Chapter 1- Introduction |
Chapter 2- Collection of Data |
Chapter 3- Organisation of Data |
Chapter 4- Presentation of Data |
Chapter 5- Measures of Central Tendency |
Chapter 6- Measures of Dispersion |
Chapter 8- Index Numbers |

The unit of correlation coefficient between height in feet and weight in kgs is

(i) kg/feet

(ii) percentage

(iii) non-existent

**Answer
1** :

As there is non-existent of correlation between the height in feet and weight in kilograms, so the unit of correlation between the two is zero.

The range of simple correlation coefficient is

(i) 0 to infinity

(ii) minus one to plus one

(iii) minus infinity to infinity

**Answer
2** :

The range of simple correlation coefficient is from (–) 1 to (+) 1

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 increases X does not change

**Answer
3** :

When the variables Y and X share positive relationship (i.e. when Y and X both increases simultaneously), then the value of r_{xy} is positive.

If r_{xy} = 0 the variable X and Y are

(i) linearly related

(ii) not linearly related

(iii) independent

**Answer
4** :

The value of r_{xy} becomes 0 when the two variables are not linearly related to each other. It may happen that both the variables may be non-linearly related to each other. It does not necessarily imply that both are independent of each other.

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

**Answer
5** :

Scatter diagram can measure any type of relationship whether the variables are highly related or not at all related. Just by looking at the diagram, the viewer can easily conclude the relationship between the two variables involved. On the other hand, Karl Pearson’s coefficient of correlation is not suitable for the series where deviations are calculated from assumed mean. Likewise, Spearman’s rank correlation also disqualifies to measure any kind of relationship as its domain is restricted only to the qualitative variables (leaving quantitative variables).

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

**Answer
6** :

Generally, all the properties of Karl Pearson’s coefficient of correlation are similar to that of the rank correlation coefficient. However, rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient. The reason for this difference between the two coefficients is because the rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information. If the precisely measured data are available, then both the coefficients will be identical.

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

**Answer
7** :

Although correlation coefficient is similar to the covariance in a manner that both measure the degree of linear relationship between two variables, but the former is generally preferred to covariance due to the following reasons.

1. The value of the correlation coefficient (r) lies between 0 and 1. Symbolically –1 ≤ r ≤ +1

2. The correlation coefficient is scale free.

Can r lie outside the –1 and 1 range depending on the type of data?

**Answer
8** :

No, the value of r cannot lie outside the range of –1 to 1. If r = – 1, then there exists perfect negative correlation and if r = 1, then there exists perfect positive correlation between the two variables. If at any point of time the calculated value of r is outside this range, then there must be some mistake committed in the calculation.

Does correlation imply causation?

**Answer
9** :

No, correlation does not imply causation. The correlation between the two variables does not imply that one variable causes the other. In other words, cause and effect relationship is not a prerequisite for the correlation. Correlation only measures the degree and intensity of the relationship between the two variables, but surely not the cause and effect relationship between them.

When is rank correlation more precise than simple correlation coefficient?

**Answer
10** :

Rank Correlation method is more precise than simple correlation coefficient when the variables cannot be measured quantitatively. In other words, rank correlation method measures the correlation between the two qualitative variables. These variable attributes are given the ranks on the basis of preferences. For example, selecting the best candidate in a dance competition depends on the ranks and preferences awarded to him/her by the judges. Secondly, the rank correlation method is preferred over the simple correlation coefficient when extreme values are present in the data. In such case using simple correlation coefficient may be misleading.

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