Brief Answer Questions: (Attempt All Questions)
[10 × 2 = 20]Find the combined mean from the following data:
| Group | A | B | C |
|---|---|---|---|
| Number | 200 | 250 | 300 |
| Mean | 25 | 10 | 15 |
Coefficient of variation of a distribution is found to be 20% and variance of distribution is 36. Find the mean value of the distribution.
Find the Karl Pearson's Coefficient of Skewness, when mean = 45, mode = 48 and standard deviation = 15.
If P(A) = 0.6, P(B) = 0.56 and P(A∪B) = 0.75 find P(A∩B). Where A and B are not disjoint events.
The quartile deviation of a distribution is 2 and the difference between P9 and P10 is 8. Calculate the coefficient of Kurtosis.
Calculate coefficient of correlation between X and Y if the regression coefficient of Y on X is -0.667 and regression coefficient of X on Y is -0.75.
Find the simple aggregative price index number for the year 2021:
| Commodities | A | B | C | D | E |
|---|---|---|---|---|---|
| Price in 2020 | 10 | 20 | 18 | 15 | 12 |
| Price in 2021 | 15 | 22 | 20 | 22 | 18 |
What are the components of a time series.
Find the value of determinant:
| 1 | 5 | 6 |
| 2 | 3 | 7 |
| 3 | 5 | 6 |
7 8 6 3
Find 7(A - B) where A = 9 10 and B = 3 2
2 5 7 5
Descriptive Answer Questions (Attempt any FIVE Questions)
[5 × 10 = 50]Calculate the Karl Pearson's Coefficient of Skewness and interpret the result.
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
|---|---|---|---|---|---|---|---|---|
| Freq. | 4 | 5 | 14 | 17 | 25 | 18 | 10 | 7 |
Solve the following equations by using determinant or matrix method:
2x + 2y + z = 5
4x + 2y + 3z = 10
x + 3y + 4z = 7
Following two groups of samples describes the age of the students in regular morning MBS program and evening MBS program of National College. If homogeneity of the class is a positive factor for learning which of the two programs will be easier to teach.
| 24 | 30 | 28 | 23 | 25 | 22 | 26 | 27 | 28 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Evening MBS | 24 | 30 | 28 | 23 | 25 | 22 | 26 | 27 | 28 | 25 |
| Morning MBS | 28 | 27 | 34 | 33 | 29 | 27 | 28 | 29 | 33 | 26 |
The following table gives the changes in the price and the consumption (quantity) of certain major constituents of the consumption basket of the labor class.
| Commodity | Unit | 2020 | 2021 | ||
|---|---|---|---|---|---|
| Price | Qty | Price | Qty | ||
| Wheat | Quintals | 1000 | 10 | 1100 | 6 |
| Rice | Quintals | 1500 | 15 | 1700 | 18 |
| Cloth | Meters | 50 | 50 | 40 | 30 |
(a) The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability that at least one of them will get the scholarship? (b) The following table is the conditional payoff table:
| Strategy | N₀(10) | N₁(11) | N₂(12) | N₃(13) | N₄(14) |
|---|---|---|---|---|---|
| S₁(10) | 400 | 400 | 400 | 400 | 400 |
| S₁(11) | 380 | 440 | 440 | 440 | 440 |
| S₁(12) | 360 | 420 | 480 | 480 | 480 |
| S₁(13) | 340 | 400 | 460 | 520 | 520 |
| S₁(14) | 320 | 380 | 440 | 500 | 560 |
Solve the following Linear Programming problem graphically:
Maximize Z = 30x + 50y
Subject to constraints: x + y ≤ 30 x + 2y ≤ 40
and x ≥ 0, y ≥ 0
Long Answer Questions (Attempt any TWO Questions)
[2 × 15 = 30]Test for the normality of these two distributions of wages (in Rs.) and interpret the result on the basis of the information given below:
| Daily wages in Rs. | No. of Workers X | No. of Workers Y |
|---|---|---|
| 20 - 30 | 15 | 25 |
| 30 - 40 | 30 | 40 |
| 40 - 50 | 44 | 60 |
| 50 - 60 | 60 | 35 |
| 60 - 70 | 30 | 20 |
| 70 - 80 | 14 | 15 |
| 80 - 90 | 7 | 5 |
Before and after the implementation of an economic program to uplift the economic condition of a community following information were found.
| Monthly Income (in Rs. '00) | Prior to the plan No. of families | After the plan No. of families |
|---|---|---|
| 4 - 6 | 10 | 65 |
| 6 - 8 | 70 | - |
| 8 - 10 | 35 | 37 |
| 10 - 12 | 20 | 15 |
| 12 - 14 | 10 | 15 |
| 14 - 16 | 3 | 5 |
| 16 - 18 | 2 | 5 |
The income and expenditure of 100 families is given below:
| Income (Rs) | Expenditure (Rs) | |||
|---|---|---|---|---|
| 0 - 500 | 500 - 1000 | 1000 - 1500 | 1500- 2000 | |
| 0 - 1000 | - | - | - | 3 |
| 1000 - 2000 | - | 4 | 9 | 4 |
| 2000 - 3000 | 3 | 10 | 19 | 8 |
| 3000 - 4000 | 7 | 6 | 12 | 5 |
| 4000 - 5000 | 9 | 7 | - | - |
(b) Co-efficient of correlation between income and expenditure.
(c) Estimate the expenditure when income is Rs 10,000.