1. Define what we mean by a variable, and explain the difference between a quantitative variable and a qualitative variable. (4 marks) 2. Define Statistics. Explain its types, and importance to trade, commerce and business.(4marks) 3. Describe the process of planning a statistical enquiry with special reference to its scope and purpose. (6marks) 4. In a survey of 102 male population of a village in Baragoi actively in cattle rustling, their ages (in years) were recorded arbitrary as follows; 34, 67, 40, 72, 37, 33, 42, 62, 49, 32, 52, 40, 31, 19, 68, 55, 57, 54, 37, 32, 54, 38, 20, 50, 56, 48, 35, 52, 29, 56, 68, 65, 45, 44, 54, 39, 29, 56, 43, 42, 22, 30, 26, 20, 48, 29, 34, 27, 40, 28, 45, 21, 42, 38, 29, 26, 62, 35, 28, 24, 44, 46, 39, 29, 27, 40, 22, 38, 42, 39, 26, 48, 39, 25, 34, 56, 31, 60, 32, 24, 51, 69, 28, 27, 38, 56, 36, 25, 46, 50, 36, 58, 39, 57, 55, 42, 49, 38, 49, 36, 48, 44 Summarizing data in a continuous frequency table making classes of 18 - 22, 23 - 27 etc. and calculate the following; a. Arithmetic mean, (1.5marks) b. Geometric mean (1.5 marks) C. Harmonic mean (1.5 marks) d. Median (1.5 marks) e. Mode (1.5 marks) f. 25 percentile, (1.5 marks) g. 3 quintile (1.5 marks) h. 4"decile (1.5 marks) i. Standard deviation (2 marks) j. Coefficient of variation (1marks) k. Coefficient of determination (1marks) 1. Kurtosis(1.5 marks)m. skewness(1.5 marks) 5. A manufacturer of metal pistons finds that on average, 12% of his pistons are rejected because they are either oversized or undersized. What is the probability that a batch of 10 pistons will contain (a) no more than 2 rejects? (1.5 marks) (b) at least 2 rejects? (1.5 marks) 6. Mrs. Anastacia is the marketing Manager of healthy foods limited. She understands that from economic point of view, demand and price are related and she intends to determine the actual relationship between the price of their foods and demand. She has provided you with the following data from the company's records. Unit Price Demand('0 (Sh.) 00' 195 10.6 390 8 135 13 352 8 383 6 270 10 140 11.7 218 11.3 Required i) The linear regression line for demand against price using least squares method 4 marks ii) The coefficient of determination. Interpret your answer (3mks) iii) The estimated demand if price is sh. 350 (1mk)