# Free Correlation 01 Practice Test - 11th Grade - Commerce

### Question 1

Observe the scatter plot and identify the type of correlation.

Positive correlation

Negative correlation

Zero correlation

None of these

#### SOLUTION

Solution :B

Here, Y decreases with an increase in X. Hence the correlation is negative.

### Question 2

Select the options that are likely to show a negative correlation.

Price of a product and its sales

Monthly average rainfall and umbrella sales

Percentage body fat and number of hours of exercise

Marks scored in an exam and the number of hours spent studying

#### SOLUTION

Solution :A and C

As the price of a product increases, people are less likely to buy it. Greater the number of hours spent exercising, greater will be the reduction in percentage body fat. These two examples show a negative correlation.

### Question 3

A strong correlation between the dependent and the independent variable suggests that the change in the independent variable is caused by the change in the dependent variable. State true or false.

True

False

#### SOLUTION

Solution :B

Correlation does not imply causation. Even if the independent variable and the dependent variable are interchanged, the correlation remains the same. Hence, the statement is false.

### Question 4

Use the line of best fit to predict the approximate value of y when x is equal to 10.

20

30

40

50

#### SOLUTION

Solution :B

Draw a line parallel to the y-axis through x=10 to intersect the line of best fit. Through this point, draw a line parallel to the x-axis to intersect the y-axis. It can be seen that this line cuts y-axis near 30. Hence the approximate value of y corresponding to x=10 is 30.

### Question 5

Calculate the correlation coefficient for the following data.

XY243649510611713817

0.878

0.925

0.965

0.982

#### SOLUTION

Solution :D

xyx−¯x(x−¯x)2(y−¯y)(y−¯y)2(x−¯x)(y−¯y)24−39−6361836−24−416849−11−1115100000061111111713243968173974921∑=28∑=112∑=55

¯x=∑xn=357=5

¯y=∑yn=707=10r=∑ni=1(xi−¯x)(yi−¯y)√∑ni=1(xi−¯x)2√∑ni=1(yi−¯y)2=55√28×112=5556=0.982

### Question 6

Spearman's rank coefficient is used to understand the correlation between variables which can be clearly quantified. State true or false.

True

False

#### SOLUTION

Solution :B

False. Spearman’s Rank coefficient helps us understand the correlation between the variables which can’t be very meaningful and predominantly subjective. It is generally used to find the correlation in case of qualitative variables.

### Question 7

The ages and weights of 5 children are given below. Calculate covariance.

Age, X)Weight, Y720925113613411548

14.6

22.7

28.8

36

#### SOLUTION

Solution :C

XYX−¯XY−¯Y(X−¯X)(Y−¯Y)720−4−1456925−2−918113602013412714154841456∑=144

¯X=∑XN=555=11

¯Y=∑YN=1705=34Cov(X,Y)=(X−¯X)(Y−¯Y)N=1445=28.8

### Question 8

The number of hours spent studying and percentage marks for 5 students are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

No. of hours%Marks375485580682788

0.685

0.735

0.825

0.935

#### SOLUTION

Solution :B

XiYiX2iY2iXiYi37595625225485167225340580256400400682366724492788497744616∑=25∑=410∑=135∑=33718∑=2073

r=N∑ni=1(XiYi)–(∑ni=1Xi)(∑ni=1Yi)√N∑ni=1X2i–(∑ni=1Xi)2√N∑ni=1Y2i–(∑ni=1Yi)2=1157.07×22.14=0.735

### Question 9

The quantity of goods produced and costs incurred by a firm are tabulated below. Find the correlation coefficient using Karl Pearson's formula.

Quantity producedTotal cost1012020230303154042550510

0.85

0.93

0.97

0.99

#### SOLUTION

Solution :D

XiYiX2iY2iXiYi1012010014400120020230400529004600303159009922594504042516001806251700050510250026010025500∑=150∑=1600∑=5500∑=607250∑=57750

r=N∑ni=1(XiYi)–(∑ni=1Xi)(∑ni=1Yi)√N∑ni=1X2i–(∑ni=1Xi)2√N∑ni=1Y2i–(∑ni=1Yi)2=4875070.71×690.11=0.999

### Question 10

Spearman's rank coefficient can be used to answer the question:

Does the number of symptoms a patient has indicate a higher severity of illness?

#### SOLUTION

Solution :B

Spearman's rank coefficient helps to understand the type of correlation by looking at non-linear ranked data. Hence this question can be answered using the same.