Basic Statistics 2080
Section A
Long Answer Questions
Attempt any TWO questions. [2 × 10 = 20]
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1. Distinguish between descriptive and inferential statistics. The following table represents the marks obtained by a batch of 10 students in class tests in Basic Statistics and Computer Science:
| Marks in Basic Statistics | 53 | 55 | 52 | 32 | 30 | 60 | 47 | 46 | 35 | 58 |
|---|---|---|---|---|---|---|---|---|---|---|
| Marks in Computer Science | 57 | 45 | 24 | 31 | 25 | 84 | 43 | 80 | 32 | 72 |
Indicate in which subject the level of performance is more consistent. [10]
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2. Define regression. From the following table, compute the line of regression for estimating blood pressure:
| Blood pressure Y | 147 | 125 | 160 | 118 | 149 | 128 |
|---|---|---|---|---|---|---|
| Age in years X | 56 | 42 | 72 | 36 | 63 | 47 |
(i) Fit a regression equation that best describes the above data.
(ii) Estimate the blood pressure when age is 50 years.
(iii) Interpret the regression coefficient. [10]
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3. Under which situations is the Normal distribution used? The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000.
(a) What is the probability that people earn less than $40,000?
(b) What is the probability that people earn between $45,000 and $65,000?
(c) What is the probability that people earn more than $70,000? [10]
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Section B
Short Answer Questions
Attempt any EIGHT questions. [8 × 5 = 40]
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4. Describe the role of Statistics in information technology. [5]
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5. The following table shows the mode of transport used by 400 students of a school. Represent the information on a bar diagram and a Pareto diagram:
| Mode of transport | Bus | Bicycle | On foot | By car |
|---|---|---|---|---|
| No. of students | 200 | 100 | 80 | 20 |
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6. Write the properties of correlation. A study relates aptitude scores to productivity in a factory after six months of training. The figures for six randomly selected workers are:
| Aptitude Scores (X) | 9 | 18 | 18 | 20 | 20 | 23 |
|---|---|---|---|---|---|---|
| Productivity Index (Y) | 12 | 33 | 23 | 42 | 29 | 30 |
Find the coefficient of correlation between aptitude score and productivity index and comment on the value. Also, find the coefficient of variation for each variable. [5]
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7. Define random variable. A random variable X has the following probability function:
| X | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| P(X) | 0.1 | C | 0.2 | 2C | 0.3 | C |
Find:
(i) The value of C.
(ii) P(X < 3), P(X ≥ 1).
(iii) Mean and variance. [5]
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8. Define binomial distribution. Fit a binomial distribution on the following data:
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| f | 28 | 62 | 46 | 10 | 4 |
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9. The probability that an integrated circuit chip will have a defective etching is 0.12, the probability that it will have a crack defect is 0.29, and the probability that it has both defects is 0.07. What is the probability that a newly manufactured chip will have either an etching or a crack defect? [5]
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10. If the first four moments about the mean are 0, 2.8, -2, and 24.5, respectively, compute the coefficient of skewness and kurtosis and comment on the result. [5]
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11. The fuel consumption of a new model of cars is being tested. In one trial, 50 cars chosen at random were driven under identical conditions, and the distances, x km, covered on 1 liter of petrol were recorded. The results gave the following totals: Σx = 525, Σx² = 5625. Calculate the 99% confidence interval for the mean petrol consumption, in km per liter. Interpret the result. [5]
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12. Write short notes on the following:
- a. Use of Box and whisker plot
- b. Parameter and Statistic
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