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Brief Answer Question
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If mean = 35, mode = 40 and standard deviation = 10. Find Karl Pearson's coefficient of skewness and interpret the result.
Find Karl Pearson's correlation coefficient between X and Y from the following information. N = 10, ΣX = 125, ΣY = 50, ΣX² = 2080, ΣY² = 2085, ΣXY = 1050
The standard deviation of mesokurtic distribution is 7. What must be the value of fourth moment about mean?
Ram and Sita appear for an interview for two different posts. The probabilities of their selection are 3/4 and 1/5 respectively. Find the probability that (a) both of them will be selected (b) none of them will be selected.
The year of origin of the following trend line equation of sales (in millions rupees) is 2015. Y = 50 + 2.5X Estimate the sales for the year 2022.
The following table shows the monthly income of workers of two manufacturing companies A and B
| Company A | Company B | |
|---|---|---|
| Mean-monthly income | Rs. 2550 | Rs. 2800 |
| Number of workers | 100 | 110 |
Find simple aggregative price index number for the year 2021 from the following information.
| Commodities | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Price in 2020 (Rs.) | 160 | 140 | 150 | 130 | 155 | 120 |
| Price in 2021 (Rs.) | 170 | 135 | 155 | 140 | 150 | 30 |
Find 7(A+B) where A=
Find the value of determinant of following matrix:
What is chronological classification? Give an example.
Descriptive Answer Question
Attempt any Five questions
The marks distribution of 100 students of a College is as follows:
| Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
|---|---|---|---|---|---|---|---|
| No. of Students | 8 | 16 | 25 | 22 | 15 | 9 | 5 |
An enquiry into the budget of middle class families in a certain locality of a city gave the following information:
| Expenses on | Food | Rent | Clothing | Fuel | Misc. |
|---|---|---|---|---|---|
| 30% | 15% | 20% | 10% | 25% | |
| Price in 2021 (Rs.) | 160 | 60 | 110 | 30 | 80 |
| Prices in 2022 (Rs.) | 184 | 70 | 135 | 55 | 100 |
Solve the following linear programming problem:
Minimize Z = 2x + 3y
Subject to Constraint:
5x + y ≥ 10
2x + 2y ≥ 12
x + 4y ≥ 12
x & y ≥ 0
a) From the given Pay-off table, give the decision according to
(i) Maximax approach
(ii) Maximin approach
(iii) Minimax Regret approach.
| State of nature | Strategies | ||
|---|---|---|---|
| S₁ | S₂ | S₃ | |
| N₁ | 400 | 200 | 700 |
| N₂ | 100 | 600 | 300 |
| N₃ | 500 | 300 | 100 |
(i) a sum of 8 or 9
(ii) a sum less than 5?
The following table reveals the sales distribution of a business house from the year 2016 to 2020:
| Year | 2016 | 2017 | 2018 | 2019 | 2020 |
|---|---|---|---|---|---|
| Sales (in 000 Rs) | 50 | 51 | 60 | 75 | 100 |
Solve the following system of linear equations by using determinant or matrix method: 2x - y + 2z = -1
x - 2y + 3z = 4
4x + y + z = 4
Analytical Answer Question
Attempt any Two questions
A factory produces two types of electric lamps A and B. In an experiment relating to their life, the following results were obtained:
| Life (in years) | Number of Motors | |
|---|---|---|
| Model A | Model B | |
| 0 - 2 | 5 | 4 |
| 2 - 4 | 11 | 30 |
| 4 - 6 | 26 | 12 |
| 6 - 8 | 10 | 8 |
| 8 - 10 | 8 | 6 |
(b) Calculate the combined standard deviation.
The following data shows the income distribution of families of a certain locality of a city. Calculate the coefficient of skewness and kurtosis and hence comment on the nature of the income distribution.
| Income (in millions Rs.) | Number of Families |
|---|---|
| 10-20 | 5 |
| 20-30 | 9 |
| 30-40 | 18 |
| 40-50 | 26 |
| 50-60 | 20 |
| 60-70 | 12 |
| 70-80 | 7 |
| 80-90 | 3 |
The following two way table shows the sales revenue (in lakhs Rs.) and advertising expenditure (in lakhs Rs.) of a company. Find correlation coefficient between them and interpret the result. Also test the significance of correlation coefficient. Estimate the sales revenue when advertising expenditure is Rs. 50 lakhs
| Sales Revenue (in lakhs Rs) | Advertising Expenditure (in lakhs Rs) | ||||
|---|---|---|---|---|---|
| 5-15 | 15-25 | 25-35 | 35-45 | Total | |
| 75-125 | 3 | 4 | 4 | 8 | 19 |
| 125-175 | 8 | 6 | 5 | 7 | 26 |
| 175-225 | 2 | 2 | 3 | 4 | 11 |
| 225-275 | 3 | 3 | 2 | 2 | 10 |
| Total | 16 | 15 | 14 | 21 | 66 |