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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.

QMT245OCT2008

QUESTION 1 The IQ (Intelligent Quotient) scores of the fifty students in the Essential Years Kindergarten are recorded as follows. IQ Scores 80 - 89 90 - 99 100 - 109 110-119 120 - 129 130-139 Frequency 6 13 16 9 4 2 a) Construct a histogram for the above table, Estimate the mode based on the plotted graph. (5 marks) b) Calculate the mean and median. (4 marks) c) Find the variance and standard deviation of the IQ scores. (5 marks) d) Determine the shape of the distribution using the values obtained from central tendency measurements. (2 marks)QUESTION 1 Thirty six batteries were tested to see how long they would last. The frequency distribution is shown here. Lifespan (Hours) 11-13 14-16 17-19 20-22 23-25 Frequency 3 12 15 3 3 a) Display the data using frequency polygon. (4 marks) b) Find the median and mode for this set of grouped data. (7 marks) c) Calculate the mean and standard deviation of the above distribution. (6 marks)QUESTION 1 The masses of 45 prawns in a pond are given in the following table. Mass (in g) 30-39 40-49 50-59 60-69 70-79 Frequency, f 2 8 17 13 5 a Draw a histogram and estimate the mode. Comment on the distribution. (8 marks) b) Find the median. (3 marks) c) Calculate the mean and variance of the above distribution. (6 marks)QUESTION 1 An industrial organisation gives an aptitude test to all applicants for employment. The results in the case of 105 people taking the test are as follows: Score 0-2 2-4 4-6 6-8 8-10 Total Frequency 6 26 36 22 15 105 For the above frequency distribution, a) construct a frequency polygon, (3%% marks) b) find the modal score. (215 marks) QUESTION 2 For the set of numbers, x : 6.5, 8.5, 9.3, 9.9, 9.7, 9.5, calculate a) the median. (2 marks) b) the variance by using the formula s' = [ E (x - x )" ] where x is the mean of x. n - (4 marks)