Statistics
Q1. Calculate the mean for the following distribution:
x: | 5 | 6 | 7 | 8 | 9 |
f: | 4 | 8 | 14 | 11 | 3 |
Q2. If the mean of the following data is 20.6. Find the value of p.
x: | 10 | 15 | p | 25 | 35 |
f: | 3 | 10 | 25 | 7 | 5 |
Q3. Find the value of p for the following distribution whose mean is 16.6
x: | 8 | 12 | 15 | p | 20 | 25 | 30 |
f. | 12 | 16 | 20 | 24 | 16 | 8 | 4 |
Q4. Find the missing frequency (p) for the following distribution whose mean is 7.68.
x: | 3 | 5 | 7 | 9 | 11 | 13 |
f: | 6 | 8 | 15 | p | 8 | 4 |
Q5. Find the value of p, if the mean of the following distribution is 20.
x: | 15 | 17 | 19 | 20 + p | 23 |
f: | 2 | 3 | 4 | 5p | 6 |
Q6. The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students
Age (in years): 15 | 16 | 17 | 18 | 19 | 20 |
No. of students: 3 | 8 | 10 | 10 | 5 | 4 |
Q7. Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
X: 10 | 30 | 50 | 70 | 90 |
|
f: 17 | f1 | 32 | f2 | 19 | Total 120. |
Q8. The arithmetic mean of the following data is 14. Find the value of k
𝑥𝑖: | 5 | 10 | 15 | 20 | 25 |
𝑓𝑖: | 7 | k | 8 | 4 | 5. |
Q9. The arithmetic mean of the following data is 25, find the value of k.
𝑥𝑖: | 5 | 15 | 25 | 35 | 45 |
𝑓𝑖: | 3 | k | 3 | 6 | 2 |
Q10. If the mean of the following data is 18.75. Find the value of p.
𝑥𝑖: | 10 | 15 | p | 25 | 30 |
𝑓𝑖: | 5 | 10 | 7 | 8 | 2 |
Q11. Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0,1,2,3,4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss
No. of heads per toss (x): | 0 | 1 | 2 | 3 | 4 | 5 |
No. of tosses (f): | 38 | 144 | 342 | 287 | 164 | 25 |
Q12. The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:
Marks(x): | 15 | 20 | 22 | 24 | 25 | 30 | 33 | 38 | 45 |
Frequency (f): | 5 | 8 | 11 | 20 | 23 | 18 | 13 | 3 | 1 |
Find the average number of marks.
Q13. The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table:
No. of students absent (x): | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
No. of days(f): | 1 | 4 | 10 | 50 | 34 | 15 | 4 | 2 |
Find the mean number of students absent per day.
Q14. In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:
No. of misprints per page (x): 0 | 1 | 2 | 3 | 4 | 5 |
No. of pages (f): 154 | 95 | 36 | 9 | 5 | 1 |
Find the average number of misprints per page.
Q15. The following distribution gives the number of accidents met by 160 workers in a factory during a month.
No. of accidents (x): | 0 | 1 | 2 | 3 | 4 |
No. of workers (f): | 70 | 52 | 34 | 3 | 1 |
Find the average number of accidents per worker.
Q16. Find the mean from the following frequency distribution of marks at a test in statistics:
Marks(x): | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
No. of students (f): | 15 | 50 | 80 | 76 | 72 | 45 | 39 | 9 | 8 | 6 |
Q17. The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.
Expenditure (in rupees) (x) | Frequency (fi) | Expenditure (in rupees) (x1) | Frequency (fi) |
100 – 150 | 24 | 300 – 350 | 30 |
150 – 200 | 40 | 350 – 400 | 22 |
200 – 250 | 33 | 400 – 450 | 16 |
250 – 300 | 28 | 450 – 500 | 7 |
Find the average expenditure (in rupees) per household.
Q18. A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
Number of plants: | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 12-14 |
Number of houses: | 1 | 2 | 1 | 5 | 6 | 2 3 |
Which method did you use for finding the mean, and why?
Q19. Consider the following distribution of daily wages of 50 workers of a factory Daily wages (in Rs). 100 - 120 120 - 140 140 - 160 160 - 180 180 - 200 Number of workers: 1 2 14 8 6 10
Find the mean daily wages of the workers of the factory by using an appropriate method.
Q20. Find the mean of each of the following frequency distributions: (5 − 14)
I. | Class interval: | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24-30 |
| Frequency: | 6 | 8 | 10 | 9 | 7 |
II. Class interval: 50 - 70 70 - 90 90 – 110 110 - 130 130 - 150 150 – 170
Frequency: 18 12 13 27 8 22
III. | Class interval: 0-8 | 8- 16 | 16- 24 | 24-32 | 32-40 |
| Frequency: 6 | 7 | 10 | 8 | 9 |
IV. |
Class interval: 0-6 |
6- 12 |
12- 18 |
18-24 |
24-30 |
| Frequency: 7 | 5 | 10 | 12 | 6 |
V. | Class interval: | 0- 10 | 10- 20 | 20-30 | 30-40 | 40-50 |
| Frequency: | 9 | 12 | 15 | 10 | 14 |
VI. Class interval: 0-8 8- 16 16-24 24-32 32 -40
Frequency: 5 9 10 8 8
| VII. | Class interval: | 0-8 | 8- 16 | 16- 24 | 24-32 | 32-40 | |||||
|
| Frequency: | 5 | 6 | 4 | 3 | 2 | |||||
VIII. Class interval: 10-30 30-50 |
50-70 |
70-90 |
90-110 |
110- 130 |
| |||||||
Frequency: 5 8 | 12 | 20 | 3 | 2 |
| |||||||
IX. Class interval: 25-35 35-45 45-55 55 - 65 65 – 75
Frequency: 6 10 8 12 4
X. | Classes: | 25 -29 30-34 | 35-39 | 40-44 | 45-49 | 50-54 | 55-59 |
| Frequency: | 14 22 | 16 | 6 | 5 | 3 | 4 |
Q21. For the following distribution, calculate mean using all suitable methods:
Size of item: | 1 -4 | 4-9 | 9- 16 | 16-27 |
Frequency: | 6 | 12 | 26 | 20 |
Q22. The following table shows the marks scored by 140 students in an examination of a certain paper:
Marks: 0- 10 10-20 20-30 30-40 40-50
Number of students: 20 24 40 36 20
Calculate the average marks by using all the three methods: direct method, assumed mean deviation and shortcut method.
Q23. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f1 and f2.
Class: | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 – 120 |
Frequency: | 5 | f1 | 10 | f2 | 7 | 8 |
Q24. The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.
Class interval: 11-13 13-15 15-17 17-19 19-21 21-23 23-25
Frequency: 7 6 9 13 - 5 4
Q25. If the mean of the following distribution is 27, find the value of p.
Class: 0 - 10 10 – 20 20 - 30 30 – 40 40-50
Frequency: 8 p 12 13 10
Q26. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
Number of mangoes: 50 - 52 53 – 55 56 - 58 59 - 61 62 -64
Number of boxes: 15 110 135 115 25
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Q27. The table below shows the daily expenditure on food of 25 households in a locality
Daily expenditure (in Rs): 100 - 150 150 - 200 200 - 250 250 - 300 300 -350
Number of households: 4 5 12 2 2
Find the mean daily expenditure on food by a suitable method.
Q28. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
Number of days: | 0 - 6 | 6 - 10 | 10 - 14 | 14 - 20 | 20 -28 | 28 - 38 | 38 - 40 |
Number of students: | 11 | 10 | 7 | 4 | 4 | 3 | 1 |
Q29. Following are the lives in hours of 15 pieces of the components of aircraft engine. Find the median:
715, 724, 725, 710, 729, 745, 694, 699, 696, 712, 734, 728, 716, 705, 719.
Q30. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Literacy rate (in %): 45 - 55 55 - 65 65 - 75 75 - 85 85 -95
Number of cities: 3 10 11 8 3
Q31. To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
Concentration of SO2 (in ppm) | Frequency |
0.00-0.04 | 4 |
0.04-0.08 | 9 |
0.08-0.12 | 9 |
0.12-0.16 | 2 |
0.16-0.20 | 4 |
0.20-0.24 | 2 |
Find the mean concentration of SO2 in the air.
Q32. Following is the distribution of I.Q. of loo students. Find the median I.Q.
I.Q.: 55-64 65-74 75-84 85-94 95-104 105-114 115-124 125-134 135-144
No of Students: 1 2 9 22 33 22 8 2 1
Q33. Calculate the median from the following data:
Rent (in Rs.): | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 | 85-95 |
No. of Houses: | 8 | 10 | 15 | 25 | 40 | 20 | 15 | 7 |
Q34. Calculate the median from the following data:
Marks below: | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
No. of students: | 15 | 35 | 60 | 84 | 96 | 127 | 198 | 250 |
Q35. An incomplete distribution is given as follows:
Variable : 0 – 10 10 - 20 20 – 30 30 - 40 40 – 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.
Q36. Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.
Age in years: 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40-50 |
No. of persons: 5 | 25 | ? | 18 | 7 |
Q36. Find the missing frequencies and the median for the following distribution if the mean is 1.46.
No. of accidents: | 0 | 1 | 2 | 3 | 4 | 5 | Total |
Frequency (No. of days): | 46 | ? | ? | 25 | 10 | 5 | 200 |
Q38. If the median of the following frequency distribution is 28.5 find the missing frequencies:
Class interval: 0-10 10-20 20-30 30-40 40-50 50-60 Total
Frequency: 5 f1 20 15 f2 5 60
Q39. The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:
Class interval | Frequency | Class interval | Frequency |
0-100 | 2 | 500-600 | 20 |
100-200 | 5 | 600-700 | f2 |
200-300 | f1 | 700-800 | 9 |
300-400 | 12 | 800-900 | 7 |
Q40. If the median of the following data is 32.5, find the missing frequencies.
Class interval: 0- 10 10-20 20-30 30-40 40-50 50-60 60-70 Total
Total Frequency: f1 5 9 12 f2 3 2 40
