The Math Factory

1. 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
2. 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
3. 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
4. The median of the data set 6,10,5,4,9,11,20,186,10,5,4,9,11,20,18 (a) 9 (b) 10 (c) 9.25 (d) 9.5
5. If the average of the first ten natural numbers is A and the median is M, then the relationship between A and M is — (a) \(A\gt M\) (b) \(A\lt M\) (c) \(A=\cfrac{1}{M}\) (d) \(A=M\)
6. 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
7. If the average of \( x_1, x_2, x_3, \dots, x_n \) is \( \bar{x} \), then what is the average of \( ax_1, ax_2, ax_3, \dots, ax_n \) ? (a) \(\bar{x}\) (b) \(a\bar{x}\) (c) \(n\bar{x}\) (d) None of these
8. The median of 10, 14, 8, 16, 20, 15, 9 is (a) 20 (b) 16 (c) 15 (d) 14
9. The median of the numbers 67, 62, 70, 68, 90, 84, 94, 98: (a) 77 (b) 70 (c) 68 (d) 84
10. If the average of \(n\) natural numbers is \(\cfrac{n+8}{4}\), then what is the value of \(n\)? True / False
11. The median of 8, 15, 10, 11, 7, 9, 11, 13, 16 is: (a) 15 (b) 10 (c) 11.5 (d) 11
12. If 35 is not present in the data set 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by (a) 2 (b) 1.5 (c) 1 (d) 0.5
13. If the mode of the numbers 64, 60, 48, x, 43, 48, 43, 34 is 43. Then the value of \((x+3)\) is. (a) 44 (b) 45 (c) 46 (d) 48
14. If the 25th term of a sequence with 49 terms is 57 and the 26th term is 62, the median of the sequence will be? (a) 59.5 (b) 57 (c) 62 (d) 57.5
15. If the data arranged in ascending order, 8, 9, 12, 17, x+2, x+4, 30, 31, 34, 39 has a median of 24, then the value of x - (a) 22 (b) 21 (c) 20 (d) 24
16. 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
17. If the data set 30, 34, 35, 36, 37, 38, 39, 40 excludes 35, the median increases (a) 2 (b) 1.5 (c) 1 (d) 0.5
18. If \(u_i = \cfrac{x_i - 35}{10}\), \(∑f_i u_i = 30\), and \(∑f_i = 60\), then the value of \(\bar{x}\) is – (a) 40 (b) 20 (c) 80 (d) None of these
19. Let the length of each edge of the cube be \(a\) cm \(\therefore\) The total surface area of the cube = \(6a^2\) square cm If the edge length is increased by 20%, the new edge length = \(a + a \times \cfrac{20}{100}\) cm \(= a + \cfrac{a}{5} = \cfrac{6a}{5}\) cm \(\therefore\) New total surface area of the cube = \(6\left(\cfrac{6a}{5}\right)^2\) square cm = \(\cfrac{216a^2}{25}\) square cm \(\therefore\) Percentage increase in surface area \(= \cfrac{\cfrac{216a^2}{25} - 6a^2}{6a^2} \times 100\%\) \(= \cfrac{(216a^2 - 150a^2) \times 100}{25 \times 6a^2}\%\) \(= \cfrac{4 \times 66a^2}{6a^2}\%\) \(= 44\%\) (a) (b) (c) (d)
20. What is the median of 3, 9, 7, 4, 8, and 6? (a) 5 (b) 5.5 (c) 6 (d) 6.5
21. What will be the median of 33, 86, 68, 32, 80, 48, 70, 64, and 75? (a) 64 (b) 68 (c) 70 (d) 75
22. 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
23. 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
24. The maximum value of a data set is 520. What should be the minimum value for the range of the data to be 100? (a) 120 (b) 320 (c) 420 (d) 500
25. If \(\sum f_iu_i = 10\), class width = 20, \(\sum f_i = 40 + k\), the combined mean is 54, and the assumed mean is 50, then what is the value of \(k\)? (a) (b) (c) (d)
26. If \(\sum{f_ix_i} = 216\), \(\sum{f_i} = 16\), and the combined mean is \(13.5 + p\), then what is the value of \(p\)? (a) 0 (b) 1 (c) 0.1 (d) 0.01
27. If \(u_i = \cfrac{x_i - 20}{10}\), \(\sum{f_iu_i} = 15\), and \(\sum{f_i} = 80\), then what will be the value of \(\bar{x}\)? (a) 21.875 (b) 20.875 (c) 21.800 (d) 20.125
28. If \(\sum \limits_{i=1}^n (x_i - 7) = -8\) and \(\sum \limits_{i=1}^n (x_i + 3) = 72\), then what are the values of \(\bar{x}\) (the mean of \(x_i\)) and \(n\) (the number of terms)? (a) \(\bar{x}=5, n=8\) (b) \(\bar{x}=6, n=8\) (c) \(\bar{x}=4, n=7\) (d) \(\bar{x}=8, n=6\)
29. If class width = 20, assumed mean \(A = 25\), total frequency \(y = 50\), and \(\sum f_u = -5\), then the combined mean \(\bar{x}\) will be — (a) 25 (b) 23 (c) 24 (d) 27
30. 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
31. If the assumed mean is 22, class width is 10, total frequency is 80, and the value of \(\sum{f_iu_i}\) is 16, then the actual (or true) mean will be — (a) 23 (b) 24 (c) 25 (d) 26
32. 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
33. Expressing (10×1)+(10×2)+(10×3)+...+(10×10) using symbols will be — (a) \(\sum \limits_{10}^{i=1}(10\times i)\) (b) \(\sum \limits_{i}^{10}(10\times i)\) (c) \(\sum \limits_{10}^{i}(10\times i)\) (d) \(\sum \limits_{i=1}^{10}(10\times i)\)
34. To draw a histogram on graph paper from a frequency distribution table, the frequencies are plotted. (a) Along the X-axis (b) Along the Y-axis (c) Along the origin (d) Along any axis
35. If the combined mean of \(n\) quantities is \(\bar{x}\), and the sum of the first \((n-1)\) quantities is \(k\), then the \(n\)th quantity will be — (a) \(k+n\) (b) \(\bar{x}+k\) (c) \(\bar{x}-k\) (d) \(n\bar{x}-k\)
36. 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
37. If \(\sum\limits_{i=1}^5 x_i = 5\) and \(\sum\limits_{i=1}^5 x_i^2 = 14\), then the value of \(\sum\limits_{i=1}^5 2x_i(x_i - 3)\) will be — (a) 2 (b) -2 (c) 0 (d) 4
38. In a frequency distribution table, if \(\sum f_i d_i = 1000\) and \(\sum f_i = 30\), then the mean deviation will be — (a) 33.33(approximately) (b) 33 (c) 3.33(approximately) (d) 30.33(approximately)
39. The median of the quantities 94, 33, 86, 68, 32, 80, 48, 70 will be — (a) 68 (b) 67 (c) 69 (d) 70
40. 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
41. In the dataset 12, 18, 24, 31, 32, 38, 43, 48 — if the number 31 were not present, how much would the median decrease or increase? (a) 1.5 decrease (b) 1.5 increase (c) 0.5 decrease (d) 0.5 increase
42. 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
43. From a statistical frequency distribution table, the given values are: \(n = 84,\) \(L = 30,\) \(f = 30,\) \(h = 30,\) \(cf = 40\) Therefore, the median of the distribution will be — (a) 30 (b) 32 (c) 34 (d) 36
44. If the combined average of the expressions ???? − 3 , ???? − 1 , 7 , ???? , 2 ???? − 1 , and 3 ???? − 5 is 3.5, then what will be the median of these expressions? (a) 3.5 (b) 4.5 (c) 5 (d) 5.5
45. 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
46. "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.
47. 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
48. 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. (a) 15 (b) 16 (c) 17 (d) 19
49. If the mode and the combined mean of a statistical distribution are ₹12.30 and ₹18.48 respectively, then the median of the distribution will be — (a) ₹ 16 (b) ₹ 17 (c) ₹ 16.42 (d) ₹ 17.42
50. The average deviation from the combined mean of the data series 46, 79, 26, 85, 39, 65, 99, 29, 56, 72 will be — (a) 20.4 (b) 21.4 (c) 19.4 (d) 21
51. If \(∑f_i(x_i - a) = 400\), \(∑f_i = 50\), and \(a\) (assumed mean) = 52, then the value of the combined mean \(\bar{x}\) is – (a) 52 (b) 60 (c) 80 (d) 90
52. 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
53. If \(∑f_i d_i = 400\), \(∑f_i = 50\), and \(a =\) assumed mean \(= 52\), then the value of the combined mean is – (a) 52 (b) 60 (c) 80 (d) 55
54. 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
55. The median of the data set 3, 7, 2, 3, 5, 7 will be – (a) 3 (b) 1.5 (c) 4 (d) 4.5
56. The median of all multiples of three between 1 and 20 is – (a) 9.5 (b) 10.5 (c) 11.5 (d) None of these
57. The chart that helps to find the median of a statistical distribution is— (a) Statistical Line (b) Statistical Polygon (c) Bar Chart (d) Ogive
58. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x is— (a) 15 (b) 16 (c) 17 (d) 19
59. If the average of \(n\) natural numbers is \(\cfrac{n+8}{4}\), then find the value of \(n\). (a) 4 (b) 6 (c) 8 (d) 10
60. 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
61. If the average of the numbers 6, 7, x, 8, y, and 16 is 9, then—? (a) x + y = 21 (b) x + y = 17 (c) x - y = 21 (d) x - y = 19
62. 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
63. The mode of the numbers 1, 3, 2, 8, 10, 8, 3, 2, 8, 8 is—? (a) 2 (b) 3 (c) 8 (d) 10
64. If a perpendicular is drawn from the point of intersection of two ogives to the x-axis, then the foot of that perpendicular on the x-axis represents the median. True / False
65. 3, 5, 3, 4, 3, 6, 3, 7, 4, 8, 4. The frequency of 6 is 1 and the mode is 3. True / False
66. The mode of the following frequency distribution is 3
Score12345
Number of Students36475
True / False
67. 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 \(h\bar{x} + c\). True / False
68. The median of the data 2, 3, 9, 10, 9, 3, 9 is 10. True / False
69. The median of the data set 3, 14, 18, 20, 5 is 18. True / False
70. The mode of the data set 3, 4, 5, 6, 3, 3 is 3. True / False
71. The mode of the data set 5, 2, 4, 3, 5, 2, 5, 2, 5, 2 is 2. True / False
72. If \(n\) is an even number, then the median will be the average of the \(\left(\cfrac{n}{2}\right)\)-th and \(\left(\cfrac{n}{2}−1\right)\)-th observations. True / False
73. A locus is always a straight line. True / False
74. The median of the data set 3, 14, 18, 20, 5 is 18. True / False
75. Given that the combined mean of the following distribution is 50 and the total frequency is 120, find the values of \(f_1\) and \(f_2\): | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|--------|--------|--------|---------| | Frequency | 17 | \(f_1\) | 32 | \(f_2\) | 19 |
76. Prepare a greater-than cumulative frequency table from the following frequency distribution and draw an ogive on graph paper. | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | |----------------|------|--------|--------|--------|--------|--------| | Frequency | 7 | 10 | 23 | 50 | 6 | 4 |
77. 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.
78. Find the mode of the following frequency distribution: | Class Interval | 50–59 | 60–69 | 70–79 | 80–89 | 90–99 | 100–109 | |----------------|--------|--------|--------|--------|--------|----------| | Frequency | 5 | 20 | 40 | 50 | 30 | 6 |
79. If the combined mean of the following frequency distribution table is 54, determine the value of \(K\):
Class Interval0-2020-4040-6060-8080-100
Frequency711K913
80. If the data arranged in ascending order is 8, 9, 12, 17, x+2, x+4, 30, 34, 39 and the median is 24, then the value of x is _____.
81. If the average of the \(n\) numbers \(x_1, x_2, x_3, ..., x_n\) is \(\bar{x}\), then the average of \(Kx_1, Kx_2, Kx_3, ..., Kx_n\) is —— (where \(K \ne 0\)).
82. In a group of \(n\) numbers with an average of \(\bar{x}\), if the sum of the first \((n - 1)\) numbers is \(K\), then the \(n\)th number will be \((n - 1)\bar{x} + K\).
83. In a statistical distribution, the average (mean) is 7 and \(\sum f_i x_i = 140\). Find the value of \(\sum f_i\).
84. The numbers 11, 12, 14, \(x - 2\), \(x + 4\), \(x + 9\), 32, 38, 47 are arranged in ascending order, and their median is 24. Find the value of \(x\).
85. Here is the English translation: > Find the mode of the following data:
Marks 0–5 5–10 10–15 15–20 20–25 25–30 30–35 35–40
Number of Students 2 6 10 16 22 11 8 5
86. Here is the English translation: > Calculate the average (mean) from the following frequency distribution using any method:
Class Interval 85–105 105–125 125–145 145–165 165–185 185–205
Frequency 3 12 18 10 5 2
87. If the average of \( (p + q) \) numbers is \( x \), and the average of \( p \) of those numbers is \( y \), then the average of the remaining \( q \) numbers will be _____ .
88. Calculate the average (mean) from the following frequency distribution using any method:
Class Interval 85–105 105–125 125–145 145–165 165–185 185–205
Frequency 3 12 18 10 5 2
Class Midpoint 95 115 135 155 175 195
\(f_i x_i\) 285 1380 2430 1550 875 390
Total \( \sum f_i = 50 \) \( \sum f_i x_i = 6910 \)
> Mean using direct method = \(\frac{\sum f_i x_i}{\sum f_i} = \frac{6910}{50} = 138.2\)
89. If the median of the following data is 32 and the total frequency is 100, find the values of \(x\) and \(y\): | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|--------|--------| | Frequency | 10 | \(x\) | 25 | | Class Interval | 30–40 | 40–50 | 50–60 | |----------------|--------|--------|--------| | Frequency | 30 | \(y\) | 10 |
90. Find the mode of the following frequency distribution: | Class Interval | 0–5 | 5–10 | 10–15 | |----------------|-----|------|--------| | Frequency | 5 | 12 | 18 | | Class Interval | 15–20 | 20–25 | 25–30 | 30–35 | |----------------|--------|--------|--------|--------| | Frequency | 28 | 17 | 12 | 8 |
91. The modal class of the above frequency distribution is 15–20. So, the mode is calculated as: \[ \text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h \] Where: - \(l = 15\) (lower boundary of modal class) - \(f_1 = 28\) (frequency of modal class) - \(f_0 = 18\) (frequency of class before modal class) - \(f_2 = 17\) (frequency of class after modal class) - \(h = 5\) (class width) Substituting the values: \[ = 15 + \left(\frac{28 - 18}{2 \times 28 - 18 - 17}\right) \times 5 = 15 + \frac{10}{21} \times 5 = 15 + \frac{50}{21} = 15 + 2.38 = 17.38 \quad \text{(approx)} \] ✅ Therefore, the mode is approximately **17.38**.
92. The measures of central tendency are mean, median, and ——.
93. The median of the data set 3, 14, 18, 20, 5 is 14.
94. The ages of 100 people present at a program are given in the table below. Calculate the average age of these 100 people using any appropriate method. | Age (in years) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | |----------------|-------|-------|-------|-------|-------|-------| | Number of people | 08 | 12 | 20 | 22 | 18 | 20 |
95. If the median of the following data is 32 and \(x + y = 100\), determine the values of \(x\) and \(y\). | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|-------|-------| | Frequency | 10 | x | 25 | | Class Interval | 30–40 | 40–50 | 50–60 | |----------------|--------|--------|--------| | Frequency | 30 | y | 10 | ---
96. Create a cumulative frequency (less than type) table from the given data and draw an ogive on graph paper. | Class Interval | 0–10 | 10–20 | 20–30 | |----------------|------|-------|-------| | Frequency | 1 | 6 | 15 | | Class Interval | 30–40 | 40–50 | 50–60 | 60–70 | |----------------|--------|--------|--------|--------| | Frequency | 20 | 15 | 6 | 1 |
97. Compound mean, median, and mode are measures of ____ tendency.
98. 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?
99. From the following frequency distribution table of candidates' ages in an entrance examination, find the **mode**: | Age (in years) | 16–18 | 18–20 | 20–22 | 22–24 | 24–26 | |----------------|--------|--------|--------|--------|--------| | Number of Candidates | 45 | 75 | 38 | 22 | 20 |
100. From the following frequency distribution of candidates' ages in an entrance examination, find the median: | Class Interval | 1–5 | 6–10 | 11–15 | 16–20 | 21–25 | 26–30 | 31–35 | |----------------|-----|------|-------|-------|-------|-------|-------| | Frequency | 2 | 3 | 6 | 7 | 5 | 4 | 3 |
101. **English Translation:** Draw the **less than ogive** (cumulative frequency curve) for the following frequency distribution: | Marks Obtained | 50–60 | 60–70 | 70–80 | 80–90 | 90–100 | |----------------|-------|-------|-------|-------|--------| | Frequency | 4 | 8 | 12 | 6 | 10 |
102. Based on the given data, prepare a cumulative frequency (greater than type) table and draw an ogive on graph paper: | Class Interval | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | |----------------|------|-------|-------|-------|-------|-------| | Frequency | 7 | 10 | 23 | 50 | 6 | 4 |
103. If the variables \(x_1, x_2, ..., x_{100}\) are arranged in ascending order, then their median is ______.
104. If the middle number of the first \((2n + 1)\) consecutive natural numbers is \(\frac{n + 103}{3}\), then find the value of \(n\).
105. The median of the data set 2, 3, 4, 5 is _____.
106. If \(\sum_{i=1}^n (x_i - 3) = 0\) and \(\sum_{i=1}^n (x_i + 3) = 66\), then find the values of \(\bar{x}\) (the mean) and \(n\).
107. If the median of the following data is 32, find the values of \(x\) and \(y\) given that the total frequency is 100.
Class Interval0-1010-2020-3030-4040-5050-60
Frequency10x2530y10
108. What will be the median of the numbers 8, 15, 10, 11, 7, 9, 11, 13, and 16?
109. If the mean and median of a statistical distribution are 35 and 33, respectively, determine the mode of the distribution.
110. If the combined (weighted) mean of the following frequency distribution table is 54, then find the value of K: | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|-------|-------|-------|--------| | Frequency | 7 | 11 | K | 9 | 13 |
111. From the following cumulative frequency distribution table, construct a frequency distribution table and determine the **mode** of the data: | Class Boundary | Less than 10 | Less than 20 | Less than 30 | Less than 40 | Less than 50 | Less than 60 | Less than 70 | Less than 80 | |--------------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------|--------------| | Cumulative Frequency | 4 | 16 | 40 | 76 | 96 | 112 | 120 | 125 |
112. From the following table, calculate the average marks of 52 students in Class 10 of a school using both the **direct method** and the **assumed mean method**: | Number of Students | 4 | 7 | 10 | 15 | 8 | 5 | 3 | |--------------------|---|---|----|----|---|---|---| | Marks |30 |33 | 35 | 40 |43 |45 |48 |
113. The ages (in years) of some students are: 10, 11, 9, 7, 13, 8, 14; the median of their ages is _____ years.
114. If the data set \(6, 8, 10, 12, 13, x\) arranged in ascending order has equal mean and median, find the value of \(x\).
115. If the mean of a statistical distribution is 4.1, \(∑f_i x_i = 132 + 5k\), and \(∑f_i = 20\), then what is the value of \(k\)?
116. If for a set of data, \[ \sum_{i=1}^n (x_i - 7) = -8 \quad \text{and} \quad \sum_{i=1}^n (x_i + 3) = 72, \] then find the values of \(\bar{x}\) (the mean) and \(n\) (the number of data points).
117. Determine the combined mean using the step deviation method from the following data:
Class Interval0 - 1010 - 2020 - 3030 - 4040 - 5050 - 60
Frequency7561282
118. If the median of the following data is 28.5 and the total frequency is 60, determine the values of x and y.
Class Interval0-1010-2020-30
Frequency5x20
30-4040-5050-60
15y5
119. Determine the mode of the following grouped frequency distribution:
Class Interval3-66-99-12
Frequency2612
12-1515-1818-2121-24
2421123
120. If \(u_i = \frac{x_i − 35}{10}\), \(Σf_iu_i = 30\), and \(Σf_i = 60\), then find the value of \(\bar{x}\).
121. If 12 is removed from the dataset 10, 14, 12, 16, 8, 9, 24, 20, then the median will increase by _____.
122. Given: \(u_i = \frac{x_i - 20}{10}\), \(\sum f_i u_i = 50\), \(\sum f_i = 100\) Find the value of \(\bar{x}\) (mean).
123. If the median of the following data is 28.5, and the total frequency is 60, determine the values of x and y.
Class Interval0-1010-2020-30
Frequency5x20
30-4040-5050-60
15y5
124. If the median of the given data is 32, determine the values of \( x \) and \( y \) when the total frequency is 100.
Class Interval0-1010-2020-3030-4040-5050-60
Frequency10x2530y10
125. Calculate the average marks obtained by the students, given the following cumulative frequency distribution: | Marks | Number of Students | |--------------|--------------------| | Less than 10 | 6 | | Less than 20 | 10 | | Less than 30 | 18 | | Less than 40 | 30 | | Less than 50 | 46 |
126. Find the median from the following grouped frequency distribution: | Class Interval | Frequency | |----------------|-----------| | 0–10 | 4 | | 10–20 | 7 | | 20–30 | 10 | | 30–40 | 15 | | 40–50 | 10 | | 50–60 | 8 | | 60–70 | 5 |
127. Find the mode from the following grouped frequency distribution: | Class Interval | Frequency | |----------------|-----------| | 3–6 | 2 | | 6–9 | 6 | | 9–12 | 12 | | 12–15 | 24 | | 15–18 | 21 | | 18–21 | 12 | | 21–24 | 3 |
128. Given that the mean of the data is \( 20.6 \), determine the value of \( a \).
\( x_i \)1015\( a \)2535
\( f_i \)3102575
129. If \( u_i = \frac{x_i - 45}{10} \), \( ∑f_i u_i = -16 \), and \( ∑f_i = 200 \), then what is the value of \( \bar{x} \)?
130. If \(u_i = \frac{x_i - 30}{10}\), \(∑f_i = 50\), and \(∑u_i f_i = 25\), then what is the value of \(\bar{x}\)?
131. If the median of the given data is 28.5 and the total frequency is 60, determine the values of x and y.
Class Interval0-1010-2020-30
Frequency5x20
30-4040-5050-60
15y5
132. If the median of the following data is 32, find the values of \(x\) and \(y\) when the total frequency is 100:
Class interval0–1010–2020–3030–4040–5050–60
Frequency10\(x\)2530\(y\)10
133. Given that the combined (weighted) mean of the following frequency distribution is 50 and the total frequency is 120, find the values of \( f_1 \) and \( f_2 \). | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|--------|--------|--------|---------| | Frequency | 17 | \( f_1 \) | 32 | \( f_2 \) | 19 |