Download App

Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation3 Marks
Question
What is Karl Pearson's coefficient of correlation? State its properties.
✓

Answer

Karl Pearson's coefficient of correlation, denoted by rk, measures the degree and direction of relationship between two variables. It is calculated as :$\text{r}_\text{k}=\frac{\Sigma\text{xy}}{\text{N}.\sigma_\text{x}.\sigma_\text{y}} \ \text{or}\ \frac{\Sigma\text{xy}}{\sqrt{\Sigma\text{x}^2}\sqrt{\Sigma\text{y}^2}}$
$\text{r}_\text{k}=\frac{\Sigma(\text{X}-\overline{\text{X}})(\text{Y}-\overline{\text{Y}})}{\sqrt{\Sigma(\text{X}-\overline{\text{X}})^2}\sqrt{\Sigma(\text{Y}-\overline{\text{Y}})^2}}$
$\text{where, x}=\text{X}-\overline{\text{X}},\text{y}=\text{Y}-\overline{\text{Y}}$
Properties of Karl Pearson's coefficient of correlation:
  1. The value of correlation coefficient lies between -1 and +1. Symbolically, -1
  2. Correlation coefficient is independent of the change of origin and scale, i.e., the value of ‘r, 'is unaffected by the change of origin and scale.
  3. If r = 0, the two variables are not related. There is no linear relationship between them. They are independent.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Correlation→Correlation — all question types→Economics STD 11 Commerce question papers→CBSE Board STD 11 Commerce question papers→CBSE Board question paper generator→

Similar questions

Analyse the $MR$ curves given alongside and comment upon the price prevailing in case of each $MR$ curve.
→
'Statistics are figures, but all figures are not statistics'. Justify the statement.
→
Given the following data.
School Mean Income (in ₹) Standard Deviation (in ₹)
A 800 120
B 900 135
Compare the variability in income of teachers in two schools.
→
Two distributions with $100$ and $200$ items have a mean of $20$ and $10$. Find the combined mean of two distributions.
→
The price elasticity of supply of a commodity is 2. When its price falls from ₹ 10 to ₹ 8 per unit, its quantity supplied falls by 500 units. Calculate the quantity supplied at the reduced price.
→
Complete the following table:
Output (Units)Total Revenue (₹)Marginal Revenue (₹)Average Revenue (₹)
114--
224--
324--
416--
→
What price a consumer is ready to pay for a commodity in a state of his equilibrium?
→
Enumerate the different cases for which this method of survey is suitable.
→
The marginal utility from the consumption of commodity-X is given in following table
Units of X12345
$M U_{ X }$10973-5
Calculate total utility for each unit of consumption of commodity-X.
→
Marks obtained by seven students in Economics are as under. Find out the range and coefficient of range:
S.No. 1 2 3 4 5 6 7
Marks Scored 20 50 75 25 80 40 60
→