1The mathematics marks of 27 students of class 10 in the second terminal examination are: 25, 15, 30, 22, 27, 12, 25, 30, 22, 24, 15, 23, 19, 27, 28, 17, 19, 22, 25, 15, 14, 13, 28, 26, 18, 20, 22. What is the average mark?
2For the same 27 marks, how many students scored less than the average and how many scored more?
3For the same 27 marks, find the median, the first quartile and the third quartile.
4For the same 27 marks, which mark was obtained by the largest number of students? How many obtained it, and what is this value called?
5Find the mean of 35, 36, 42, 45, 48, 52, 58, 60.
6Find the mean of 13.5, 14.2, 15.8, 15.2, 16.9, 16.5, 17.4, 19.3, 15.3, 15.9.
7Find the mean: x = 5, 8, 10, 12, 14, 16 with frequencies f = 4, 5, 8, 10, 2, 2.
8In a national football league, players scored these goals: 12 goals by 2 players, 13 by 4, 14 by 6, 15 by 12, 16 by 10 and 17 by 6. Find the mean number of goals.
9Find the mean age of bus passengers by the direct method and the short-cut method. Age (years): 0-10, 10-20, 20-30, 30-40, 40-50. Number of persons: 5, 9, 15, 7, 4.
10Find the mean science mark of class 10 students by both methods. Marks: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70. Students: 1, 4, 10, 8, 7, 5.
11Find the mean daily wage of workers by both methods. Wages (Rs.): 200-400, 400-600, 600-800, 800-1000, 1000-1200. Workers: 3, 7, 10, 6, 4.
12Find the mean mathematics mark of class 10 students by both methods. Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60. Students: 7, 5, 6, 12, 8, 2.
13Find N when \( \overline{X} = 49 \) and \( \sum fm = 980 \).
14Find \( \sum fm \) when \( \overline{X} = 102.25 \) and \( N = 8 \).
15Find \( \sum fd \) when \( A = 100 \), \( \overline{X} = 90 \) and \( N = 10 \).
16Find A when \( \overline{X} = 41.75 \), \( \sum fd = 270 \) and \( N = 40 \).
17The mean is 32.5. Find k. Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60. Students: 5, 10, k, 35, 15, 10.
18The mean is 46.2. Find p. X: 0-20, 20-40, 40-60, 60-80, 80-100. f: 35, 400, 350, p, 65.
19The mean is 36.4. Find y. Marks: 16-24, 24-32, 32-40, 40-48, 48-56, 56-64. Students: 6, 8, y, 8, 4, 2.
20The mean daily expenditure is 264.67. Find the missing frequency. Expenditure: 0-100, 100-200, 200-300, 300-400, 400-500, 500-600. Students: 20, 30, ?, 20, 18, 12.
21Prepare a frequency distribution table with class interval 10 and find the mean: 15, 51, 32, 12, 32, 33, 23, 43, 35, 46, 57, 19, 59, 25, 20, 38, 16, 45, 39, 40.
22Prepare a frequency distribution table with class interval 5 and find the mean: 25, 15, 24, 42, 22, 35, 34, 41, 33, 38, 54, 50, 36, 40, 27, 18, 35, 16, 51, 31, 23, 9, 16, 23, 31, 51, 7, 30, 17, 40, 60, 32, 50, 10, 23, 12, 21, 28, 37, 20, 58, 39, 10, 41, 13.
23Find the mean. Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60. Frequency: 8, 10, 14, 10, 8, 10.
24Find the mean daily wage. Wages (Rs.): 0-50, 50-100, 100-150, 150-200, 200-250, 250-300. Workers: 1, 2, 3, 4, 1, 2.
25Why is the mid-value of each class used to find the mean of a continuous series?
26A student takes A = 35 and finds \( \sum fd = -340 \). Before finishing, how can the student tell whether the mean is above or below 35?
27Find the mean age of the 24 park visitors again, this time by the assumed mean method with A = 35. The frequencies for 0-10 up to 50-60 are 3, 4, 5, 6, 4, 2.