Correlation(11th Grade > Statistics ) Questions and answers for exam Preparation

11th Grade > Statistics

CORRELATION MCQs

Total Questions : 30 | Page 1 of 3 pages

Question 1.

Correlation implies causation. State true or false.

True
False

Discuss Question

Answer: Option B. -> False
:
B

Correlation does not imply causation. It only says the two factors are related somehow - not that change in one affects the others directly. For example, the sales of ice-cream and sales of air conditioners may both go up during the summer season. Hence, they are correlated but one is not the cause of the other. In certain cases, correlation may be because of a causal relationship (eg: poverty and malnutrition) but this is not always the case. It is very important to understand this distinction.

Question 2.

If the y value increases as the x value increases, the correlation is called ___ correlation.

Discuss Question

Answer: Option B. -> False
:

If the y value increases as the x value increases, the correlation is called positive correlation.

Question 3.

Which of the following scatter charts shows zero correlation?

Discuss Question

Answer: Option A. ->

:
A

For option A, there is no positive or negative correlation. The points are randomly scattered.

Question 4.

While representing a bivariate frequency distribution using a scatter chart, which of the following is correct?

the x-axis represents variables and the y-axis represents their frequencies
the y-axis represents variables and the x-axis represents their frequencies
The axes represent the two variables of the frequency distribution
The axes represent the frequency of the two variables.

Discuss Question

Answer: Option C. -> The axes represent the two variables of the frequency distribution
:
C

In a bivariate frequency distribution, there are two variables. In a scatter chart, the x-axis and y-axis contain the two variables of the frequency distribution.

Question 5.

For perfect positive correlation, the value of r = ___

Discuss Question

Answer: Option C. -> The axes represent the two variables of the frequency distribution
:

For perfect positive correlation, the value of r = 1.

Question 6.

Which of the following cannot be the value of a correlation coefficient?

-1
1
0.5
2

Discuss Question

Answer: Option D. -> 2
:
D

The correlation coefficient can take any value between (and including) -1 and 1. Hence, 2 cannot be a value of the correlation coefficient.

Question 7.

Identify the correct formula for calculating r using the step deviation method, where U and V are the step deviations of X and Y.

$r = \frac{N \sum (U_{i} V_{i}) - N (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$
$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$
$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{(N \sum U_{i}^{2} - (\sum U_{i})^{2}) (N \sum V_{i}^{2} - (\sum V_{i})^{2})}$
$r = \frac{N \sum (U_{i} V_{i}) - N (\sum U_{i}) (\sum V_{i})}{(N \sum U_{i}^{2} - (\sum U_{i})^{2}) (N \sum V_{i}^{2} - (\sum V_{i})^{2})}$

Discuss Question

Answer: Option B. ->

r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}

:
B

The shortcut formula for calculating r is
$r = \frac{N \sum (U_{i} V_{i}) - (\sum U_{i}) (\sum V_{i})}{\sqrt{N \sum U_{i}^{2} - (\sum U_{i})^{2}} \sqrt{N \sum V_{i}^{2} - (\sum V_{i})^{2}}}$

Question 8.

If the value of the simple correlation coefficient is zero, it means that there no relation whatsoever between the variables. State true or false.

True
False
0.5
2

Discuss Question

Answer: Option B. -> False
:
B

Karl Pearson's coefficient is used to measure correlation when the relationship between the variables is linear. Hence, zero correlation need not mean the absence of any type of relationship between the two variables. For example, for a relation of the form $Y = X^{2}$ , the correlation coefficient will be zero. The given statement is false.

Question 9.

What is the value of r when there is no linear correlation between two variables?

0
+1
-1
None of the above

Discuss Question

Answer: Option A. -> 0
:
A
When there is no linear correlation between two variables, r is 0.

Question 10.

Which of the following values of correlation coefficient indicates the strongest correlation?

-0.86
0.83
2
0.34

Discuss Question

Answer: Option A. -> -0.86
:
A
The value of the correlation coefficient lies between -1 and 1. Values closer to 1, irrespective of sign, indicate a stronger relationship, while the sign indicates the direction. From the given numbers, 0.86 is the closest number to 1 and hence has the strongest correlation.