#### Descriptive Statistics and Probability Three Marks Questions

11th Standard

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Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Compared to the previous year the overhead expenses went up by 32% in 1995, they increased by 40% in the next year and by 50% in the following year. Calculate the average rate of increase in overhead expenses over the three years.

2. From the following data compute the value of Harmonic Mean.

 Marks 10 20 30 40 50 No. of students 20 30 50 15 5
3. Calculate the value of quartile deviation and its coefficient from the following data

 Roll No. 1 2 3 4 5 6 7 Marks 20 28 40 12 30 15 50
4. A factory has 3 machines A1, A2, A3 producing 1000, 2000, 3000 screws per day respectively. A1 produces 1% defectives, A2 produces 1.5% and A3 produces 2% defectives. A screw is chosen at random at the end of a day and found defective. What is the probability that it comes from machines A1?

5. X speaks truth 4 out of 5 times. A die is thrown. He reports that there is a six. What is the chance that actually there was a six?

6. Find the geometric mean of 3, 6, 24, 48

7. Find the harmonic mean of 6, 14, 21, 30

8. A bg contains (2n+1) coins. It is known that n of these coins have a head on both sides whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is $\frac { 31 }{ 42 }$ , determine the value of n.

9. A card from pack 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. Find the probability of the missing card to be a heart?

10. Find the mean deviation about the mean of the following observations 2, 3, 5, 6, 9, 10, 12, 17, 20, 26 and n = 10