, 5, and 6, while Judge B's rankings for the same performers were 2, 3, 1, 5, 6, and 4. Find Spearman's rank correlation coefficient ρ to see how closely the two judges agreed.
d = A−B: −1,−1,2,−1,−1,2. Σd=0 ✓. d²: 1,1,4,1,1,4 → Σd²=12
n=6. n(n²−1)=6×35=210
ρ = 1 − 72/210 = 0.657
✓ Spearman's ρ ≈ 0.657 → Moderately strong agreement
Q10 Spearman's ρ
A school principal wants to check whether students who do well in Maths also tend to do well in Science. She collects the marks of 8 students: Maths (X) scores were 70, 65, 80, 55, 90, 75, 85, and 60, while their Science (Y) scores were 68, 60, 75, 50, 85, 70, 80, and 65. Find Spearman's rank correlation coefficient ρ and interpret what it tells the principal.
Ranks computed for both (highest=Rank1); d values: 0,−1,0,0,0,0,0,1 → Σd²=2
n=8. n(n²−1)=8×63=504
ρ = 1 − 12/504 ≈ 0.976
✓ ρ ≈ 0.976 → Very strong positive correlation: good in Maths → good in Science
Regression Analysis
📌 More examples on the dedicated page

This is a brief introduction. The Regression Analysis page has 5 fully worked examples covering regression equations from raw data, finding r from coefficients, validity checks, and real-world predictions.

Q11 Finding r from Coefficients
While analysing a dataset, a researcher has already worked out both regression coefficients: bYX = 0.8 and bXY = 0.2. Use these to find the coefficient of correlation r between the two variables.
r = ±√(bYX × bXY) = ±√(0.8 × 0.2) = ±√0.16 = ±0.4
Since both regression coefficients are positive, r is also positive
✓ r = +0.4
Q12 Regression Equation from Means
A market analyst is studying the relationship between two variables X and Y for a set of products. From her data she has computed X̄=40, Ȳ=45, σX=6, σY=8, and r=0.75. Find the regression equation of Y on X that she can use for prediction.
bYX = r·(σY/σX) = 0.75×(8/6) = 1.0
Y − Ȳ = bYX(X − X̄) → Y − 45 = 1.0(X − 40)
✓ Regression line of Y on X: Y = X + 5
Q13 Validity of Coefficients
A student submits a project report claiming the regression coefficients for her dataset are bYX = 2.5 and bXY = 0.8. Before accepting this, check whether these two values could realistically be the regression coefficients of the same data set.
Check: bYX × bXY = 2.5 × 0.8 = 2.0
Since r² = bYX × bXY ≤ 1 always, r²=2.0 would mean r > 1, which is impossible
✓ NO — these cannot be valid regression coefficients

📈 Want the Complete Regression Guide?

Concept explanation, correlation-vs-regression comparison, 6 key properties and 5 fully worked examples — all on one dedicated page.

📈 Explore Regression Analysis →
4-Mark Questions

Case Studies

Board-pattern case questions across all Unit 5 topics. Click Show Answer for each part.

🏏

Case Study 1: Comparing Two Batsmen (Dispersion)

A coach wants to select between two batsmen based on their last 7 innings. Batsman A: 25, 85, 40, 80, 120, 10, 60 runs. Batsman B: 50, 70, 65, 45, 80, 60, 70 runs.
(i)

Find the mean score of each batsman.

(ii)

Find the standard deviation of Batsman A.

(iii)

Find the Coefficient of Variation for both batsmen.

(iv)

Which batsman should the coach select for consistency, and why?

(i)Mean A = 420/7 = 60. Mean B = 440/7 ≈ 62.86.
(ii)σA = √(8750/7) ≈ 35.36.
(iii)CVA = (35.36/60)×100 ≈ 58.9%. CVB = (11.30/62.86)×100 ≈ 18.0%.
(iv)Batsman B — his lower CV (≈18%) means he is much more consistent despite having a similar average to A, who has wild swings in form.
🎓

Case Study 2: Ranking Students by Percentile (Percentile Rank)

In a school of 200 students, a student named Aman scored higher than 170 of his classmates in the annual exam.
(i)

Find Aman's percentile rank.

(ii)

Does this mean Aman scored 85 marks? Explain.

(iii)

Another student, Priya, ranks 15th from the top in the same class. Find her percentile rank.

(iv)

Who performed relatively better, Aman or Priya?

(i)Percentile Rank = (170+0.5)/200 × 100 = 85.25 ≈ 85th percentile.
(ii)No. Percentile rank shows relative standing, not an absolute score. It only tells us Aman performed better than 85% of his class — his actual marks could be anything.
(iii)Students below Priya = 200−15 = 185. Percentile Rank = (185+0.5)/200×100 = 92.75 ≈ 93rd percentile.
(iv)Priya — her percentile rank (93) is higher than Aman's (85), meaning she outperformed a larger fraction of the class.
📈

Case Study 3: Study Hours and Exam Scores (Correlation)

A researcher records study hours (X) and exam scores (Y) of 5 students: X: 2,4,6,8,10  |  Y: 50,55,65,70,80.
(i)

Find the mean of X and Y.

(ii)

Karl Pearson's r for this data works out to approximately 0.99. Interpret this value.

(iii)

Can the researcher conclude that more study hours CAUSE higher scores?

(iv)

What tool would let the researcher actually predict a score given study hours?

(i)X̄ = 30/5 = 6. Ȳ = 320/5 = 64.
(ii)r ≈ 0.99 indicates an almost perfect positive linear relationship — as study hours increase, exam scores increase almost proportionally.
(iii)Not strictly. Correlation only measures association, not causation. Other factors (prior knowledge, tutoring, sleep) could also be influencing scores alongside study hours.
(iv)Regression analysis — fitting a regression line of Y on X (Score = a + b×Hours) would let the researcher plug in any value of X and predict Y.
💼

Case Study 4: Predicting Sales from Advertising (Regression)

A company's regression line of Sales (Y, ₹ lakh) on Advertising spend (X, ₹ lakh) is found to be Y = 3X + 20, based on past data with X̄ = 10.
(i)

Predict the sales when advertising spend is ₹15 lakh.

(ii)

Find Ȳ, the mean sales value, using the fact that the regression line passes through (X̄, Ȳ).

(iii)

If bYX = 3 and bXY = 0.25, find the correlation coefficient r between advertising and sales.

(iv)

Why would the company use this regression equation rather than just the correlation coefficient r for planning next year's budget?

(i)Y = 3(15)+20 = 45+20 = ₹65 lakh.
(ii)Ȳ = 3(10)+20 = ₹50 lakh (since the line passes through the means).
(iii)r = √(bYX × bXY) = √(3 × 0.25) = √0.75 ≈ 0.866 (strong positive correlation).
(iv)Correlation (r) only tells the company how strongly spend and sales are related — it gives no actual numbers. The regression equation lets them plug in any planned ad-spend figure and get a specific predicted sales value, which is essential for budget planning.

📈 Master Regression with 5 Fully Worked Examples

Equation derivation from raw data, finding r from coefficients, validity checks, and real-world prediction problems.

📈 Explore Regression Analysis →
Score Full Marks

Exam Tips — Unit 5: Descriptive Statistics

What separates 9-mark answers from 6-mark answers in this unit.

✅ Tip 1 — Dispersion Formulas

Always write the formula before substituting values. Write σ² = Σ(xᵢ−x̄)²/n explicitly, then build a table for the deviations. This earns method marks even if a single arithmetic step is wrong.

✅ Tip 2 — Percentile Rank

Remember the +0.5 adjustment in the formula. Percentile Rank = (number below + 0.5)/n × 100. Students who forget the 0.5 lose marks even with the right logic.

✅ Tip 3 — Correlation

Never claim causation from correlation alone. If a question asks you to interpret r, mention strength AND direction, and explicitly note that correlation does not imply causation — examiners reward this distinction.

✅ Tip 4 — Regression

Always check which line you need — Y on X, or X on Y. Use the Y on X line to predict Y from a given X, and the X on Y line to predict X from a given Y. Mixing these up is the most common error in regression questions.

❌ Common Mistakes to Avoid in Unit 5

  • Confusing variance and standard deviation (SD = √variance, not the same number)
  • Forgetting the +0.5 in the percentile rank formula
  • Claiming correlation proves causation
  • Using the wrong regression line (Y on X vs X on Y) for the prediction asked
  • Forgetting both regression coefficients must have the SAME sign
  • Not checking that bYX × bXY ≤ 1 when verifying regression coefficients
  • Mixing up Σd² in Spearman's formula with raw rank values
Common Questions

Frequently Asked Questions

Questions students ask most about Class 11 Applied Maths Unit 5.

Unit 5 (Descriptive Statistics) covers four areas: Measures of Dispersion (Range, Mean Deviation, Variance, Standard Deviation, Coefficient of Variation), Percentiles (percentile rank calculation), Correlation (Karl Pearson's coefficient and Spearman's Rank Correlation), and Regression (regression lines, regression coefficients, and their properties). The unit carries 10 marks.
Correlation measures the strength and direction of a relationship using a single value r between −1 and +1. Regression goes further and gives an equation that allows actual prediction of one variable from another. Correlation tells you if and how strongly variables move together; regression tells you exactly how much one changes when the other changes. See our dedicated Regression page for a full comparison.
Unit 5 (Descriptive Statistics) carries 10 marks in the CBSE Class 11 Applied Maths annual exam.
Spearman's rank correlation coefficient is ρ = 1 − 6Σd²/[n(n²−1)], where n is the number of paired observations and d is the difference between the ranks of each pair. It is used when data is given as ranks rather than raw measurements.
Coefficient of Variation (CV) is a relative, unit-free measure of dispersion: CV = (σ/x̄) × 100. It is used to compare the consistency of two or more data sets, especially when they have different units or very different means — like comparing the consistency of two batsmen's scores.
The correlation coefficient r is the geometric mean of the two regression coefficients: r = ±√(bYX × bXY). This means bYX × bXY can never exceed 1, since r² can never exceed 1 — a useful check for validating regression coefficients.
Yes — Regression Analysis is syllabus topic 6.4 in the official CBSE 2026-27 Applied Mathematics curriculum for Class 11, covering the concept, dependent/independent variables, regression coefficients, regression equations and their properties. Since it's a recently added topic with limited textbook coverage, we've built a complete dedicated guide with full concept explanation and worked examples.
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