1st PUC Economics Question Bank Chapter 7 Correlation

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Karnataka 1st PUC Economics Question Bank Chapter 7 Correlation

1st PUC Economics Correlation TextBook Questions and Answers

Question 1.
The unit of correlation coefficient between height in feet and weight in kgs is
Answer:

  1. kg / feet
  2. percentage
  3. non – existent.

Question 2.
The range of simple correlation coefficient is :
Answer:

  1. 0 to infinity
  2. Minus one to plus one
  3. Minus infinity to infinity

Question 3.
If rxy is positive, the relation between X and Y is of the type.
Answer:

  1. When Y increases, X increases
  2. When Y deceases, X increase
  3. When Y increases, X does not change.

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Question 4.
If r =0, the variable X and Y are
Answer:

  1. Linearly related
  2. Not linearly related
  3. Independent

Question 5.
Of the following three measures which can measure any type of relationship:
Answer:

  1. Karl Pearsons’s coefficient of correlation
  2. Spearman’s rank correlation
  3. Scatter diagram

Question 6.
If precisely measured data are available, the simple correlation coefficient is:
Answer:

  1. More-accurate than rank correlation coefficient.
  2. Less accurate than rank correlation coefficient.
  3. As accurate as the rank correlation coefficient.

Question 7.
Why is ‘r’ preferred to co-variance as a measure of association?
Answer:
‘r ’ is Perferred to co-variance as a measure of association because it studies and Measures the direction and intensity of relationship among variables.
It is due to the following reasons:

  1. The correlation co – efficient (r) has no unit.
  2. The correlation co – efficient is independent of origin as well as a scale

Question 8.
Can ‘r’ lie outside -1 and 1 range depending on the type of data?
Answer:
For any type of data, correlation (r) cannot lie outside the -1 and +1 range. The minimum limit of ‘r’ is -1 and +1 range. The minimum limit of ‘r’ is -1 and the maximum limit of r is +1. As a result, r can never lie outside these two limits. Symbolically.
-1 ≤ r ≥ 1
If in any exercise, ‘r’ is outside this range it indicates error in calculation.

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Question 9.
Does correlation imply causation?
Answer:
No, zero correlation does not imply causation. It implies co-variation. It should never be interpreted as implying causes and effect relation. Correlation studies and measures the direction and intensity of relationship among variable.

Question 10.
When is rank correlation more precise than simple correlation coefficient?
Answer:
Rank correlation is more precise than simple correlation when the variables cannot be measured meaningfully as in the case of prices, income, weight etc. Ranking may be more meaningful when the measurement of the variables are suspect. Ranking may be a better alternative to quantification of qualities.

Question 11.
Does zero correlation does not mean independence?
Answer:
No, zero correlation does not mean independence. If there is zero correlation, it means the two variables are not correlated and there is no linear relation between them. However, other types of relation may be there and they may be not independent.

Question 12.
Can simple correlation co – efficient measure any type of relationship?
Answer:
Simple correlation co-efficient cannot measure any type of relationship. It measures any type of relationship only between two variables. If the variables are more than two or we want to measure the correlation between the productivity of wheat, temperature, and quantity of rain, then simple correlation cannot measure this type of relationship. This type of relationship can be measured with the help of partial or multiple correlation co – efficient.

Question 13.
Collect the prices of five vegetables from your local market everyday for a week. Calculate their correlation co – efficient. Interprt the result. Name of vegetables and their prices (in Rs.)
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 1

r = 1 – \(\frac{6 \sum D^{2}}{N^{3}-N}\)

i. Correlation between potato and cabbage:
r = 1 – \(\frac{6 \times 51}{(343-7)}\) = 1 – \(\frac{306}{306}\) = 1 – 0.911 = 0.089

ii. Correlation between cabbage and tomato:
r = 1 – \(\frac{6 \times 36}{343-7}\) = 1 – \(\frac{216}{336}\) = 1 – 0.64 = 0.36

iii. Correlation between tomato and peas:
r = 1 – \(\frac{6 \times 37}{343-7}\) = 1 – \(\frac{222}{336}\) = 1 – 0.66 = 0.34

iv. Correlation between peas and carrot:
r = 1 – \(\frac{6 \times 29}{343-7}\) = 1 – \(\frac{174}{336}\) = 1 – 0.52 = 0.48

v. Correlation between peas and carrot:
r = 1 – \(\frac{6 \times 37}{343-7}\) = 1 – \(\frac{222}{336}\) = 1 – 0.66 = 0.34

vi. Correlation between carrot and potato:
r = 1 – \(\frac{6 \times 49}{343-7}\) = 1 – \(\frac{294}{336}\) = 1 – 0.875 = 0.13

Interpretation of Result:
It is clear from the above result that every vegetable is corre-lated. There is a positive correlation among these vegetables. Co-relation of peas and carrot is 0.48 which is highest and correlation of potato and cabbage is 0.089 which is lowest.

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Question 14.
Measure the height of your classmates. Ask them the height of their benchmate. Calculate the correlation coefficient of these two variables. Interpret the result.

1st PUC Economics Question Bank Chapter 7 Correlation image - 2
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 3
1st PUC Economics Question Bank Chapter 7 Correlation image - 4

r = 0.688 Ans
It is clear from the above analysis that there is a positive correlation between the asked height and measured height of the classmates.

Question 15.
Measure the hieght of your classmates. Ask them the height of their benchmate. Calculate the correlation coefficient of these two variables. Interpret the resuit.
Answer:
Impartiality, secularism, beauty, honesty, patriotism etc are some variables where accurate measurement is difficult.

Question 16.
Interpret the values of r as 1, -1, and 0.
Answer:

  1. r as 1 means that there is perfect positive relationship between two variables.
  2. r as -1 means that there is perfect negative relationship between two variables.
  3. r as 0 means that there is lack of correlation between two variables.

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Question 17.
Why does rank correlation co-efficient differ from Pearsonian correlation coefficient?
Answer:
Rank correlation co-efficient is more often used to measure the linear relationship between the qualitative variable whereas Karl Pearsn’s method of correlation co – efficient measures the linear relationship between the quantitative variables.

Question 18.
Calculate the correlation co – efficient between the heights of fathers in inches (X) and their sons (Y)
1st PUC Economics Question Bank Chapter 7 Correlation image - 34
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 6

Question 19.
Calculate the correlation co-efficient between X and Y and comment on their relationship.
1st PUC Economics Question Bank Chapter 7 Correlation image - 7
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 8
1st PUC Economics Question Bank Chapter 7 Correlation image - 9
Hence, r 0
Two values X and Y are un – correlated.
There is no linear correlation between them.

Question 20.
Calculate the correlation co-efficient between X and Y and comment on their relationship.
1st PUC Economics Question Bank Chapter 7 Correlation image - 35
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 11

1st PUC Economics Correlation Additional Questions and Answers

1st PUC Economics Correlation Very Short Answer Type Questions

Question 1.
Define Correlation?
Answer:
According to the Croxton and Cowden correlation is defined as “when the relationship is of a quantitative nature the appropriate statistical tool for discovering and measuring the relationship and expressing it in a brief formula is shown as correlation’’.

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Question 2.
What are the principal methods of calculating coefficient of correlation?
Answer:
The principal methods are as under:

  1. Scattered Diagram method
  2. Carl Pearson’s coefficient or correlation
  3. Spearman’s Rank correlation coefficient

Question 3.
What is the difference between positive and negative correlation?
Answer:
When two variables move in same direction such a relation is called positive correlation for example relationship between price and supply when two variable change in different direction it is called negative correlation for example relationship between price and demand.

Question 4.
State the kinds of correlation?
Answer:

  1. Positive and negative correlation
  2. Linear and non-linear correlation
  3. Simple and multiple correlation.

Question 5.
Coefficient of correlation is between -1 and +1. How would you express it arithmetically?
Answer:
-1 < r < +1

Question 6.
What is the nature of correlation of variables when they move in the same direction?
Answer:
Positive correlation.

Question 7.
What is the principal shortcoming of scattered diagram as a method of estimates correlation.
Answer:
A Scattered diagram does not measure the precise extent of correlation it give only an approximate idea of the relationship, it is not a quantitative measure of the relationship.

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Question 8.
When is rank correlation method used?
Answer:
Rank correlation method is used for the variable whose quantitative measurement is not possible such as beauty, bravery or wisdom.

Question 9.
What does correlation measure?
Answer:
Correlation measures the direction and intensity of relationship it measures covariation and not causation.

Question 10.
What does the presence of correlation between two variables X and Y simply mean?
Answer:
The presence of correlation between variables X and Y simply means that when value of one variables is found to change in one direction the value of other variables is  found to change either in the same direction or in the opposite direction but indefinite way.

Question 11.
Can ‘r’ lie outside -1 and +1 range depending on the type of data?
Answer:
No. ‘r ’ cannot lie outside -1 and +1 range depending on the types of data, it lies between minus one and plus one symbolically -1 if in any excercise ‘r ’ is outside this range it indicates error in calculation.

Question 12.
Does correlation imply causation?
Answer:
No correlation does not imply causation it implies covariation it should never be interpreted as implying causes and effect relation.

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Question 13.
When is Rank Correlation more precise than simple correlation coefficient?
Answer:
Rank Correlation is more precise than simple correlation when the variable cannot be measured meaningfully as in the case of price income weight etc ranking may be move meaningful when the measurement of the variable are suspect ranking may be a better alternative to quantification qualities.

Question 14.
When is Rank correlation preffered to Person’s co-efficient?
Answer:
Rank correlation is preffered to Person’s coefficient when extreme values are present.

Question 15.
What is the relationship between r and in general?
Answer:
In general  \({ r }_{ \swarrow }\)≤ r

Question 16.
What is the limitation of spearman rank correlation?
Answer:
Spearman’s rank correlation is not as accurate as the ordinary method this is due to fact that all the information concerning the data is not utilised.

Question 17.
When do r and rk give identical results?
Answer:
v and vk give identical results when the first difference of the values of the items in the series of arranged in the order or magnitude are constant.

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Question 18.
In which situation is the use of rank correlation method suitable?
Answer:
The use of rank correlation is suitable when data cannot be directly quantitatively measured.

Question 19.
Which type of correlation is indicated by the values of X and Y variables.
1st PUC Economics Question Bank Chapter 7 Correlation image - 12
Answer:
Here r = + 1 as values of X and variables move in the same direction.

Question 20.
Under what situation is r = -1.
Answer:
r = -1 when the values of two variables X and Y move in the opposite directions.

Question 21.
When is the correlation called linear?
Answer:
When the change ratio in values of the two variables is constant.

Question 22.
If a change in a variable does not bring about change in the other variable in the same relation there will be what kind of correlation between them.
Answer:
Non-linear correlation.

Question 23.
Where does correlation between two variables concentrate?
Answer:
Correlation between two variables concentrate between + 1 and – 1.

Question 24.
What do you mean by absence of correlation?
Answer:
By absence of correlation we mean that there is no relationship between the values of series, in this case, r = 0.

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Question 25.
Which type of correlation is indicated by the following scatter diagram?
Answer:
The scattered diagram given in the question indicate the positive relation.
1st PUC Economics Question Bank Chapter 7 Correlation image - 13

Question 26.
Which type of correlation between two variables is indicated by a scatter line sloping downward to right?
Answer:
Negative relation between two variables.

Question 27.
Which type of correlation is indicated by the values of X and Y variables?
1st PUC Economics Question Bank Chapter 7 Correlation image - 14
Answer:
Here r = – 1 because the value of x and y variables move in the opposite direction.

Question 28.
What does a high value of ‘r’ indicate?
Answer:
A high value of ‘r ’ indicates linear relationship. If value is said to be high when it is close to +1 or -1.

Question 29.
Give anyone property of correlation coefficient? (r)
Answer:
The value of ‘r’ is unaffected by the change of origin and change of scale.

Question 30.
What does a low value of ‘r’ indicate?
Answer:
A low value of ‘r ’ indicates a weak linear relation its value is said to be low when it is close to zero.

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Question 31.
Give the formula of ranking coefficient of correlation of spearman.
Answer:
\(\mathrm{V}_{\mathrm{k}}=1-\frac{6 \sum \mathrm{D}^{2}}{\mathrm{n}\left(\mathrm{n}^{2}-\mathrm{n}\right)}\)

Question 32.
If the points in a scatter diagram tend to cluster about a straight line which makes an angle of 30 with the X axis what would you say about the strength of association between X and Y?
Answer:
It shows less than proportionate change of there exists a low degree of association between X and Y.

Question 33.
Correlation remains always between -1 and +1 how is it expressed in mathematical language?
Answer:
-1 ≤ r ≤ + 1

Question 34.
Why is ‘r’ preferred to co-variance as a measure of association?
Answer:
‘r ’ is preffered to co-variance as a measure of association because it studies and mean some the direction and intensity of relationship among variables.

Question 35.
Does zero correlation mean independence?
Answer:
No, but there is possibility o independence.

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Question 36.
Can simple correlation co-efficient measure any type of relationship?
Answer:
No.

Question 37.
Collect the price of five vegetable from your local market every day for a week. Calculate their correlation co – efficient interpret the result?
Answer:
Students are supposed of collect the price of any five vegetables from the market over a week. Then they should calculate their correlation of co – efficients.

Question 38.
List some Variables, Where accurate measure is difficult?
Answer:
Impartiality is secular is unbeauty, honesty, Patritism etc -are some variable where accurate measurement is difficult.

Question 39.
Interpret the values of V as 1,-1 and 0.
Answer:

  1. r as 1 means that it is perfect positive relationship between two variables.
  2. r as -1 means that there is perfect negative relationship between two variables.
  3. r as O means that there is Lack of correlation between two variables.

Question 40.
Why does rank correlation co – efficient differ from Pearsonian correlation co-efficient.
Answer:
Because rank correlation co-efficient provider & measure of time association between ranks to these limits and not their values.

1st PUC Economics Correlation Short Answer Type Questions

Question 1.
Give the definition of correlation give the meaning of following. r = 0, r = +1, r = -1.
Answer:
According to Croxton and Cowden, ‘when the relationship is of a quantitative nature the appropriate statistical tool for discovering and the measuring the relationship and expressing it in a brief formula is known as statistics.

  1. When r = 0, It implies that there exists no relationship between two variables X and Y in other ways r = 0 shows the absence of relationship.
  2. r = 1, Shows that there is perfect correlation between two variables X and Y.
  3. r = -1, Shows that there is perfect negative relationship between two variables X and Y.

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Question 2.
Give the value of correlation under following position.

  1. Perfect correlation and negative
  2. Perfect correlation and positive
  3. No correlation.

Answer:

  1. When correlation is perfect and negative than the value of r = -1.
  2. When correlation is perfect and positive than the value of r = +1
  3. When there is no correlation then the value of r = 0.

Question 3.
Define positive and negative correlation with examples?
Answer:
1. Positive correlation:
When two variables move in the same direction that is when one increases the other also increases and when one decreases the other also decreases, such a relationship is called positive correlation for example the relation between price and supply.
Increase in the value of both variables:
1st PUC Economics Question Bank Chapter 7 Correlation image - 15

2. Negative correlation:
When two variables change in different direction, it is called negative correlation for example relationship between price and demand when prices rise other things remaining constant, demand falls and when price falls demand rises.
1st PUC Economics Question Bank Chapter 7 Correlation image - 16

Question 4.
What is perfect correlation give two examples?
Answer:
Perfect correlation is that when changes in two related variables are exactly proportional It is of two types.

  1. Positive perfect correlation and
  2. Negative perfect correlation

There is perfect positive correlation between the two variables if equal proportional changes are the same direction. It is expressed as +1. If equal proportional changes are in the reverse direction then there is negative perfect correlation and it is described as -1.

a. Example of positive perfect correlation
1st PUC Economics Question Bank Chapter 7 Correlation image - 17
b. Example of perfect negative correlation
1st PUC Economics Question Bank Chapter 7 Correlation image - 18

Question 5.
Define simple and Partial correlation.
Answer:
1. Simple correlation:
When the relationship between two variables is studied and if these are is dependent then such correlation is called simple correlation. For example relationship between income and expenditure.

2. Partial correlation:
When more than two variables are involved and out of these the relationship between two variables is studied only treating other variables as constant, then such correlation is partial.

1st PUC Economics Correlation Long Answer Type Questions

Question 1.
Calculate r with the help of following data.
1st PUC Economics Question Bank Chapter 7 Correlation image - 19
Answer:
Calculation of r between schooling of farmers and annual yields.
1st PUC Economics Question Bank Chapter 7 Correlation image - 20

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Question 2.
What steps are involved in the procedure calculating Karl Pearson’s coefficient of correlation by the direct method?
Answer:
Steps involved in the procedure of calculation of Karl Pearson’s coefficient by direct method.

  1. Calculate mean value X and Y
  2. Calculate deviations of values of X series from mean value
  3. Square the deviations.
  4. Calculate deviation of values of Y series from mean value
  5. Square the deviation
  6. Multiply the square of deviation of X series with the square of deviations of Y series

Use the following formula for calculating correlation coefficient

\(\mathrm{r}=\frac{\sum \mathrm{XY}}{\sqrt{\mathrm{x}^{2}} \sqrt{\mathrm{y}^{2}}}\)
\(\mathrm{r}=\frac{\sum \mathrm{XY}}{\sigma \mathrm{x} \times \sigma \mathrm{y}}\)

σ x = S. D of X series
σ y = S. D of Y series

Question 3.
Calculate the height and weight of the student of a class.
1st PUC Economics Question Bank Chapter 7 Correlation image - 21
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 22
1st PUC Economics Question Bank Chapter 7 Correlation image - 23

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Question 4.
Calculate Karl Pearson’s co-efficient of correlation the help of following data?
1st PUC Economics Question Bank Chapter 7 Correlation image - 24
Answer:
Calculation of Pearson’s co – efficient of correlation X Series \(\overline{\mathrm{x}}\) = 18, Y series
\(\bar{y}=\) = 19.
1st PUC Economics Question Bank Chapter 7 Correlation image - 25

Question 5.
Calculation of Karl Peasson’s correlation co – efficient.
1st PUC Economics Question Bank Chapter 7 Correlation image - 26
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 27
= \(\frac{1720}{1790.81}\) = 0.96

Question 6.
Calculate Karl Peasson’s co-efficient from the following data
1st PUC Economics Question Bank Chapter 7 Correlation image - 28
Answer:
Calculation of Karl Peasson’s correlation co – efficient.
1st PUC Economics Question Bank Chapter 7 Correlation image - 29

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Question 7.
Calculate correlation between the two variables.
1st PUC Economics Question Bank Chapter 7 Correlation image - 30
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 31

Question 8.
Calculate the co-efficient of raqnic correlation from the following data:
1st PUC Economics Question Bank Chapter 7 Correlation image - 32
Answer:
1st PUC Economics Question Bank Chapter 7 Correlation image - 33

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