972+X977984+X1,0051,013+X1,0141,016+X1,0411,052+X1,0801,093+X1,094Construct a frequency table based on these data, using a reasonable number of class groupings (5 marks). Rage = 1095 – 686 = 409Desired class groups = 6Width of interval = 409/6 = 68.17 rounded to 70Length of life (in hours)Intervals of time686 but less than 7563756 but less than 8263826 but less than 89613896 but less than 96615966 but less than 103691036 but less than 110651106 but less than 11760Draw a histogram of the frequency distribution that you have obtained in a) (5 marks). c) Make appropriate comments on the data (5 marks). Range provided variability of data obtained.
For example, in our case, the range of the bulbs is 409. Moreover, it is evident that the lifeline of the bulbs is between 826-966 accounting to more than a half of available data. Question 2 (10 marks)Sales of 2010 model light trucks and sport utility vehicles for the Ford Motor Company far outpaced their 2009 counterparts according to a Wall Street Journal article. The following table indicates unit sales for selected vehicles for March 2009 and March 2010.ModelMarch 2010March 2009Ranger 45,181 +100*X26,147 +50*XMustang17,750 +100*X13,178 +50*XFusion 20,608 +100*X16,564 +50*XExplorer39,014 +100*X34,913 +50*XTaurus34,058 +100*X32,254 +50*XLincoln Continental3,784 +100*X3,052 +50*XConstruct a visual representation that best conveys the information above (5 marks).
ModelMarch 2010March 2009Ranger 4538126247Mustang1795013278Fusion 2080816664Explorer3921435013Taurus3425832354Lincoln Continental39843152Discuss the changes in the distribution of sales between March 2009 and March 2010 (5 marks). The sales of Ranger model in the period ending March 2010 indicates a large increase in number of sales compared to all models, and this model is among the best products of the company according to the amount of sales compared to other models. The least sold model is Lincoln Continental that shows small increase in number of sales.
The same tendency is indicated by the Taurus model. Nevertheless, Mustang, Fusion, and Explorer have also seen an increase in number of sales, with each increasing the number of sales within comparable amounts. Question 3 (25 marks) A manufacturer of flashlight batteries took a sample of 25 batteries from a day’s production and used them continuously until they were drained. The numbers of hours they were used until failure were: 344+X428+2*X320+3*X545+4*X264+5*X 451+X1,049+2*X631+3*X255+4*X492+5*X288+X920+2*X428+3*X766+4*X394+5*X374+X1,104+2*X544+3*X654+4*X746+5*X421+X820+2*X762+3*X564+4*X392+5*XCompute the arithmetic mean, median, first quartile, and third quartile (6 marks). Mean = 14126/25 = 565.04Median = 502First quartile = 402Third Quartile = 756In what ways would the information obtained in question a) be useful to the manufacturer?
Discuss (4 marks). The mean summirises the large sum of sata into a simple number meaning that it can easily be understood and interpreted. Moreover, the mean enables the producer to compare easily with means from other days to determine the approximate amount of period that the batteries can last. Median – The median provides a chance for the producer to group information into a situation that is more favourable and can provide a better understanding of the data.
The mean provides only a summary of the information but the median allows the producer to determine the limits for different batteries since the mean is sometimes biased. Quartiles – The quartiles are important because the producer can easily seen and understand the lifespan of the batteries. The mean is sometimes is subjective meaning that the quartiles easily provides a means of understanding what should be down to reduce the lifespan of batteries on the lower quartile while determining the best batteries through the upper quartile.