Advertisements
Advertisements
Question
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.
Solution
Let X = Sales (in lakh Rs.)
Y = Advertisement Expenditure (in Thousand Rs.)
Bivariate frequency table can be prepared by taking class intervals 115 – 125, 125 –135, ....etc for X and 60 – 62, 62 – 64, …. etc for Y.
Bivariate frequency distribution is as follows:
| Y/X | 115 – 125 | 125 – 135 | 135 – 145 | 145 –155 | 155 – 165 | 165 – 175 | Total (fy) |
| 60 – 62 | II (2) | I (1) | – | – | – | – | 3 |
| 62 – 64 | I (1) | – | III (3) | – | – | – | 4 |
| 64 – 66 | I (1) | I (1) | II (2) | I (1) | – | – | 5 |
| 66 – 68 | – | II (2) | – | II (2) | – | – | 4 |
| 68 – 70 | – | I (1) | I (1) | – | I (1) | I (1) | 4 |
| Total (fx) | 4 | 5 | 6 | 3 | 1 | 1 | 20 |
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?
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)
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.
The regression equation of Y on X is y = `2/9` x and the regression equation of X on Y is `x=y/2+7/6`
Find:
- The correlation coefficient between X and Y.
- `σ_y^2 if σ _x^2=4`
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 - 3D2. 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 byx = -1.2 and bxy = -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.
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?
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 in Statistics (X) |
37 | 20 | 46 | 28 | 35 | 26 | 41 | 48 | 32 | 23 | 20 | 39 | 47 | 33 | 27 | 26 |
| Marks in English (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.
