Skip to content
← Statistics

Statistics · Class 12 Commerce

Ch 2Linear Correlation — Class 12 Statistics, concept-first.

Correlation measures the extent and direction of the statistical relationship between two variables — how far a change in one variable tends to be associated with a change in the other.

42

Q&A

5

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Meaning and Types of Correlation

Correlation measures the extent and direction of the statistical relationship between two variables. By direction, correlation is positive (both variables move the same way, e.g.

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Meaning and Types of Correlation

Correlation measures the extent and direction of the statistical relationship between two variables — how far a change in one variable tends to be associated with a change in the other.

2

Scatter Diagram

A scatter diagram (or scatter plot) is the simplest and most direct way to get a first visual impression of whether — and how — two variables are related.

3

Karl Pearson's Coefficient of Correlation

Karl Pearson's Coefficient of Correlation (denoted ) is the most widely used numerical measure of the degree of linear correlation between two quantitative variables and .

4

Spearman's Rank Correlation Coefficient

When the data available are already in the form of ranks — or consist of a qualitative attribute that can only be ordered, not measured (e.g., ranking contestants by beauty, honesty, or leadership qua…

5

Interpretation and Properties of the Correlation Coefficient

A computed correlation coefficient is only useful once it is correctly interpreted. Both Karl Pearson's and Spearman's share the same range and the same rules of interpretation.

Exercises

+Show 4 questions4 questions
  1. Q5Distinguish between positive, negative, and zero (no) correlation, giving one real-life example of each.Free
  2. Q6The correlation coefficient between the price of a commodity (X) and its quantity demanded (Y) is computed as $r=-0.85$. Interpret this resu…Free
  3. Q7The monthly income (X) and monthly savings (Y) of 8 households are plotted on a scatter diagram, and the points are found to cluster closely…Preview
  4. Q8The price of a commodity (X, in Rs.) and the quantity demanded (Y, in units) over 5 months are given below. Compute Karl Pearson's Coefficie…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 31 questions31 questions
  1. Q1Which of the following values is not possible as a value of $r$? (a) $0.99$ (b) $-1.07$ (c) $-0.85$ (d) $0$Preview
  2. Q2In which situation, the values of Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient are equal?Preview
  3. Q3If $n = 20$, $\mathrm{Cov}(x, y) = -50$, $S_x = 15$, $S_y = 8$, find the value of correlation coefficient $r$.Preview
  4. Q4Ten students were ranked on the basis of their proficiency in sports and general knowledge. The rank correlation co-efficient obtained from…Preview
  5. Q5From the following information obtained from a sample of 7 families of a society regarding height of father (in cms) and height of his adult…Preview
  6. Q6What is the range of the correlation coefficient $r$? (a) $-1 < r < 1$ (b) 0 to 1 (c) $-1 \le r \le 1$ (d) $-1$ to 0Preview
  7. Q7If $r(-x, y) = -0.5$ then what is the value of $r(x, -y) = $ ? (a) 0.5 (b) $-0.5$ (c) 1 (d) 0Preview
  8. Q8What is the main limitation of scatter diagram method to find correlation coefficient?Preview
  9. Q9If $n = 10$, $Cov(x, y) = 30$, S.D. of $X = 5$ and variance of $Y = 144$ then find Correlation Coefficient.Preview
  10. Q10Ten students were ranked on the basis of their proficiency in sports and general knowledge. The rank correlation coefficient obtained from t…Preview
  11. Q11From the following information, find correlation coefficient between heights and weights. | Height (cm) $x$ | 155 | 165 | 158 | 162 | 153 |…Preview
  12. Q12From the following information of heights of husband and wife, Calculate the rank correlation coefficient between their heights. | Height of…Preview
  13. Q13What does the numerator indicate in the formula for calculating correlation coefficient by Karl Pearson's method? (a) (A) Product of varianc…Preview
  14. Q14If all the points plotted in a scatter diagram lie on a single line only, then what will be the value of $r$?Preview
  15. Q15Find the value of $r$ if $\text{cov}(x, y) = 240$, $S_x = 24$, $S_y = 30$.Preview
  16. Q16The following ranks are obtained about the sales and profits of different electric companies. Find rank correlation coefficient. | Ranks of…Preview
  17. Q17The following information is obtained to study the effect of use of fertilizer on yield of corn in a rural area: | Use of fertilizer (quinta…Preview
  18. Q18What is the range of the correlation coefficient $r$ ? (a) $-1 < r < 1$ (b) $0$ to $1$ (c) $-1 \le r \le 1$ (d) $-1$ to $0$Preview
  19. Q19In the method of rank correlation, in usual notations if $R_x = R_y$ for each pair of observations then what is the value of the $r$ ? (a) $…Preview
  20. Q20What is the main limitation of scatter diagram method?Preview
  21. Q21If the correlation coefficient between two variables $X$ and $Y$ is 0.8 find the value of the following : (i) $r(x, -y)$ (ii) $r(-x, -y)$Preview
  22. Q22The following results are obtained from a bivariate data, $n = 10$, $\Sigma(x - \bar{x})(y - \bar{y}) = 72$, $S_x = 3$, and $\Sigma(y - \bar…Preview
  23. Q23The following information is obtained to study the relationship between the advertisement cost and the sales of electric fans of the compani…Preview
  24. Q24From the following information, find the rank correlation coefficient between the sales (in thousand units) and the profit (in lakh ₹) : | S…Preview
  25. Q25Which kind of the correlation can be obtained if the two variables are varying in opposite direction in constant proportion? (a) Partial Pos…Preview
  26. Q26If $r(x, y) = 0.7$ then what is the value of $r(x + 0.2, y + 0.2)$? (a) $0.7$ (b) $0.9$ (c) $1.1$ (d) $-0.7$Preview
  27. Q27Define correlation coefficient.Preview
  28. Q28The following results are obtained from a bivariate data $n = 10,\ \Sigma(x - \bar{x})(y - \bar{y}) = 72,\ S_x = 3$ and $\Sigma(y - \bar{y})…Preview
  29. Q29The following data is available for two variables rainfall in mm(X) and yield of crop Qtl/Hec(Y): $n = 10,\ \bar{x} = 120,\ \bar{y} = 150,\…Preview
  30. Q30To know the relation between the average monthly income (in $\text{\rupee}$) and income due to overtime of workers (in $\text{\rupee}$), the…Preview
  31. Q31The following data is obtained to know the relation between maximum day temperature and the sale of ice-cream in Ahmedabad city: | Maximum T…Preview

More questions

7 Q
+Show 4 questions4 questions
  1. Example 1The advertisement expenditure (X, in Rs. lakh) and the corresponding sales (Y, in Rs. lakh) of a firm over 5 years are given below. Compute…Free
  2. Example 2The age (X, in years) and weight-index (Y) of 6 employees are given below. Compute Karl Pearson's Coefficient of Correlation by the step-dev…Free
  3. Example 3Two judges, A and B, independently rank 6 contestants in a talent contest. Compute Spearman's Rank Correlation Coefficient between the two s…Preview
  4. Example 4The marks obtained by 7 students in Statistics (X) and Accountancy (Y) are given below. Compute Spearman's Rank Correlation Coefficient, app…Preview
+Show 3 questions3 questions
  1. Q9Karl Pearson's Coefficient of Correlation, $r$, can take values only in the range: (a) 0 to 1 (b) $-1$ to 0 (c) $-1$ to $+1$ (d) $-\infty$ t…Free
  2. Q10Which measure of correlation should be used when the data available consists only of the *ranks* given to a set of items (or a quality, such…Preview
  3. Q11If every plotted point on a scatter diagram of two variables $X$ and $Y$ lies exactly on a single straight line sloping downward from left t…Preview