Question 1

Q1: The unit of correlation coefficient between height in feet and weight in kgs is (i) kg/feet (ii) percentage (iii) non-existent

Accepted Answer

The correct answer is (iii) non-existent. As explained in the chapter, the correlation coefficient (r) is a pure number and has no unit of measurement. It measures the degree and direction of the linear relationship between two variables, regardless of the units in which the variables themselves are...

Question 2

Q10: When is rank correlation more precise than simple correlation coefficient?

Accepted Answer

The term "more precise" can be interpreted as more appropriate or reliable in certain situations. According to the chapter, Spearman's rank correlation coefficient is preferred over the simple (Karl Pearson's) correlation coefficient in the following cases:    Qualitative Data: When dealing with att...

Question 3

Q11: Does zero correlation mean independence?

Accepted Answer

No, a zero correlation does not necessarily mean the variables are independent. A correlation coefficient (r) of zero specifically indicates that there is no linear relationship between the two variables. However, as the chapter mentions, there might still be a strong non-linear relationship. For ex...

Question 4

Q12: Can simple correlation coefficient measure any type of relationship?

Accepted Answer

No, the simple (Karl Pearson's) correlation coefficient cannot measure any type of relationship. It is designed specifically to measure the strength and direction of only a linear relationship between two variables. The chapter advises that it is important to first examine a scatter diagram to see i...

Question 5

Q13: Collect the price of five vegetables from your local market every day for a week. Calculate their correlation coefficients. Interpret the result.

Accepted Answer

This is a practical activity. The steps to complete it are as follows: 1.  Data Collection: Visit a local market for seven consecutive days. Each day, record the price per kg of five different vegetables (e.g., tomatoes, potatoes, onions, carrots, bell peppers). 2.  Data Tabulation: Create a table w...

Question 6

Q14: Measure the height of your classmates. Ask them the height of their benchmate. Calculate the correlation coefficient of these two variables. Interpret...

Accepted Answer

This is a practical activity involving data collection and analysis. 1.  Data Collection: Create two lists. List X will be the height of each student in your class. List Y will be the height of their corresponding benchmate. 2.  Tabulation: Create a table with two columns, one for student height (X)...

Question 7

Q15: List some variables where accurate measurement is difficult.

Accepted Answer

The chapter provides several examples of variables, particularly attributes, where accurate numerical measurement is difficult or impossible. These variables are better suited for ranking. Some examples include:    Honesty: This is a personal trait that cannot be assigned a precise numerical value....

Question 8

Q16: Interpret the values of r as 1, -1 and 0.

Accepted Answer

The values of the correlation coefficient (r) are interpreted as follows:    r = 1: This indicates a perfect positive linear correlation. It means that the two variables have an exact linear relationship, and they move in the same direction. When one variable increases, the other increases by a perf...

Question 9

Q17: Why does rank correlation coefficient differ from Pearsonian correlation coefficient?

Accepted Answer

Spearman's rank correlation coefficient differs from Pearsonian (simple) correlation coefficient primarily because they use different inputs from the data: 1.  Use of Ranks vs. Actual Values: Pearson's coefficient is calculated using the actual numerical values of the variables. In contrast, Spearma...

Question 10

Q18: Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y) X 65 66 57 67 68 69 70 72 Y 67 56 65 68 72 72 69...

Accepted Answer

To calculate the Karl Pearson's correlation coefficient (r), we will construct a table to find the necessary sums. | X | Y | X² | Y² | XY | |---|---|---|---|---| | 65 | 67 | 4225 | 4489 | 4355 | | 66 | 56 | 4356 | 3136 | 3696 | | 57 | 65 | 3249 | 4225 | 3705 | | 67 | 68 | 4489 | 4624 | 4556 | | 68 |...

Question 11

Q19: Calculate the correlation coefficient between X and Y and comment on their relationship: X -3 -2 -1 1 2 3 Y 9 4 1 1 4 9 (Ans. r = 0)

Accepted Answer

To calculate the correlation coefficient, we first find the required sums. | X | Y | X² | Y² | XY | |---|---|---|---|---| | -3 | 9 | 9 | 81 | -27 | | -2 | 4 | 4 | 16 | -8 | | -1 | 1 | 1 | 1 | -1 | | 1 | 1 | 1 | 1 | 1 | | 2 | 4 | 4 | 16 | 8 | | 3 | 9 | 9 | 81 | 27 | | ΣX=0 | ΣY=28 | ΣX²=28 | ΣY²=196...

Question 12

Q2: The range of simple correlation coefficient is (i) 0 to infinity (ii) minus one to plus one (iii) minus infinity to infinity

Accepted Answer

The correct answer is (ii) minus one to plus one. The chapter states that one of the properties of the correlation coefficient is that its value always lies between -1 and +1, inclusive. This can be represented as -1 ≤ r ≤ 1.

Question 13

Q20: Calculate the correlation coefficient between X and Y and comment on their relationship X 1 3 4 5 7 8 Y 2 6 8 10 14 16 (Ans. r = 1)

Accepted Answer

To calculate the correlation coefficient, we construct a table for the required sums. | X | Y | X² | Y² | XY | |---|---|---|---|---| | 1 | 2 | 1 | 4 | 2 | | 3 | 6 | 9 | 36 | 18 | | 4 | 8 | 16 | 64 | 32 | | 5 | 10 | 25 | 100 | 50 | | 7 | 14 | 49 | 196 | 98 | | 8 | 16 | 64 | 256 | 128 | | ΣX=28 | ΣY=5...

Question 14

Q3: If r_xy 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 increa...

Accepted Answer

The correct answer is (i) When Y increases X increases. A positive correlation coefficient (r > 0) indicates that the two variables move in the same direction. This means that an increase in one variable is associated with an increase in the other, and a decrease in one is associated with a decrease...

Question 15

Q4: If r_xy = 0 the variable X and Y are (i) linearly related (ii) not linearly related (iii) independent

Accepted Answer

The correct answer is (ii) not linearly related. As stated in the chapter, if r = 0, it means the two variables are uncorrelated, which signifies the absence of a linear relationship between them. However, it does not rule out the possibility of a non-linear relationship, so they are not necessarily...

Question 16

Q5: Of the following three measures which can measure any type of relationship (i) Karl Pearson's coefficient of correlation (ii) Spearman's rank correlat...

Accepted Answer

The correct answer is (iii) Scatter diagram. The chapter explains that a scatter diagram is a visual tool that can present the form of any relationship, whether it is linear or non-linear. In contrast, both Karl Pearson's coefficient and Spearman's rank correlation are designed to measure the streng...

Question 17

Q6: If precisely measured data are available the simple correlation coefficient is (i) more accurate than rank correlation coefficient (ii) less accurate...

Accepted Answer

The correct answer is (i) more accurate than rank correlation coefficient. The chapter suggests that Spearman's rank correlation is used when precise measurements are not possible (e.g., for attributes like honesty) or when data contains extreme values. The simple (Karl Pearson's) correlation coeffi...

Question 18

Q7: Why is r preferred to covariance as a measure of association?

Accepted Answer

The correlation coefficient (r) is preferred to covariance as a measure of association for two main reasons: 1.  Standardized Value: The value of 'r' is standardized and lies within a fixed range of -1 to +1. This makes it easy to interpret the strength of the relationship. A value close to 1 or -1...

Question 19

Q8: Can r lie outside the -1 and 1 range depending on the type of data?

Accepted Answer

No, the correlation coefficient (r) cannot lie outside the -1 and 1 range, regardless of the type of data. The chapter explicitly states as a property of the correlation coefficient: "The value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If, in any exercise, the v...

Question 20

Q9: Does correlation imply causation?

Accepted Answer

No, correlation does not imply causation. The chapter strongly emphasizes this point, stating, "Correlation measures covariation, not causation. Correlation should never be interpreted as implying cause and effect relation." The presence of a correlation between two variables simply means that they...

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