#### Chapters

## Chapter 5: Correlation

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

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 |

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 |

Find correlation coefficient between x and y series for the following data.

n = 15, `bar"x"` = 25, `bar"y"` = 18, σ_{x }= 3.01, σ_{y} = 3.03, `sum("x"_"i" - bar"x") ("y"_"i" - bar"y")` = 122

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.

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

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

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

x |
3 | 6 | 2 | 9 | 5 |

y |
4 | 5 | 8 | 6 | 7 |

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.

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

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.

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.

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.

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

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.

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 |

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 |

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

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

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

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

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

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

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

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

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 5 (Correlation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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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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