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

2. 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?

3. What will be the mode of the data: 2, 3, 4, 6, 7, 3, 3, 2, 5, 6, 7?

(a) 7 (b) 6 (c) 4 (d) 3

4. 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)

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

6. If the combined average of the data set 7, 5, 2, 10, x, 6, 4, y, 8, 1 is 5, then what is the value of \(x + y\)?

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

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

8. The median of the data set 10, 12, 14, 18, 15, 200, 100, 20, 22, 24 will be —

(a) 19 (b) 21 (c) 23 (d) 50

9. 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.

10. Here’s the English translation of your math problem: If the ascending data set is \[ 27,\ 31,\ 46,\ 52,\ x,\ y + 2,\ 71,\ 79,\ 85,\ 90 \] and the median of the set is \(64\), then what is the value of \(x + y\)?

(a) 125 (b) 126 (c) 127 (d) 128

11. If 29 is removed from the dataset 20, 22, 25, 26, 27, 28, 29, 30, the median will decrease by –

(a) 2 (b) 1.5 (c) 1 (d) 0.5

12. 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

13. 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

14. 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

15. If the combined average of 5, 15, 22, x, y, 25, and z is 14, then which of the following is correct?

(a) x+y+z=42 (b) x+y+z=31 (c) x+y=z (d) x+y=2z

16. A, B, and C started a business with capital investments of ₹65,000, ₹52,000, and ₹91,000 respectively. After exactly one year, they made a profit of ₹14,400. If \(\frac{2}{3}\) of that profit is divided equally among them and the remaining portion is divided in proportion to their capital investments, how much profit will each person receive?

17. 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?

18. 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?

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

20. The three values of a variable are \(4, 5,\) and \(7\), and their frequencies are \(p - 2, p + 1,\) and \(p - 1\) respectively. If the combined (weighted) mean of the variable is \(5.4\), what is the value of \(p\)?

(a) 1 (b) 2 (c) 3 (d) 4

21. Translate: If the data 9, 10, 12, 15, (x + 1), (x + 3), 32, 35, 36, 40 are arranged in ascending order, the median is 20. Find the value of x.

(a) 16 (b) 17 (c) 18 (d) 20

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

23. The median of the data set 6,7,8,8,9,15,10,15,20,19,25,24,216,7,8,8,9,15,10,15,20,19,25,24,21 is:

(a) 10 (b) 15 (c) 9 (d) 19

24. The combined mean of the numbers 9, 12, 15, 18, 20, 22 increases by 2 if the number ___ is taken instead of 15.

(a) 27 (b) 19 (c) 21 (d) 25

25. Range of the data: 12, 25, 15, 18, 17, 20, 22, 26, 6, 16, 11, 8, 19, 10, 30, 20, 32

(a) 10 (b) 15 (c) 18 (d) 26

26. A weaving cooperative society borrowed ₹15,000 from a bank to purchase a power loom. After 5 years, the society had to repay ₹22,125 to settle the loan. Determine the annual rate of interest charged by the bank.

27. Three friends contributed ₹8,000, ₹10,000, and ₹12,000 respectively and started a business by also taking a loan from the bank. At the end of the year, they made a profit of ₹13,400. After repaying the bank’s annual installment of ₹5,000 from the profit, they divided the remaining amount among themselves in proportion to their capital contributions. How much will each of them receive from the remaining profit?

28. The median of the data set 2, 3, 4, 5 is _____.

29. The mode of the data set 2, 3, 9, 10, 9, 3, 9 is 9.

30. The mode of the data set 2, 3, 9, 10, 9, 3, 9 is 9.