Question types

PART 1 : LINEAR CORRELATION question types

94 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.

94
Questions
6
Question groups
5
Question types
Sample Questions

PART 1 : LINEAR CORRELATION questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
What is the value of rank correlation coefficient if $n=10$ and $3 \Sigma d^2=495\ ?$
  • A
    $-1$
  • $0$
  • C
    $0.5$
  • D
    $1$

Answer: B.

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Q 2MCQ1 Mark
What is the value of rank correlation coefficient if the value of $n\left(n^2-1\right)$ is $12$ times $\Sigma d^2$ ?
  • A
    $-0.5$
  • B
    $-1$
  • $0.5$
  • D
    $1$

Answer: C.

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Q 3MCQ1 Mark
What is the value of $C F$ in the calculation of rank correlation coefficient, if one observation is repeated twice in series $X$, one observation is repeated thrice in series $Y$ and the rest of the observations come once ?
  • A
    $0.5$
  • B
    $2$
  • C
    $5$
  • $2.5$

Answer: D.

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Q 4MCQ1 Mark
What is the value of $\Sigma d$ if the ranks of two correlated variables $X$ and $Y$ are exactly in the reverse order?
  • A
    $1.1$
  • B
    $1$
  • $0$
  • D
    $-1$

Answer: C.

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Q 5MCQ1 Mark
What is the value of $r$ if the ranks of two correlated variables $X$ and $Y$ are same ?
  • A
    $-1$
  • B
    $0$
  • $1$
  • D
    $1.1$

Answer: C.

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Q 61 Marks Each1 Mark
If correlation coefficient between two variables $X$ and $Y$ is $0.64$, what is the correlation coefficient for $\left(2 X, \frac{Y}{3}\right)$ ? Why ?
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Q 71 Marks Each1 Mark
If correlation coefficient between two variables $X$ and $Y$ is $0.8$ then what is the correlation coefficient between $(50-X)$ and $Y$ ?
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Q 112 Marks Each2 Marks
For a sample data collected to know the relation between number of customers and sales $($thousand $₹)$ visiting a mall, the ranks are as follows.
Rank for number of customers $R_{(x)}$ $6$ $4.5$ $3$ $4.5$ $1$ $2$
Rank for sales
$($thousand $₹) R_{(y)}$
$4.5$ $4.5$ $2.5$ $6$ $1$ $2.5$

Calculate the rank correlation coefficient.
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Q 122 Marks Each2 Marks
For $9$ observations of a bivariate data, the sum of squares of differences in their ranks is $96 .$ Find the rank correlation coefficient.
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Q 142 Marks Each2 Marks
The coefficient of rank correlation between two related variables was found to be $0.5$. If the number of pairs of observations is $8 ,$ find sum of squares of differences of ranks.
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Q 163 Marks Each3 Marks
The coefficient of rank correlation between two related variables for $8$ pairs is $0.6$. Later on, it was found that one of the difference of ranks was taken as $-3$ instead of $5 .$ Find the correct rank correlation coefficient.
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Q 173 Marks Each3 Marks
Find Spearman's rank correlation coefficient from the following data of the time of usage of cars $($years$)$ and their annual maintenance expenditure $($thousand $₹ )$ for different models of a car manufacturing company.
Time of usage of cars $($years$) x$ $4$ $4.5$ $5$ $6.8$ $4.7$
Maintenance expenditure $($thousand $₹) y$ $3.5$ $3.5$ $3.5$ $3.5$ $3.5$
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Q 183 Marks Each3 Marks
A test of students is conducted to know the relation between the understanding of English $\operatorname{grammar}(X)$ and Gujarati grammar $(Y)$. The marks obtained in this test are as follows. Find rank correlation coefficient.
Marks of understanding English grammar $(x)$ $28$ $15$ $5$ $10$ $15$ $25$ $15$ $20$
Marks of understanding Gujaratigrammar $(y)$ $27$ $10$ $22$ $20$ $6$ $14$ $10$ $8$
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Q 193 Marks Each3 Marks
Ranks given by two judges to seven competitors $A , B , \ldots ., G$ in a patriotic song competition are as follows.
Find correlation coefficient.
Rank $1$ $2$ $3$ $4$ $5$ $6$ $7$
Judge $I$ $C$ $F$ $A$ $B$ $E$ $D$ $G$
Judge $II$ $B$ $D$ $F$ $A$ $C$ $E$ $G$
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Q 203 Marks Each3 Marks
Ranks given by two judges to ten competitors in a dance competition are as follows. Find Spearman's rank correlation coefficient.
Rank by judge $(I)$ $1$ $6$ $5$ $10$ $3$ $2$ $4$ $9$ $7$ $8$
Rank by judge$(II)$ $3$ $5$ $8$ $4$ $7$ $10$ $2$ $1$ $6$ $9$
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Q 214 Marks Each4 Marks
The information is obtained for $7$ students regarding their marks in Statistics $(X)$ and marks of Economics $(Y)$. The observations of the data were ranked. The sum of squares of differences of ranks was found to be $10.$ If two students got $48$ marks, two students got $40$ marks in Statistics and three students got $55$ marks in Economics, find the rank correlation coefficient.
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Q 224 Marks Each4 Marks
The marks obtained by $10$ students in a subject in $80$ marks written examination and $20$ marks oral examination of a university are as follows. Find the rank correlation coefficient.
Marks of written exam $50$ $55$ $55$ $60$ $65$ $65$ $65$ $60$ $60$ $50$
Marks of oral exam $11$ $13$ $14$ $16$ $16$ $15$ $15$ $14$ $13$ $13$
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Q 234 Marks Each4 Marks
The difference between the marks of the first test and the marks of the second test for a subject of standard $10$ and standard $12$ of six students are given below. Find Karl Pearson's correlation coefficient and write its interpretation.
Difference of Std $10$ marks $-12$ $-16$ $-8$ $16$ $12$ $8$
Difference of Std $12$ marks $-10$ $-6$ $-4$ $4$ $6$ $2$
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Q 244 Marks Each4 Marks
Find Karl Pearson's correlation coefficient from the information given below for imports $($in ten million $₹)$ and exports $($in ten million $₹)$ of last seven years in India.
Import $($ten million $₹)$ $18$ $19$ $20$ $21$ $22$ $23$ $24$
Export $($ten million $₹)$ $95$ $88$ $70$ $66$ $57$ $50$ $44$
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Q 254 Marks Each4 Marks
The following data is obtained while studying the height of father $($in cms$)$ and height of his adult son $($in cms$).$ Find the correlation coefficient.
Height of Father $(cm)$ $150$ $163$ $155$ $164$ $163$ $160$ $165$
Height of Son $(cm)$ $156$ $160$ $153$ $160$ $163$ $158$ $163$
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Q 265 Mark Each5 Marks
Find Spearman's correlation coefficient from the data given below for the temperature $\left({ }^{\circ} C \right)$ on a certain day of a month and number of tourists visiting on that day to various hill stations of a mountainous region and interpret it.
Weekly income $(100 ₹)$ $20$ $25$ $30$ $28$ $27$ $30$ $29$ $28$ $24$ $22$
Weekly expenditure $(00 ₹)$ $18$ $20$ $27$ $27$ $25$ $29$ $27$ $28$ $22$ $20$
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Q 275 Mark Each5 Marks
Find Spearman's correlation coefficient from the data given below for the weekly income $( 100 ₹)$ and weekly expenditure $( 100 ₹ ).$
Weekly income $(100 ₹)$ $20$ $25$ $30$ $28$ $27$ $30$ $29$ $28$ $24$ $22$
Weekly expenditure $(00 ₹)$ $18$ $20$ $27$ $27$ $25$ $29$ $27$ $28$ $22$ $20$
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Q 285 Mark Each5 Marks
The following information is obtained for two related variables $X$ and $Y$.
$n=6, \Sigma x=40, \Sigma y=58, \Sigma x^2=316, \Sigma y^2=606$ and $\Sigma x y=431$
Later on, it was found that one pair of observations was taken as $(10,13)$ instead of $(11,14)$ and one pair of observations $(9,11)$ was not taken. Find the correct correlation coefficient and interpret it.
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Q 295 Mark Each5 Marks
Find correlation coefficient from the data given below for the temperature $\left({ }^{\circ} C \right)$ on different days and the sale of woollen coats $($in pieces$)$ during a week of the month of December.
Temperature $(@)x$ $-4$ $-3$ $-2$ $0$ $1$ $3$ $5$
Sale of woollen coats $($pieces$) y$ $19$ $15$ $12$ $10$ $8$ $5$ $4$
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Q 305 Mark Each5 Marks
Find correlation coefficient from the data given below for the price $($in thousand $₹) X$ of different models of two wheelers and their annual sales $(100$ units$) Y$ of a company and also interpret it.
Price of vehicle
$($thousand $₹) x$
$60$ $58$ $70$ $75$ $65$ $80$ $63$
Annual sales $(100$ units$) y$ $4$ $3$ $10$ $12$ $8$ $18$ $7$
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