Honours
ENGLISH PROGRESSING ACADEMY
Rafique Mansion, House no-Y7, Road no-01, Block-A, Chandgaon R/A, Ctg.
Directed by- S.M. Towhidul Alam, Lecturer Department of Accounting
Anwara University College, Anwara, Chittagong.
Committed to provide the service for H.S.C, BBA/ BBS (Hon’s/Pass), MBS (Preli&Final)
Solution for course relating Accounting, Finance, Mathematics & Statistics.
Mobile: 01819-062856
Measures of dispersion
1. The following data give the number of finished goods turned out per day by different no. of workers in a factory:
No. of articles: 18 19 20 21 22 24 25 26 27
No. of workers: 3 7 11 14 17 13 8 5 4
Find the mean value, standard deviation, co-efficient of variation, of daily output of finished articles.
2. Find out the range, mean deviation, Quartile deviation, variance and co-efficient of variation from the following distribution.
Profit (in crores) no. of companies
Less than 10 8
” ” 20 20
” ” 30 40
” ” 40 70
” ” 50 90
” ” 60 100
Also determine the interquartile range and semi-interquartile range
3. The following frequency distribution gives the weight of a group of people in a city.
Weight (lb) frequency weight (lb) frequency
110-119 5 150-159 16
120-129 7 160-169 10
130-139 12 170-179 7
140-149 20 180-189 3
i) What is mean weight? ii) calculate the variance
iii) Calculate the co-efficient of variation. iv) calculate the co-efficient of Q.D.
4. A collar manufacturer is considering the production of a new style of collar to attract young men. The following statistics of neck size are available base on measurement of a typical group of the college students.
Mid value (in inches): 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16
No. of students : 2 16 36 60 76 37 18 3 2
Compute the S.D. and use the criterion where is the A.M and — is the S.D to determine the largest and the smallest size of the collar. He should make in order to meet the needs of pratically all. The customers bearing in mind that collars are worn on average 3/4 inch longer than neck size.
5. The scores of two batsmen A and B. in ten consecutive innings
A: 70 34 46 58 62 39 11 80 20 50
B: 48 52 66 44 32 58 80 42 68 40
Find who is better scorer and which of the batsman is more consistent in scoring.
6. Following are the marks obtained by two students A and B in 10 tests of 100 marks in each.
Tests : 1 2 3 4 5 6 7 8 9 10
A : 44 80 76 48 52 72 68 56 60 54
B : 48 75 54 60 63 69 72 71 57 66
If the consistency of results in the only criterion for awarding a prize who should get the prize?
7. The mean and S.D of two observation are 7 and 1 respectively. Find the two observations.
8. co-efficient of variation of two series are 60% and 80 %.Their standard deviations are 20 and 16. What are their arithmetic mean?
9. Lives of two model of refrigerators in recent survey -
Life No. of refrigerators
(No. of years) Model A Model B
0-2 5 2
2-4 16 7
4-6 13 12
6-8 7 19
8-10 5 9
10-12 4 1
What is the average life of each model of these refrigerators? Which model has greater uniformity?
10. For two firms A and B belonging to same industry. The following details are available.
Firm- A Firm- B
No. of Employees: 100 200
Average wage per month: Tk. 240 Tk. 170
Variance of wage per month: Tk. 36 Tk. 64
Find. i) Which firm pays out longer amount or monthly wage?
ii) Which firm shows greater variability in the distribution of wages?
iii) The average monthly wages and the S.D of the wages of all employees in both the firm.
11. An analysis of monthly wages paid to the workers in the mill X, Y and Z gives in following
Results-
Mill No. of workers monthly wages (Average) S.D
X 50 113 6
Y 60 120 7
X 90 115 8
i) Calculate the mean wages and S.D of all workers taken together.
ii) Which mill is more consistent in wage payment?
12. The first of two subgroups has 100 items with mean 15 and S.D 3. If the whole group has 250 items with mean 15.6 and S.D . Find the mean and S.D of the second sub-group.
13. Find the missing information from the following:
Group I Group II Group III combined
Number : 50 ? 90 200
Standard Deviation : 6 7 ? 7.746
Mean : 113 ? 115 116
14. The average marks by obtained by close of 100 students was found to be 58 with a standard deviation of 16 marks. Later it was discovered that the score of two students were wrongly taken as 68 and 25 instead of 86 and 52 respectively. Find the correct mean and S.D
15. The mean and S.D of 30 items are found to be 10 and 5 respectively. At the time of checking it was found that one item 8 was incorrect. Calculate the correct mean and S.D if,
i) The wrong item is omitted ii) it is replaced by 10.
16. The mean and S.D of a sample size 10 were found to be 9.5 and 2.5 respectively. Later on an additional observation become available. This was 15.0 and included in the origin sample. Find the mean and S.D of the 11 observation.
17. The mean and S.D calculate from 20 observation are 15 and 10 respectively. If and additional observation 36. Left out through oversight be included in the calculation find the correct mean and S.D.
18. Construct a box plot on the basis of quartile deviation and comment on the distribution.
Midvalue of classes: 14 16 18 20 22 24 26
No. of students: 12 14 50 60 32 20 10
19. You are supplied with the following data about height of boys and girls of a college.
Boys Girls
Number: 72 38
Average height 68kg 67 kg
Variance of height 9 kg 4 kg
a) complete the combined average height to the student.
b) complete the combined standard deviation of the students.
c) obtain measures of variability separately for boys and girls.
Who has greater variability in heights?
20. Calculate mean deviation from median and mode of the following wage distribution:
Weekly wages (in Tk) No. of workers
140-150 4
150-160 6
160-170 10
170-180 18
180-190 9
190-200 3
21. The mean of 200 items is 48 and their standard deviation is 3. Find the sum and sum of square of all this.