What is statistics? Write a note on various functions and applicability of statistics in business.
[7 marks]What do you understand by 'Central tendency'? Describe the measures of central tendency. Also, define the related positional measures, like quartiles, deciles and percentiles.
[7 marks]Compute the Mean, median, Mode, Variance and Standard deviation on the following data. Class Frequency 20-30 30-40 40-50 1 50-60 0 60-70 70-80 1
[3 marks]Construct a histogram, a frequency polygon, and Ogive for the following frequency distribution. Class interval Frequency 50-60 13 60-70 27 70-80 43 80-90 31 90-100 9
[7 marks]Explain the measures of dispersion? What does a measure of variation serve? In the light of these, comment on some of the well-known measures of variation.
[7 marks]Machines A, B, and Call produce the same two parts, Xand Y. Of all the parts produced, machine Aproduces 60%, machine Bproduces 30%, and machine C produces 10%. In addition, 40% of the parts made by machine Aare part X. 50% of the parts made by machine Bare part X. 70% of the parts made by machine Care part X. Apart produced by this company is randomly sampled and is determined to be an Xpart. With the knowledge that it is an Xpart, revise the probabilities that the part came from machine A, B, or C.
[7 marks]Explain the properties of Correlation and Regression in detail. Differentiate r and r2 OR1
[7 marks]What is Probability? What are the different approaches of probability explain in detail. Explain the structure of probability in brief.
[7 marks]Determine the value of the coefficient of correlation for the following data. X 4 6 7 11 14 17 21 Y 18 12 13 8 7 7
[4 marks]Asample of 12 small accounting firms reveals the following numbers of professionals per office. 6 , 8, 10, 13, 11, 9, 7, 15, 12, 5, 13, 1. Determine the mean 2. Determine the mode 3. Determine the median 4. Determine the range 5. Determine the standard deviation 6. What is the CV for this data 7. Determine P15
[4 marks]Differentiate between Permutation and Combination with appropriate examples.
[7 marks]Abag contains 10 items of which 3 are defective. If three items are drawn one after another without replacement, find the probability that all are defective.
[7 marks]Compute a spearman’s rank correlation for the following variables to determine the degree of association between the two variables. X 23 41 37 29 25 17 33 41 40 28 19 Y 201 259 234 240 231 209 229 246 248 227 200
[7 marks]Arithmetic mean and standard deviation of monthly profits of two companies X and Yfor a year are given below : X Y Mean 100 90 Standard Deviation 25 18 Comment on the consistency of these companies with respect to their profits by applying coefficient of variation technique.
[7 marks]What is Probability? Explain the structure of probability in brief.
[7 marks]Aproduction department uses a sampling procedure to test the quality of newly produced items. The department employs the following decision rule at an inspection plan: If a sample of 14 items has a variance of more than 0.005, the production line must be shut down for repair. The following data have just been collected: 3.43, 3.45, 3.43, 3.48, 3.52, 3.50, 3.39, 3.48, 3.41, 3.38, 3.49, 3.45, 3.51, and 3.50. Should the production line be shut down? Why or why not?
[7 marks]Find the regression equation of Yon Xwhere Yand Xare the marks obtained by 10 students as given below: Y 20 60 55 45 75 35 25 90 10 50 X 20 45 65 40 55 35 15 80 25 50
[7 marks]