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Kindly give correct answers and step by step working.do not skip steps.Mention clearly about the formula and the conversion.be very clear.do not skip steps.be very clear.NUMBER THE Ans CLEARLY.

QMT110 OCT2007

QUESTION 1 A group of 60 students was given a biology test, with a total score of 40 marks. The marks obtained by the students are summarized below. Mark 20 25 27 28 30 31 34 37 38 39 Number of student 2 5 6 3 10 9 7 4 6 a) Find the mean, mode and the median marks obtained by the students in the test (6 marks) Interpret the value of the mode obtained in (a). (1 mark) c) Find the standard deviation for the marks of students. (4 marks) d) Calculate the coefficient of skewness. Hence, comment on the shape of the distribution. (4 marks) QUESTION 2 The following table shows the time (to the nearest 0.1 minute) of each call for 100 telephone calls received in a financial office. Time (minute) Number of call 2.0-3.9 4 4.0 -5.9 11 6.0 - 7.9 16 8.0 - 9.9 38 10.0 -11.9 24 12.0 - 13.9 14.0 - 15.9 a) Calculate the mean and standard deviation for the time distribution. (7 marks) b) Calculate the median of time call and explain its meaning. (4 marks) c) Given the mean and the variance of time calls at the management office are 10.30 minutes and 1.51 minutes respectively, determine which distribution is more consistent in time call. (4 marks)QUESTION 1 a) Identify the types of variables (discrete or continuous): the number of mango trees in a village. the length of a human arm. the number of rooms in a hotel. the expansion of a metal rod when heated. (2 marks) b) The following table shows the income distribution (RM per month) of 120 fishermen. Income (RM per month) No. of Fishermen 250 and under 300 5 300 and under 350 10 350 and under 400 20 400 and under 450 28 450 and under 500 32 500 and under 550 18 550 and under 600 7 Calculate the mean income of the fishermen. (4 marks) Calculate the standard deviation of the income of the fishermen. (4 marks) Calculate the coefficient of variation. (2 marks)