1. If the average of the numbers 6, 7, x, 8, y, and 14 is 9, then
(a) x+y=21 (b) x+y=19 (c) x-y=21 (d) x-y=19
2. If the average of the numbers 6, 7, x, 8, y, 14 is 9,
3. If the average of the numbers 6, 7, \(x\), 8, \(y\), 14 is 9, then –
(a) x+y=21 (b) x+y=29 (c) x-y=21 (d) x+y=19
4. 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 \(x + y\)?
5. 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
6. If 16, 15, 17, 16, 15, x, 19, 17, 14 have a mode of 15, then the value of x is-
(a) 15 (b) 16 (c) 17 (d) 19
7. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x is—
8. If the mode of the data 16, 15, 16, 16, 15, x, 19, 17, 14 is 16, then the value of x must be 16.
9. From each of the numbers 6, 10, 9, and 16, if the same number is subtracted, the resulting values are in proportion. What is that number?
(a) 1 (b) 2 (c) 3 (d) 4
10. What will be the median of the numbers 8, 15, 10, 11, 7, 9, 11, 13, and 16?
11. The daily amounts of money received by our 16 friends for school commuting and other expenses are: 15, 16, 17, 18, 17, 19, 17, 15, 15, 10, 17, 16, 15, 16, 18, 11 Let us determine the **mode** of the amounts received daily by our friends.
12. 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)
13. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x is—
14. In a game, scores of 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 were obtained; the average score was 10.
15. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x will be 15.
16. 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
17. The median of 8, 15, 10, 11, 7, 9, 11, 13, 16 is:
(a) 15 (b) 10 (c) 11.5 (d) 11
18. 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
19. What is the median of 3, 9, 7, 4, 8, and 6?
(a) 5 (b) 5.5 (c) 6 (d) 6.5
20. 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
21. 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
22. If the average of the first four numbers out of five is 26, and the average of the last four numbers is 25, then find the difference between the first and the last number.
23. A, B, and C started a business together with capital investments of ₹6,000, ₹8,000, and ₹9,000 respectively. After a few months, A invested an additional ₹3,000 into the business. At the end of the year, the total profit was ₹30,000, and C received ₹10,800 as his share of the profit. When did A invest the additional ₹3,000?
24. 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
25. A, B, and C started a business by investing ₹6,000, ₹8,000, and ₹10,000 respectively, with the condition that A would manage the business. For this, A would receive \(\frac{3}{20}\) of the total profit. The remaining profit would be divided among the three in proportion to their capital. If C received ₹391 more than B, what was the total profit?
26. If the annual interest rate is 16% and interest is compounded quarterly, then the compound principal of ₹7,500 after 6 months will be—
(a) ₹ 8500 (b) ₹ 9112 (c) ₹ 8112 (d) ₹ 7812
27. A and B start a business by investing 24,000 currency units and 30,000 currency units, respectively, at the beginning of the year. After 5 months, A contributes an additional 4,000 currency units. If the annual profit is 27,716 currency units, determine each person's share of the profit.
28. If the combined average of the numbers 7, \(x - 3\), 10, \(x + 3\), and \(x - 5\) is 15, then the median is _____.
(a) 16 (b) 10 (c) 18 (d) 24
29. If the ascending order of data is 8, 9, 12, 17, \(x+2\), \(x+6\), 30, 31, 34, 39 and its median is 24, determine the value of \(x\).
(a) 22 (b) 21 (c) 20 (d) 24
30. If the arithmetic mean of the given values is \(9.5\), determine the value of \(x\): \(12, 6, 7, 3, x, 10, 18, 5\).
