**Class 11 Economics Chapter 13 Correlation**, (Assam Higher Secondary Education Council) AHSEC

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**AHSEC Class 11 Economics Chapter ****13 Correlation**

**13 Correlation**

**Class 11 Economics Chapter 13 Correlation**

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**SCERT Class 11 Economics Chapter**

**13 Correlation****Solutions**provided here ensure a smooth and easy understanding of all the concepts. Understand the concepts behind every chapter and score well in the board exams.

**Correlation**

**Chapter – 13**

**PART – B**

**VERY SHORT ANSWER QUESTIONS**

**1. The unit of correlation coefficient between height in feet and weight in kgs. is ______**

**(i) Kg / ft **

**(ii) Percentage **

**(iii) Non existent **

Ans: (ii)Percentage.

**2. The range of simple correlation coefficient is ______**

**(i) 0 to infinity **

**(ii) minus one to plus one **

**(iii) minus infinity to infinity **

Ans: (ii) minus one to plus one.

**3. If rxy is positive the relation between X and Y is of the type _______**

**(i) When Y increases X increases **

**(ii) When Y decreases X increases **

**(iii) When Y increases X does not change**

Ans: When Y increases X increases

**4. If rxy = 0 the variable X and Y are ______ **

**(i) linearly related **

**(ii) not linearly related **

**(iii) independent **

Ans: (iii) Independent

**5. Of the following three measures which can measure any type of relationship ______ **

**(i) Karl Pearson’s coefficient of correlation **

**(ii) Spearman’s rank correlation **

**(iii) Scatter diagram **

Ans: (i) Karl Pearson’s coefficient of correlation.

**6. If precisely measured data are available the simple correlation coefficient is ______**

**(i) more accurate than rank correlation coefficient**

**(ii) less accurate than rank correlation coefficient**

**(iii) as accurate as the rank correlation coefficient. **

Ans: More accurate than rank correlation coefficient.

**7. Why is r preferred to covariance as a measure of association ?**

Ans: Because , it can measure degree and direction simultaneously.

**8. Can ‘ r ‘ lie outside the -1 and 1 range depending on the type data ? **

Ans: No, it always lie between +1 and -1.

**9. Does correlation imply causation ? **

Ans: Do, it depends upon several other factors, besides cause effect relationship.

**10. When is rank correlation more precise than simple correlation co – efficient ? **

Ans: In case of qualitative data.

**11. Does zero correlation mean independence ? **

Ans: Yes, it means X and Y variable are independent of each other.

**12. Can simple correlation coefficient measure any type of relationship ? **

Ans: Yes.

**13. Define the term correlations : **

Ans: Two variables are said to be correlated with each other if movement in one is accompanied by the movement in others .

**14. Mention the two examples which have correlation between them. **

Ans: (a) Height and Weight,

(b) Price and Demand

**15. When correlation is of positive nature between two variables ?**

Ans: When the two variables move in the same directions.

**16. Define scatter diagram. **

Ans: It studies correlation between two variables on the basis of dots plotted on a graph paper.

**17. Give an important property of co – efficient of correlation.**

Ans: The value of correlation coefficient lies between – 1 and +1.

**18. Name two mathematical methods of measuring co – efficient of correlation. **

Ans: (a) Karl – Person’s Method.

(b) Rank Method.

**19. What is meant by degree of correlation ? **

Ans: It shows the magnitude or extent of correlation.

**20. Give a main advantage of rank difference method. **

Ans: It can be used for qualitative phenomenon.

**21. What is tied ranks ? **

Ans: When two or more items in a series are of equal value and are assigned equal ranks are known to be tied ranks.

**22. When karl pearson coefficient of correlation is equal to spearman’s rank correlation.**

Ans: When X and Y values are non-repetitive.

**SHORT & LONG TYPES ANSWER QUESTIONS :**

**1. Write the significance or importance of correlation. **

Ans: (a) Degree and direction of relationship existing between two variables can be sum up.

(b) Possibility of predictions.

(c) Helpful in decision making.

(d) Helpful in understanding economic behaviour.

**2 . What is positive correlation ? **

Ans: When two variables move in the same direction correlations is said to be positive or direct. Eg income and expenditure, money supply and

price level etc.

**3. What negative correlation ? **

Ans: When the variables move in opposite direction , correlation between such variables is said to be negative, e.g. price and demand , day temperature and sale of woolens garments etc.

**4. What is simple correlation ? **

Ans: It is one in which the relationship between two variables is studied e.g. relationship between the output of wheat and use of chemical fertiliser .

**5. What is partial correlation ? **

Ans: Here, the relationship between two variables is examined keeping other variables as constant eg. Relationship between output of wheat and use of chemical fertiliser keeping temperature as constant.

**6. What is multiple correlation ? **

Ans: It studies the relationship between more than two variables e.g.relationship of wheat output with the use of fertiliser and with temperature .

**7. What is linear correlation ? **

Ans: When changes in the values of two variables is at a constant ratio, there will be linear relationship between them.

**8. What is non – linear correlation ? **

Ans: Correlation is called non-linear if the ratio of change between two variables is not constant.

**9. Write the formula of Karl Pearson’s correlation coefficient.**

Ans: Where , r = correlation coefficient.

**10. Write the formula of spearman’s rank correlation. **

Ans: Where,

rk= rank correlation coefficient

D² = Sum of square of Rank Different

N = Number of pairs

**11. Write the difference between Pearson and spearman method of correlation.**

Ans: (a) Pearsonion method measures correlation for quantitative data whereas spearman rank correlation measures coefficient of correlation for qualitative data.

(b) Personion method uses deviations from actual or assumed mean but spearman method takes rank differences.

**12. Write the properties or features of correlation. **

Ans: (a) Correlation is a pure number.

(b) Range or value of correlation lies between – 1 to +1.

(c) Correlation coefficient is independent of the change of origin.

(d) Correlation is independent of the change in scale of reference .

**13. Write the merits and demerits of Scatter Diagram. **

Ans: **Merits:**

(a) It is a simple and attractive method to study correlation.

(b) It enables us to know the presence or absence of correlation ‘at a single glance’ of the diagram .

(c) It is not influenced by extreme values.

**Demerits: **

(a) This method does not indicate the exact numerical value of correlation.

(b) It is influenced by personal bias of the investigator.

(c) It is only a qualitative expression rather than a quantitative expression.

**14. Write the merits and demerits of karl Pareson’s correlation coefficient. **

Ans: **Merits : **

(a) It is a practical and popular method of deriving relationship among variables .

(b) Measurement of degree and direction simultaneously.

(c)It is helpful in estimation.

**Demerits: **

(a) Possibility of wrong interpretation.

(b)This method is more time consuming.

(c) The assumptions of Karl Parson’s are scientific.

**15. Write the merits and demerits of spearman’s Rank correlation coefficient.**

Ans : **Merits : **

(a) This method is easy and simple to understand and calculate.

(b) It is more useful in case the data is of a qualitative nature.

(c) When instead of actual data, only ranks are given, it is the only method to determine correlation.

**Demerits :**

(a) This method can not be used in case of grouped frequency distribution.

(b) This method becomes tedious and time consuming when number of items exceed 30 .

(c) This method lacks accuracy as compared to Karl Pearson’s method as complete information related with the variable is not used.

**16. List some variables where accurate measurement is difficult. **

Ans: (a) Honesty

(b) Handsomeness

(c) Intelligence

(d) Beauty

(e) Aptitude

**17. Interpret the values of r as 1, -1and 0**

Ans: r = 1, means positive correlation, r = -1 means negative correlation and r=0, means no correlation coefficient among the variables .

**18. List some variables where accurate measurement is difficult . **

Ans: (a) Pearsonion method measures correlation for quantitative data whereas spearman rank correlation measures coefficient of correlation for qualitative data .

(b) Personion method uses deviations from actual or assumed mean but spearman’s method takes rank differences.

**19. Calculate the correlation coefficient between the heights of fathers in inches ( X ) and their sons ( Y ) **

X: | -3 | -2 | -1 | 1 | 2 | 3 |

Y: | 9 | 4 | 1 | 1 | 4 | 9 |

Ans : For calculation we make the following table :

We know that, the formula of correlation coefficient according to the product moment method is ―

**20. Calculate the correlation coefficient between X and Y and comment on the relationship**

X: | 1 | 3 | 4 | 5 | 7 | 8 |

Y: | 2 | 6 | 8 | 10 | 14 | 16 |

Ans: For calculation we make the following table :

Now, we know that formula of correlation coefficient according to deviations from assumed mean method is―

From the above results it can be concluded that there appears positive perfect correlation among the variables X and Y.

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