###### Advertisements

###### Advertisements

Following tale gives income (X) and expenditure (Y) of 25 families:

Y/X |
200 – 300 |
300 – 400 |
400 – 500 |

200 – 300 |
IIII I | IIII I | I |

300 – 400 |
– | IIII | IIII I |

400 – 500 |
– | – | II |

Find How many families have their income Rs. 300 and more and expenses Rs. 400 and less?

###### Advertisements

#### Solution

Bivariate frequency distribution table for Income (X) and Expenditure (Y) is as follows:

Y/X |
200 – 300 |
300 – 400 |
400 – 500 |
Total (f_{y}) |

200 – 300 |
6 | 6 | 1 | 13 |

300 – 400 |
0 | 4 | 6 | 10 |

400 – 500 |
0 | 0 | 2 | 2 |

Total (f_{x}) |
6 | 10 | 9 | 25 |

The cells 300 – 400 and 400 – 500 are having income ₹ 300 and more and the cells 200 – 300 and 300 – 400 are having expenditure ₹ 400 and less. Now, the following table indicates the number of families satisfying the above condition.

Y/X |
300 – 400 |
400 – 500 |
Total |

200 – 300 |
6 | 1 | 7 |

300 – 400 |
4 | 6 | 10 |

Total |
10 | 7 | 17 |

∴ There are 17 families with income ₹ 300 and more and expenditure ₹ 400 and less.

#### APPEARS IN

#### RELATED QUESTIONS

A bakerman sells 5 types of cakes. Profits due to the sale of each type of cake is respectively Rs. 3, Rs. 2.5, Rs. 2, Rs. 1.5, Rs. 1. The demands for these cakes are 10%, 5%, 25%, 45% and 15% respectively. What is the expected profit per cake?

For the bivariate data r = 0.3, cov(X, Y) = 18, σ_{x} = 3, find σ_{y} .

Given that X~ B(n = 10, p), if E(X) = 8. find the value of p.

In a bivariate data, n = 10, `bar x` = 25, `bary` = 30 and `sum xy` = 7900. Find cov(X,Y)

If `Σd_i^2` = 25, n = 6 find rank correlation coefficient where d_{i}, is the difference between the ranks of i^{th} values.

The following table gives the ages of husbands and wives

Age of wives (in years) |
Age of husbands (in years) | |||

20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | |

15 - 25 | 5 | 9 | 3 | - |

25-35 | - | 10 | 25 | 2 |

35-45 | - | 1 | 12 | 2 |

45-55 | - | - | 4 | 16 |

55-65 | - | - | - | 4 |

Find : (i) The marginal frequency distribution of the age of husbands.

(ii) The conditional frequency distribution of the age of husbands when the age of wives lies between

25 - 35.

If the correlation coefficient between X and Y is 0.8, what is the correlation

coefficient between.

(a) X and 3Y

(b) X - 5 and Y - 3

The price P for demand D is given as P = 183 + 120D - 3D^{2}. Find d for which the price is increasing.

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 - 5"/7` and `"Y - 3"/8`

For a bivariate data b_{yx} = -1.2 and b_{xy} = -0.3. Find the correlation coefficient between x and y.

If for a bivariate data `barx = 10, bary = 12, V(X) = 9, σ_y = 4` and r = 0.6, estimate y when x = 5.

Two dice are thrown simultaneously 25 times. The following price of observation are obtained.

(2, 3) (2, 5) (5, 5) (4, 5) (6, 4) (3, 2) (5, 2) (4, 1) (2, 5) (6, 1) (3, 1) (3, 3) (4, 3) (4, 5) (2, 5) (3, 4) (2, 5) (3, 4) (2, 5) (4, 3) (5, 2) (4, 5) (4, 3) (2, 3) (4, 1)

Prepare a bivariate frequency distribution table for the above data. Also, obtain the marginal distributions.

Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.

X |
27 | 25 | 28 | 26 | 29 | 27 | 28 | 26 | 25 | 25 | 27 |

Y |
21 | 20 | 20 | 21 | 23 | 22 | 20 | 20 | 19 | 19 | 23 |

X |
26 | 29 | 25 | 27 | 26 | 25 | 28 | 25 | 27 | 26 | |

Y |
19 | 23 | 23 | 22 | 21 | 20 | 22 | 23 | 22 | 21 |

Find conditional frequency distribution of age of husbands when the age of wife is 23 years.

Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).

Marks inStatistics(X) |
37 | 20 | 46 | 28 | 35 | 26 | 41 | 48 | 32 | 23 | 20 | 39 | 47 | 33 | 27 | 26 |

Marks inEnglish(Y) |
30 | 32 | 41 | 33 | 29 | 43 | 30 | 21 | 44 | 38 | 47 | 24 | 32 | 21 | 20 | 21 |

Construct a bivariate frequency distribution table for the above data by taking class intervals 20 – 30, 30 – 40, ...... etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between 30 – 40.

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.

(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)

Construct a bivariate frequency distribution table for the above data by taking classes 115 – 125, 125 –135, ....etc. for sales and 60 – 62, 62 – 64, ...etc. for advertisement expenditure.