Illustration 11. From the following series find the 3 yearly and 5-yearly moving averages and draw the curves of both the original and trend values : 1988 1989 | 1990 1991 | 1992 | 1993 | 1994 || 1995 | 1996 | 1997 | 1998 16 Year: 2 4 7 11 22 29 37 46 56 Value:
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- Table 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?Table 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?
- For questions 1 and 2, you need to draw and shade the distribution curves.The accompanying histogram is for pulse rates for 125 people. Convert the vertical axis to relative frequency and shows the values that would replace each of the values on the vertical axis.ILLUSTRATION 22. Two brands of tyres are tested with the following results: life(in 1000 miles) Brand of tyres X Y 20-25 1 0 25-30 22 24 30-35 64 76 35-40 10 0 40-45 3 0 Question 1. Which brand of tyres between x and y have greater average life? Question 2. Compare the variability and the state of which the brand of tyres would use on your trucks?
- The following ACF plots were produced for raw data of monthly sales of two different variables, A and B. Explain in detail which variable (A or B) is likely to be easier to forecast.The table gives the population in a small coastal community for the period 1997 - 2006. Figures shown are for January 1 each year. Year Population 1997 624 1998 856 1999 1,336 2000 1,578 2001 1,591 2002 1,483 2003 994 2004 826 2005 801 2006 745 (a) What was the average rate of change of population between 1999 and 2002?(b) What was the average rate of change of population between 2003 and 2005?(c) For what period of time was the population increasing? The population was increasing from until . (d) For what period of time was the population decreasing? The population was decreasing from until .The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.350.35 and 0.650.65 is what?
- A used car company believes that there is a relationship between the amount spent on advertising and its sales. Data collected for 6 years are as follow: Amount spent on advertising Sales ($thousands) ($millions) 2.0 1 3.0 3 2.5 4 2.0 2 2.0 1 3.5 7 1. Illustrate the above on a scatter plot.John Kittle, an independent insurance agent, uses a five-year moving average to forecast the number of claims made in a single year for one of the large insurance companies he sells for. He has just discovered that a clerk in his employ incorrectly entered the number of claims made four years ago as 1,400 when it should have been 1,200.a. What adjustment should Mr. Kittle make in next year’s forecast to take into account the corrected value of the number of claims four years ago?b. Suppose that Mr. Kittle used simple exponential smoothing with a = .2instead of moving averages to determine his forecast. What adjustment is now required in next year’s forecast? (Note that you do not need to know the value of the forecast for next year in order to solve this problem.)Compare the two groups (male and female students) in terms of their measures of location and measures of dispersion. On the average, which group of students perform academically better in the previous term? Which group varies more?