Calculate ρ X , Y for the following data and comment on the result: X - 4 - 3 - 2 - 1 1 2 3 4 Y 16 9 4 1 1 4 9 16

Construct the table as per the given data X Y X 2 Y 2 X Y - 4 16 16 256 - 64 - 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 4 16 16 256 64 ∑ X = 0 ∑ Y = 60 ∑ X 2 = 60 ∑ Y 2 = 708 ∑ X Y = 0 N = 8 Coefficient of correlation r or ρ X , Y = ∑ X Y − 1 N ∑ X ∑ Y ∑ X 2 − 1 N ∑ X 2 ∑ Y 2 − 1 N ( ∑ Y ) 2 ⇒ r = 0 - 1 8 0 × 60 60 - 1 8 0 2 708 - 1 8 60 2 = 0 It shows that no linear relationship, though we see Y = X 2 .

Calculate the coefficient of correlation between income and weight: Income ( ₹ ) 100 200 300 400 500 600 Weight(lbs) 120 130 140 150 160 170

X Y X 2 Y 2 X Y 100 120 10000 14400 12000 200 130 40000 16900 26000 300 140 90000 19600 42000 400 150 160000 22500 60000 500 160 250000 25600 80000 600 170 360000 28900 102000 ∑ X = 2100 ∑ Y = 870 ∑ X 2 = 910000 ∑ Y 2 = 127900 ∑ X Y = 322000 N = 6 Coefficient of correlation r = ∑ X Y − 1 N ∑ X ∑ Y ∑ X 2 − 1 N ∑ X 2 ∑ Y 2 − 1 N ( ∑ Y ) 2 = 322000 - 1 6 2100 × 870 910000 - 1 6 2100 2 127900 - 1 6 870 2 = 17500 50 70 × 5 70 = 1 It shows perfect positive correlation.

M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST

Attempt the practice questions on Chapter 2: Correlation Analysis, Exercise 4: CHAPTER TEST with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 2 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST with Hints & Solutions

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 1

Calculate the coefficient of correlation for the ages of husbands and wives(up to three decimals):

Age of husband	$23$	$27$	$28$	$28$	$29$	$30$	$31$	$33$	$35$	$36$
Age of wife	$18$	$20$	$22$	$27$	$21$	$22$	$27$	$29$	$28$	$29$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 2

Calculate $ρ (X, Y)$ for the following data and comment on the result:

$X$	$- 4$	$- 3$	$- 2$	$- 1$	$1$	$2$	$3$	$4$
$Y$	$16$	$9$	$4$	$1$	$1$	$4$	$9$	$16$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 3

Calculate Karl Pearson's Coefficient of Correlation between $X$ and $Y$ from the following data and comment on the result:

$X$	$1$	$2$	$3$	$4$	$5$
$Y$	$7$	$6$	$5$	$4$	$3$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 4

Calculate the coefficient of correlation between income and weight:

Income $(₹)$	$100$	$200$	$300$	$400$	$500$	$600$
Weight(lbs)	$120$	$130$	$140$	$150$	$160$	$170$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 5

An examination of eight applicants for a clerical post was taken by a firm. The marks obtained by the applicants in Accountancy and Statistics papers are given below:

Applicant	$A$	$B$	$C$	$D$	$E$	$F$	$G$	$H$
Marks in Accountancy	$15$	$20$	$28$	$12$	$40$	$60$	$20$	$80$
Marks in Statistics	$40$	$30$	$50$	$30$	$20$	$10$	$30$	$60$

Calculate Spearman's coefficient of rank correlation.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 6

The following table gives the result of heights of 8 athletes and the measurements of their long jumps and high jumps (all in centimeters). Calculate the Spearman's rank correlation between height and long jump and between height and high jump. Interpret the result.

Athlete	Height	Long jump	High jump
$A$	$158$	$324$	$175$
$B$	$165$	$365$	$185$
$C$	$162$	$380$	$180$
$D$	$170$	$400$	$184$
$E$	$175$	$350$	$200$
$F$	$163$	$350$	$172$
$G$	$178$	$425$	$188$
$H$	$164$	$375$	$180$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 7

The marks of $8$ students in an examination in mathematics and statistics given below:

Student no.	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Marks in Mathematics	$70$	$48$	$58$	$55$	$54$	$50$	$60$	$52$
Marks in Statistics	$62$	$47$	$53$	$60$	$55$	$68$	$51$	$48$

Calculate Spearman's coefficient of rank correlation(up to two decimals).

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 2 - Correlation Analysis>CHAPTER TEST>Q 8

A psychologist selected a random sample of $22$ students. He grouped them in $11$ pairs so that students in a pair have nearly equal scores in an intelligent test. In each pair one student was taught by method $A$ and the other by method $B$ and examined after the course. The marks obtained by them after the course are as follows:

Pairs	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
Method $A$	$24$	$29$	$19$	$14$	$30$	$19$	$27$	$30$	$20$	$28$	$11$
Method $B$	$37$	$35$	$16$	$26$	$23$	$27$	$19$	$20$	$16$	$11$	$21$

Calculate spearman's rank correlation coefficient(three places after decimal)?

M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST

Questions from M L Aggarwal Solutions for Chapter: Correlation Analysis, Exercise 4: CHAPTER TEST with Hints & Solutions

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