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Differentiate between Convenient sampling and Systematic random sampling with suitable examples.
From the following data, find Mean and Median. Then use an empirical relation across mean, median and mode to find Mode.
| Age group | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No.of months (f) | 10 | 35 | 17 | 12 | 9 |
When Mean is 34.69 for 65 total observations, find the missing frequency from the following data.
| Expense-clases in thousand rupees | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No of 5 star hotel establishment | 9 | 12 | 25 | 10 | ? |
Use Karl Pearson’s correlation method to examine the relationship between marks obtained in two subjects:
| Students | A | B | C | D | E | F | G | H | I | J |
| Statistics | 42 | 51 | 65 | 57 | 56 | 28 | 19 | 24 | 33 | 80 |
| Mathematics | 42 | 61 | 66 | 54 | 57 | 28 | 29 | 21 | 35 | 87 |
The number of defective articles is found to be 2% in a lot of 300 sample articles per day, then find out following probabilities using suitable probability distribution that
(i) There are exactly two defective articles per day
(ii) There are at least 2 defective articles per day.
Six coins are tossed 500 times such that probability of getting a head is 21% in each toss.Fit a Binomial distribution for a number of heads with the following frequency distribution:
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | total |
| f(frequency) | 165 | 80 | 70 | 55 | 45 | 50 | 35 | 500 |
In a Hospital, the height of patients follows normal distribution with mean height of 53 inches with standard deviation of 3 inches.Then find out the following probabilities of heights of patients that:
i) less than 57 inches,
ii) more than 64 inches,
iii) between 50 and 56 inches. Use Normal table.
Attempt any TWO questions
[2x10=20]Automobile Company Sells Cars of different model during a year. Data are presented in the following table:
| Piece of cars | 12 | 13 | 40 | 15 | 16 | 70 | 80 | 90 | 15 | 77 |
| Demands of cars | 24 | 28 | 12 | 13 | 10 | 6 | 5 | 4 | 11 | 5 |
An analysis of daily wages, paid to workers in two firms A and B belonging to the same industry, gives the following results:
| Yeas | Firm A | Firm B |
| No of workers | 200 | 300 |
| CV of Daily Wages | 5 | 6 |
| Variance of distribution of wages | 67 | 86 |
b) In which firm, A or B, is there a greater consistency or uniformity or variability in individual wages?
c) Find out the combined average of both firms A and B.
Perform a one-way ANOVA to differentiate average sales of computers from three electronic shops as given below at 5% level of significance:
| Shop A | 10 | 15 | 18 | 21 | 35 |
| Shop B | 23 | 45 | 45 | 55 | 57 |
| Shop C | 45 | 67 | 78 | 78 | 90 |