Mathematical Skills for Business - Essay Example

Mathematical Skills for Business – work May Number BPP Business School Due 28th of April Mathematical Skills for Business – Coursework May 2015 1. a. Frequency table for vehicles sold last month at the Applewood Auto Group by Location Location Number of Vehicles Sold Kane 52 Olean 40 Sheffield 45 Tionesta 43 Total 180 b. A relative frequency table showing the percentage of total cars sold at each of the four locations Location Number of Vehicles Sold Percentage of Vehicles Sold Kane 52 28.89% Olean 40 22.22% Sheffield 45 25.00% Tionesta 43 23.89% Total 180 100.00% c. Bar chart of the Number of Vehicles Sold by Location d. Summary Statistics of profits on vehicles sold at the Applewood Auto Group Profit on Vehicles Sold Number of Vehicles Sold 180 Mean $1,843.17 Median $1,882.50 Mode $1,761 Standard Deviation $643.63 Range $2,998 Minimum $294 Maximum $3,292 Total $331,770 2. a. A histogram of the Profits on 180 vehicles sold at the Applewood Auto Group b. As shown in the histogram of Profits on 180 vehicles sold, there appears that the profits on vehicles sold is normally distributed, as the histogram resembles a bell-shaped curve. Most of the profits are in-between $1,200 and $2,700. The peak of the distribution is for the profit range of $1,800 and $2,100, which is desirable as the mean and median for the profit on vehicles sold are $1,843 and $1,883, respectively. 3. a. Box plot to show the distribution of the age of the buyer Note: - Boxplot made using MegaStat, an Excel-addin Using Excel, the 5-number summary is {21, 40, 46, 52.25, 73}. Minimum = 21 years First Quartile, Q1 = 40 years Median = 46 years Third Quartile, Q3 = 52.25 years Maximum = 73 years IQR = 52.25 – 40 = 12.25 years Lower Inner Fence = 40 – 1.5(12.25) = 21.625 years Upper Inner Fence = 52.25 + 1.5(12.25) = 70.625 years Lower Outer Fence = 40 – 3(12.25) = 3.25 years Upper Outer Fence = 52.25 + 3(12.25) = 89 years b. As shown in boxplot of the age of the buyer, there appears that the age of the buyer is approximately normally distributed with mild outliers. The median age of the buyer is 46 years and the middle half of the buyer’s age is in-between 40 years and 52.25 years (interquartile range = 12.25 years). The minimum and maximum age of the buyers are 21 years and 73 years, respectively. There are 4 mild outliers (21, 72, 72, and 73 years) in the data, as one buyer age is under 21.6 years (below the lower inner fence) and three buyers age is above 70.6 years (above the upper inner fence). There are no extreme outliers in the data. 4. a. A scatter diagram depicting the relationship between vehicle profits and age of the buyer b. As shown in the scatter diagram depicting the relationship between vehicle profits and age of the buyer, there appears a positive linear relationship between vehicle profits and age of the buyer. The profits on vehicles for younger buyers are less as compared to the profits on vehicles for older buyers. Thus, Applewood Auto Group’s marketing departments belief that younger buyers purchase vehicles on which lower profits are earned and the older buyers purchase vehicles on which higher profits are earned is correct. c. The value of correlation coefficient is 0.262 and the value of the coefficient of determination is 0.068. d. Based on the above analysis, the Applewood Auto Group should go ahead with the advertising campaign as planned. The correlation coefficient value of 0.262 suggests that there is a weak positive linear relationship between vehicle profits and age of the buyer. The coefficient of determination value of 0.068 indicates that buyer’s age explains about 6.8% variation in vehicle profit. Thus, the buyer’s age has a small effect on vehicle profit. However, since, the sample size is very large (n = 180), this relationship is statistically significant. Therefore, the Applewood Auto Group’s marketing department should use this information as part of an upcoming advertising campaign to try to attract older buyers on which the profits tend to be higher. 5. Figure 1 shows a line chart depicting the average house price by region or country from 1986 until 2013. Figure 1: Mean house price by region or country, 1986–2013 As shown in figure 1, there appears an increasing trend in house prices in the UK, London and North East from 1986 until 2013. In the year 1986, the average house price in the London, North East and UK were about £55,000, £25,000, and £37,000, respectively. In the year 2013, the average house price in the London, North East and UK were about £430,000, £155,000, and £250,000, respectively. Thus, the average house price increase in the London is much more as compared to the average house price increase in the North East from 1986 until 2013. Overall, there is an increase in the average house prices in the UK is about 7 times, in the London about 8 times and in the North East about 6 times. Figure 2 shows a line chart depicting the average house prices by country from 1986 until 2013. As shown in figure 2, there appears an increasing trend in house prices in the UK and all four countries. The house prices during the 2008 downturn decreased in the UK. There was a very small impact of the 2008 downturn in the average house prices in the Wales, small impact on the average house prices in the London, no impact on the average house prices in the Scotland and a very big impact on the average house prices in the Northern Ireland. In fact, the average house prices in the Northern Ireland started decreasing from year 2007 (around £235,000) and decreased to about £135,000 in the year 2012. This suggests that the 2008 downturn severely affected the average house prices in the Northern Ireland. However, there was a small or no impact in the average house prices in the England, Wales and Scotland. Figure 2: Mean house prices by country, 1986-2013 Figure 3: Mean house prices of different type of houses by country, 1986-2013 Figure 3 shows a bar chart depicting the average house prices of different type of house by country from 1986 until 2013. As shown in figure 3, the average house prices of Detached house type are higher in the UK and across four countries. Furthermore, the average house prices for all the house type is higher in England as compared to the Wales, Scotland and Northern Ireland. Read More