# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 5 - Correlation [Latest edition]

## Chapter 5: Correlation

Exercise 5.1Miscellaneous Exercise 5
Exercise 5.1 [Page 63]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 5 Correlation Exercise 5.1 [Page 63]

Exercise 5.1 | Q 1 | Page 63

Draw scatter diagram for the data given below and interpret it.

 x 10 20 30 40 50 60 70 y 32 20 24 36 40 28 38
Exercise 5.1 | Q 2 | Page 63

For the following data of marks of 7 students in physics (x) and Mathematics (y), draw scatter diagram and state the type of correlation.

 x 8 6 2 4 7 8 9 y 6 5 1 4 4 7 8
Exercise 5.1 | Q 3 | Page 63

Draw scatter diagram for the data given below. Is there any correlation between Aptitude score and Grade points?

 Aptitude score 40 50 55 60 70 80 Grade points 1.8 3.5 2.8 1.7 2.8 3.2
Exercise 5.1 | Q 4 | Page 63

Find correlation coefficient between x and y series for the following data.
n = 15, bar"x" = 25, bar"y" = 18, σx = 3.01, σy = 3.03, sum("x"_"i" - bar"x") ("y"_"i" - bar"y") = 122

Exercise 5.1 | Q 5 | Page 63

The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.

Exercise 5.1 | Q 6. (i) | Page 63

In the following data one of the value of y is missing. Arithmetic means of x and y series are 6 and 8 respectively. (sqrt(2) = 1.4142)

 x 6 2 10 4 8 y 9 11 ? 8 7

Estimate missing observation

Exercise 5.1 | Q 6. (ii) | Page 63

In the following data one of the value y of  is missing. Arithmetic means of x and y series are 6 and 8 respectively. (sqrt(2) = 1.4142)

 x 6 2 10 4 8 y 9 11 ? 8 7

Calculate the correlation coefficient

Exercise 5.1 | Q 7 | Page 63

Find correlation coefficient from the following data,["Given": sqrt(3) = 1.732]

 x 3 6 2 9 5 y 4 5 8 6 7
Exercise 5.1 | Q 8 | Page 63

Correlation coefficient between x and y is 0.3 and their covariance is 12. The variance of x is 9, Find the standard deviation of y.

Miscellaneous Exercise 5 [Pages 63 - 64]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 5 Correlation Miscellaneous Exercise 5 [Pages 63 - 64]

Miscellaneous Exercise 5 | Q 1 | Page 63

Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.

Miscellaneous Exercise 5 | Q 2 | Page 63

Find the number of pairs of observations from the following data,
r = 0.15, sigma_"y" = 4, sum("x"_"i" - bar"x")("y"_"i" - bar"y") = 12, sum("x"_"i" - bar"x")^2 = 40.

Miscellaneous Exercise 5 | Q 3 | Page 64

Given that r = 0.4, sigma_"y" = 3, sum("x"_"i" - bar"x")("y"_"i" - bar"y") = 108, sum("x"_"i" - bar"x")^2 = 900. Find the number of pairs of observations.

Miscellaneous Exercise 5 | Q 4 | Page 64

Given the following information, sum"x"_"i"^2 = 90, sum"x"_"i""y"_"i" = 60, r = 0.8, sigma_"y" = 2.5, where xi and yi are the deviations from their respective means, find the number of items.

Miscellaneous Exercise 5 | Q 5 | Page 64

A sample of 5 items is taken from the production of a firm. Length and weight of 5 items are given below. [Given : sqrt(0.8823) = 0.9393]

 Length (cm) 3 4 6 7 10 Weight (gm.) 9 11 14 15 16

Calculate the correlation coefficient between length and weight and interpret the result.

Miscellaneous Exercise 5 | Q 6 | Page 64

Calculate the correlation coefficient from the following data, and interpret it.

 X 1 3 5 7 9 11 13 Y 12 10 8 6 4 2 0
Miscellaneous Exercise 5 | Q 7 | Page 64

Calculate the correlation coefficient from the following data and interpret it.

 x 9 7 6 8 9 6 7 y 19 17 16 18 19 16 17
Miscellaneous Exercise 5 | Q 8. (i) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between 2x and y

Miscellaneous Exercise 5 | Q 8. (ii) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between "x"/2 and y

Miscellaneous Exercise 5 | Q 8. (iii) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x and 3y

Miscellaneous Exercise 5 | Q 8. (iv) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x – 5 and y – 3

Miscellaneous Exercise 5 | Q 8. (v) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between x + 7 and y + 9

Miscellaneous Exercise 5 | Q 8. (vi) | Page 64

If the correlation coefficient between x and y is 0.8, what is the correlation coefficient between ("x" - 5)/7 and ("y" - 3)/8?

Miscellaneous Exercise 5 | Q 9 | Page 64

In the calculation of the correlation coefficient between the height and weight of a group of students of a college, one investigator took the measurements in inches and pounds while the other investigator took the measurements in cm. and kg. Will they get the same value of the correlation coefficient or different values? Justify your answer.

## Chapter 5: Correlation

Exercise 5.1Miscellaneous Exercise 5

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 5 - Correlation

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 5 Correlation are Concept of Correlation, Concept of Covariance, Properties of Covariance, Concept of Correlation Coefficient, Scatter Diagram, Interpretation of Value of Correlation Coefficient.

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