1. The median of the series 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18 will be –

(a) 10 (b) 11 (c) 10.5 (d) 11.5

2. Translate the following and find the mode of the data:
8, 5, 4, 6, 7, 4, 4, 3, 5, 4, 5, 4, 4, 5, 5, 4, 3, 3, 5, 4, 6, 5, 4, 5, 4, 5, 4, 2, 3, 4
Mode = 4 (since it appears most frequently)

3. The mode of the data set 4, 6, 5, 4, 7, 2, 3, 4, 5 is 4.

4. What will be the median of 33, 86, 68, 32, 80, 48, 70, 64, and 75?

(a) 64 (b) 68 (c) 70 (d) 75

5. The median of the quantities 94, 33, 86, 68, 32, 80, 48, 70 will be —

(a) 68 (b) 67 (c) 69 (d) 70

6. If the data arranged in ascending order is 6, 9, 11, 12, x+2, x+3, 17, 20, 21, 24 and the median is 21, then the value of x will be —

(a) 13.5 (b) 15.5 (c) 18.5 (d) 21.5

7. Translate the following and find the mode of the data:
15, 11, 10, 8, 15, 18, 17, 15, 10, 19, 10, 11, 10, 8, 19, 15, 10, 18, 15, 3, 16, 14, 17, 2
Mode = 15 (since it appears most frequently)

8. In a game, scores of 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 were obtained; the average score was 10.

9. The median of the data set 3, 7, 2, 3, 5, 7 will be –

(a) 3 (b) 1.5 (c) 4 (d) 4.5

10. A group of 12 students was given 10 puzzles. The number of correct answers by each student was: 2, 4, 3, 5, 2, 5, 8, 2, 3, 9, 5, 2 What is the mode of this data?

11. Find the mode of the given data: 9, 6, 9, 3, 4, 9, 8, 6, 5, 9, 6, 4.

(a) 4 (b) 6 (c) 8 (d) 9

12. 3, 5, 3, 4, 3, 6, 3, 7, 4, 8, 4. The frequency of 6 is 1 and the mode is 3.

13. The heights (in cm) of some students in our class are given below: 131, 130, 130, 132, 131, 133, 131, 134, 131, 132, 132, 131, 133, 130, 132, 130, 133, 135, 131, 135, 131, 135, 130, 132, 135, 134, 133 Let us determine the **mode** of the students' heights.

14. If the average of the quantities \(x_1, x_2, x_3,.......,x_{10}\) is 20, then the average of \(x_1+4, x_2+4, x_3+4,...., x_{10}+4\) will be—?

(a) 20 (b) 24 (c) 40 (d) 10

15. Asit and Dipak invested ₹22,500 and ₹35,000 respectively in a joint business. If the total profit is ₹13,800, then Dipak's share of the profit will be —

(a) ₹ 8400 (b) ₹ 8600 (c) ₹ 8200 (d) ₹ 8000

16. If the mean of the numbers \(x_1, x_2, x_3, x_4, ..., x_n\) is \(\bar{x}\), then the value of \((x_1 - \bar{x}) + (x_2 - \bar{x}) + (x_3 - \bar{x}) + ... + (x_n - \bar{x})\) will be —

(a) 0 (b) 1 (c) 3 (d) 5

17. "What will be the mode of the data: 7, 9, 11, 7, 6, 5, 9, 13?

(a) 7 (b) 9 (c) 7 and 9 (d) There is no mode.

18. Here is the ogive (greater than cumulative frequency curve) based on your data: - **Class Intervals:** 0–10, 10–20, 20–30, 30–40, 40–50, 50–60 - **Frequencies:** 7, 10, 23, 50, 6, 4 - **Cumulative Frequencies (Greater Than):** Calculated from the lower bounds of each class The ogive has been successfully generated and saved.

19. In a joint business, Sumedha, Rabeya, and Rina invest 4,000 rupees, 5,000 rupees, and 6,000 rupees, respectively. After 4 months, Sumedha adds another 2,000 rupees, and after another 4 months, Rina withdraws half of her capital. If the total profit at the end of the year is 6,900 rupees, how much profit will each person receive?

20. At an annual interest rate of \( 8\frac{3}{4}\% \), calculate the interest on ₹12,500 for the period from April 14, 1953, to June 26, 1953.

21. A joint business. On January 1st, A, B, and C invest 4,000 rupees, 5,000 rupees, and 6,000 rupees, respectively. On May 1st, A invests an additional 2,000 rupees in the business. On September 1st, C withdraws half of their capital. By December 31st, if the total profit is 6,900 rupees, how much profit will each person receive?

22. The mode of the data set 3, 4, 5, 6, 3, 3 is 3.

23. If the arithmetic mean of the given values is \(9.5\), determine the value of \(x\): \(12, 6, 7, 3, x, 10, 18, 5\).

24. The mode of the data set 5, 2, 4, 3, 5, 2, 5, 2, 5, 2 is 2.

25. The modal value of the data set 2, 3, 3, 2, 5, 2, 3, 6, 5 is 6.

26. What is the median of the numbers 2, 8, 2, 3, 8, 5, 9, 5, 6?

(a) 8 (b) 6.5 (c) 5.5 (d) 5

27. The mode of the numbers 1, 3, 2, 8, 10, 8, 3, 2, 8, 8 is—?

(a) 2 (b) 3 (c) 8 (d) 10

28. If the combined mean of \(x_1, x_2, x_3, …, x_n\) is \(\bar{x}\), then the combined mean of \(\frac{x_1 - c}{h}, \frac{x_2 - c}{h}, …, \frac{x_n - c}{h}\) will be \(h\bar{x} + c\).

29. At the beginning of the year, Srikanta and Saifuddin purchased a minibus and started operating it by investing ₹2,40,000 and ₹3,00,000 respectively. Four months later, their friend Peter joined them with ₹81,000. Srikanta and Saifuddin withdrew amounts proportional to their original investments from Peter’s contribution. At the end of the year, the total profit was ₹39,150. How much profit will each of them receive?

30. A, B, and C together start a business and make a profit of ₹36,400. The ratio of capital between A and B is 5:3, and the ratio between B and C is 5:4. What will be A’s share of the profit?