27. The combined mean and variance of the salary of 250 workers of city A and city B are 560 and 5497 respectively. The mean and the variance of the salary of 100 workers of city A are 650 and 121 respectively. Find the variance of the salary in city B.28. Find the arithmetic mean from the following data: [Ans: Rs. 264.67]ExpenditureNo. of personsExpenditureNo. of persons

Above 0150Above 40030

Above 100130Above 50012

Above 200100Above 6000

Above 30050

29. Determine the mode of the following data:X:20212223242526272829

F:69421087513

[topic: measure of central tendency and dispersion]1. An examination was held to decide on the award of a scholarship. The weights of various subjects were different. The marks obtained by two candidates A and B are given below: [ans: A]SubjectsWeightsMarks obtained by

AB

Statistics46360

Accountancy26564

Marketing26066

English26050

If the betterness of the performance is the criteria for awarding a prize, who should get the prize? 2. Calculate the mode from the following distributions of quantity of petrol (in litres) used by the people per month:Quantity0 100100 200200 - 300300 400400 500500 600

Frequency13182720176

Also locate the mode graphically. [ans: 256.25]3. The arithmetic mean of scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. Find the mean score of the remaining 55% of the group. [ans: 51.36]4. 100 students took a test. The result of those who secured less than 60% mark are given below:Marks0 2020 4040 60

No. of students162430

If the average marks of all students was 50, find out the average mark of those who secured more than 60% marks. [ans: 87.33]5. The following are monthly salaries in rupees of 20 employees of a firm130 62145118125761511421109865116100103718580122132956. The firm gives bonus of Rs. 10, 15, 20, 25 and 30 for individuals in the respective salary groups exceeding Rs. 80, exceeding Rs. 80 but not exceeding Rs. 100 and so on upto exceeding Rs. 140 but not exceeding Rs. 160. Find the average bonus paid per employee. [ans: Rs. 19]7. The mean mark of 100 students was found to be 40. Later on it was discovered that a score 53 was misread as 83. Find the correct mean corresponding to the correct score. What will be the mean mark when the wrong score is omitted? [ans: 39.7 & 39.57]8. An aeroplanes travels the distance of 2500, 1200 and 500 kms. at speed 500, 400 and 250 km/hr. respectively. Find the average speed for the entire trip, commenting on the choice of your average. [ans: 420 km/hr]9. Calculate the arithmetic mean, geometric mean and harmonic mean of the following observations 32, 35, 36, 37, 39, 41, 43 and show that AM>GM>HM. [ans: 37.57, 37.41, 37.23]10. The mean mark for a group of 250 students is 57. If 3 students got mark between 0-10, 8 students between 10 20, 11 students between 20 30, 15 students between 30 40, 25 students between 50 60, 40 students between 60 70, 2 students between 80 90 and 1 student between 90 100; find the number of students getting marks between 40 50 and 70 80, if the maximum mark of the test was 100. [ans: 60, 85]11. Find the missing frequencies in the following distributions, if N = 100 and the median of the distribution is 30. [ans: 15, 10]Marks:0 1010 2020 3030 4040 5050 60

No. of students10-2530 10

12. Calculate the mode from the following data: [Ans: 44 marks]Marks:0 1010 2020 4040 5050 70

No. of students515403228

13. The table given below represents the daily wage distribution of 130 workers. Find out the range of income of the middle 60% workers.Wages (Rs. Per Workers)>70>85>100>115>130>145>160>175

No. of Workers130122109794426145

514. Find the median, two quartiles, 4th decile and the 80th percentile. Calculate the median and the quartiles for the following data:Amount of wages per dayNo. of worker receiving such rate of wagenot exceeding Rs. 885Over Rs 8 but not exceeding Rs. 1065Over Rs 10 but not exceeding Rs. 1259Over Rs 12 but not exceeding Rs. 1450None is earning less than Rs. 6Ans: Md=Rs.9.37, Q1=7.52, Q3=11.5015. The following table gives the workers and the earning in rupees of two factories A and B. Represent the data graphically so as to bring out the inequalities of the distribution of earnings:Earning:9001000110012001300140015001600Workers of A:33302421181293Workers of B:322215121062116. You are given two variables A and B. Using quartiles deviation state which is more variable:AValue:15202530354045Frequency:153356103403210BValue:100150200250300350400Frequency:8121322682Ans: For A Q1=25, Q3=35 and Coeff. Of Q.D=0.17 & For B Q1=150, Q3=250 and Coeff. Of Q.D=0.2517. Weights of a group of individuals are given below in kgs. Find out the mean, standard deviation, coefficient of s.d and the coefficient of variation:Weights (kg) above:010203040No. of persons:10088552510 [Ans: mean= 22.8 kg, coeff. Of s.d=0.502, coeff. Of variation= 50.2%]18. For a group containing 100 observations the arithmetic mean and standard deviation are 8 and . For 5 observations selected from these 100 observations, the mean and the standard deviation are 10 and 2 respectively. Find the arithmetic mean and the standard deviation of the other half.[Ans: 2=6, 2=3]19. The following data relate to the profit/loss made by various companies during 1981-92Profit/Loss (0000 Rs.)-10 to 00-1010-2020-3030-4040-50No. of Comp:192449873127Calculate the mean and the standard deviation of profits. [Ans: =22.09, =13.55]20. An analysis of the monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following result:Firm AFirm BNo. of workers:500600Average monthly wage:Rs. 586Rs. 575Variance of distribution of wage:81100i) Which firm A or B has a larger wage bill?ii) In which firm A or B is there greater variability individual wages?iii) Calculate the average monthly wage and the variance of wages of all the workers of the firm A and B taken together.iv) Which firm is more equitable in regard to wages?21. Following are the marks obtained by two students A and B in 10 test of 100 marks each:Test12345678910

Marks of A4480764527268566054

Marks of B48755460636972515766

i) Who is better?ii) Who is intelligent?iii) If the consistency of performance is the criteria for awarding a prize, who should get the prize?22. The following are the monthly salaries in rupees of 30 employees in a firm:14013912611410088627799103 10812914414813463691481321181421161231049580 85106123133The firm gave bonus of Rs. 10, 15, 20, 25, 30 and 35 for individuals in the respective salary groups, exceeding 60 but not exceeding 75, exceeding 75 but not exceeding 150. Find the average bonus paid and the standard deviation.23. Draw Lorenz curve for the following data:No. of Persons1310541

Wealth (000)Rs.78100758025

24. The mean and standard deviation of a sample of size 10 were found to be 9.5 and 2.5 respectively. Later on, an additional observation became available. This was 15.0 which is included in the original sample. Find the mean and the standard deviation of the 11 observation.25. The price of mansuli rice per Kg for the last seven days in two markets are recorded below:DaysSundayMondayTuesdayWednesdayThursdayFridaySaturday

Price per Kg.Market X8.08.59.09.259.2510.010.0

Market Y8.58.59.259.59.59.510.75

Which market shows greater variance in price?26. An analysis of the monthly wages paid to workers in two firms A and B belonging to the same industry gives the following result.Firm AFirm B

No. of Workers:160150

Average wages:260275

Variance of wage distribution100121

[ans: 25]