For the following set of data
95 76 72 67 69 48 37 76 74 60
78 80 48 86 59 68 73 77 51 82
94 95 48 58 75 69 55 51 89 91
89 93 69 81 68 49 86 74 79 100
i) construct a frequency distribution using intervals 35-44 etc.
ii) compute the sample mean from the raw data.
iii) compute the sample mean from the frequency distribution.
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If p is the length of the perpendicular from the origin to the line x/a + y/b = 1 prove that 1/p2 = 1/a2 + 1/b2.
A particle is acted on by constant forces = −3i + 2 j + 5k and 2i + j −3k and is displaced from the point (2, −1, −3) to the point (4, −3, 7) . Find the total work done by the forces.
Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient
evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?
| Group 1 | Group 2 | Group 3 | Group 4 |
| 65 | 75 | 59 | 94 |
| 87 | 69 | 78 | 89 |
| 73 | 83 | 67 | 80 |
| 79 | 81 | 62 | 88 |
| 81 | 72 | 83 |
|
| 69 | 79 | 76 |
|
|
| 90 |
|
|
In Bengal, 30% of the population has a certain blood type. What is the probability that exactly four out of a randomly selected group of 10 Bengalis will have that blood type?
Evaluate the following integrals:
i) 
ii) ∫ x ln | x + 1| dx
for a population of size N = 120 with a mean of 7.5 and a standard deviation of 1.5, find the estimated standard error of the mean for the following sample sizes:
- ) n = 9 ii) n = 25
An economist wants to estimate the relationship between a family’s annual income and the amount that the family saves. The family data for nine families are obtained
| Annual income (thousands of Rs.) | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Annual saving (thousands of Rs.) | 0.0 | 0.1 | 0.2 | 0.2 | 0.5 | 0.5 | 0.6 | 0.7 | 0.8 |