Question Paper1. A cellphone manufacturing company offered an exchange offer for the latest model. People can submit exchange their old phone by paying the additional amount. The number of days a person used a phone before exchanging it is as follows: Number of days usedLess than 400400 to 900900 to 1400More than 1400Number of phones returned21032538580What is the probability that a person uses his cell phone for more than 900 days? 2. 1500 students were interviewed about the number of sports they play in the school and the data is tabulated below: Number of sports played012Number of students211714375Find the probability that a student interviewed at plays 1 sport. 3. From the following graph, find how many generators were sold by the company in Assam? 4. The monthly expenses in lakhs in various departments of a multinational company are given below. Construct a grouped frequency distribution table by dividing the range into class intervals of equal width, each corresponding to 2 lakh rupees in such a way that the mid-value of the first class interval corresponds to 12 lakhs.14, 16, 16, 14, 22, 13, 15, 24, 12, 23, 14, 20, 17, 21, 22, 18, 18, 19, 20, 17, 16, 15, 11, 12, 21, 20, 17, 18, 19, 23. 5. Following table shows the birth month of 40 students of class IX. JanFebMarAprMayJuneJulyAugSepOctNovDec444352152243What is the probability that a student was born in August? 6. What are different numbers representing the family members of the students? 7. What is the median of the data 134, 74, 90, 109, 95, 105, 95, 85, 101, 121. 8. Find the mean of first 12 even natural numbers. 9. From the following graph, The number of students whose family members size is 10 is less than 3 times the number of students whose family size is 9. State whether this statement is true or false?10. Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes. OutcomeNo headOne headTwo headsThree headsFrequency19373113If the three coins are tossed again, find the probability of getting 2 heads. 11. What is descrete frequency distribution? 12. The mean of the following frequency distribution is 20. Find the value of p. x:151718 + p2123f:234p5613. A survey is conducted to find the demand of various shirt sizes and the following observations were obtained. Size:38394041424344TotalNumber of sales274021161487125Find the modal shirt sizes from the survey results. 14. Define the algorithm in the construction of a grouped frequency distribution. 15. The actual weights of 11 sugar bags (in kg) marked as 5 kg is given as 4.97, 5.05, 5.08, 5.03. 5.00, 5.06, 5.00, 5.07, 5.04, 4.98, 5.08.Find the probability that any of these bags chosen at random contains more than 5 kg of floor. 16. If the mean of the following distribution is 6, find the value of p x:24610p + 5f:3231217. By studying the following bar graph specify the year in which import is minimum.18. What is the information depicted by the following bar graph?19. The heights of 108 children is given in the following table. Construct a histogram and a frequency polygon on the same axes Height(in cm.)120to124124to128128to132132to136136to140140to144144to148148to152152to156156to160160to164164to168No. ofChldren169182517137642120. The news paper circulation in different languages is shown in the following bar graph. By studying the graph, calculate the excess number of newspapers published in English over those published in Urdu.1. The sum of the deviations of a set of n values x1, x2, ......, xn measured from 50 is -10 and the sum of deviations of the values from 46 is 70. Find the values of n and the mean. 2. Find the mean of first 12 even natural numbers. 3. The mean of 99 numbers is 47. If 11 is subtracted from every number, what will be the new mean? 4. Find the median of 44, 46, 130, 102, 64, 95, 74, 61, 60. If 61 is replaced by 98, what is the new median. 5. By studying the following bar graph specify the year in which export is maximum. 6. Define cumulative frequency. 7. 1500 students were interviewed about the number of sports they play in the school and the data is tabulated below:Number of sports played012Number of students211714375Find the probability that a student interviewed at plays at most one sport. 8. The average speed of 7 motorcycles is 55 kmph. The individual speeds of six of them(in kmph) are 52, 54, 55, 53, 56 and 64. Find the speed of the seventh motorcycle. 9. Find the sum of the deviations of the variate values 4, 5, 7, 9 and 15 from their mean.10. Study the following graph and state whether the statement 'The sale in the year 2006 - 2007 is twice that of the year 2005 - 2006' is true or false.11. Candidates of four schools appear in a competitive exam. The data is as follows:SchoolsNo. of CandidatesAverage marksABCD40p526050805575If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from School B.12. What are the uses of the mode?13. Find the value of p, if the mean of the following frequency distribution is 20.6.x:10p202535f:310257514. What is the class size of the following?100 - 120, 120 - 140, 140 - 160.15. Write the class size and the class limits for the following data37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87 and 92.16. Find the value of p if the mean of the following distribution is 12.58x:5810p152025f:2582274217. Three coins are tossed simultaneously 400 times and the frequencies of different outcomes is recorded below:Outcome3 heads2 heads1 headNo headFrequency4614415456Find the probability of getting two heads and one tail.18. A fertilizers manufacturing company's production is represented in the following tableYear200520062007200820092010Fertilizers(in thousand tonnes)204050405030With the help of a bar graph, find which of the following answers is correct for 'The consecutive years during which there was maximum decrease in the production of the fertilizers'1994 and 19951992 and 19931996 and 19971995 and 199619. Construct a frequency polygon for the following dataAge(in years)0 - 22 - 44 - 66 - 88 - 1010 - 1212 - 1414 - 1616 - 18Frequency357910764220. The Meteorological department in a city reported the duration of sunshine (in hours) as follow:9.7, 5.3, 3.6, 1.6, 1.7, 2.5, 2.7, 8.5, 10.4 and 10.9.Verify that10(xi - X)Σi=121. In the following figure, a cyclic quadrilateral PQRS is shown. If ∠PRQ = 25° and ∠QSR = 40°, find ∠PQR.22. In the following figure a ΔPQR is shown. S is a point on the base PR such that PQ = QS. Lines parallel to the sides PR and QS through the vertices Q and R respectively are drawn. If these lines intersect at T, prove that QTRS is a cyclic quadrilateral.