Roughly examining the data we can say that the relationship between the sales and the advertising is looking to be related as the increase in the advertising expenses relevantly increased the sales but not in a manner. The graphical representation of the data may precisely help us to compare. A bar chart is a simple graphical tool to represent and compare data from which we can say about the relationship between two data. We can also say about the shape of the distribution. The representation of the sales and advertising expenditure data is as follows.
Fig 1.1 Bar chart
From the bar graph, we can approximately say that there is a proportional increase in sales as the advertising expenditure increases. So we recommend increasing the advertising expenditures in a steady manner to increase the level of sales. At the same time, it will cause a reverse result also. If the sales are affected by any other reasons like economic crisis, the increase in the advertising expenditure will not help. So a precautionary plan must be done to increase the advertising expenditure. It is better to increase it while the purchasing power is high in the market. Also, a bar graph is not a sufficient tool to conclude, and let us look at the other descriptive tools. The other similar and powerful graph tool is a frequency polygon which shows the shape of the distribution as primary. The frequency polygon for the sale and advertising data is as follows:
Fig1.2 Frequency polygon
From the frequency polygon, we agree with the results of the bar graph and one more observation is that there is a steady increase in the advertising expenditure but an unsteady increase in sales. This shows that the advertising expenditure may not contribute to a consistent sale here. Now let us move on the descriptive data analysis where we can interpret the results more precisely and accurately. The descriptive statistics are the type of statistics where the data are analyzed by the two main measures namely the measure of central tendency and the measure of variation. The important measures of central tendencies are the mean, median, mode, and quartiles. The important measures of variations are the variance, standard deviation, and quartile deviation. The drawback of these measures is that we cannot get any information about the relationship between two data. For that, we have to perform tasks like correlation and regression. First, we do individual analysis and then relationship analysis. Let us find the important measure of central tendencies Mean as the other measures may not help this analysis.
Formula: “ = ” (Weisstein, Eric W)
Mean is the average of the data which is found by dividing the sum of the data with the number of the data. Let us tabulate the data so as to perform the calculations simple.
Mean Sales = 208 / 5 = 41.6 ($1000s)
Mean advertising expenditure = 35 / 5 = 7($1000s)
The mean sales over the period 2004 – 2009 are 41.6 ($1000s) and the mean advertising expenditure is 7($1000s). There will be no information about the growth or decline in the mean. We can decide whether to maintain the average advertising expenditure to maintain average sales. The other major drawback of the measure means is that it does not give the details about individual data and is not robust of extreme values. To overcome these problems the measures of variation will help us. The measure of variation is the measure of the variation of individual data from the mean. The important measure of the variation is the Standard deviation which is the square root of variance.
Formula = s = “SN = ” (Weisstein, Eric W)
This shows that the average deviation of sales is 12.306($1000s) and that of advertising expenditure is 4.56($1000s). This may tell us the individual property but not the relationship. The standard deviation of sales tells that the sales over one year to next year may deviate about 12.306($1000s) about the mean sales. The standard deviation of advertising expenses tells that the expenses of each year on average deviates about 4.56 ($1000s) from the mean expenses. The other important thing we have to regard is that we can control or increase the number of advertising expenses whereas we can only predict the sales. The standard deviation of expenses is higher, that is more than half of the mean which shows the gradual increase but the standard deviation of sales is less high than it is about one-fourth of the mean, which shows that although there is a gradual increase in the advertising expenses, may not lead to the same growth in the sales. In general, the correlation coefficient lies between -1 and 1. The zero shows that there is no relation, a positive show that there is a strong relationship in the same direction, and a negative show that there is a strong relation in opposite direction. Our data obtained 0.858 which is positive and we conclude that there is a strong relationship between sales and advertising expenditure in the same direction. So we need not worry to increase the advertising expenditure so that it would increase sales. We have seen the property of relationship and now we are in the position to predict the relationship in a linear form. For that, the regression helps us. Regression analysis is a statistical technique in the form of an equation; interpret the relation of a dependent variable with an independent variable. Here the dependent variable is sales and the independent variable is advertising expenditure as the sale is dependent on the advertisements to an extent.
We advise Karen to keep improving the advertising campaigns in better methods year by year to keep the sales higher. The statistical techniques used are deterministic and hence descriptive. A better forecast can be used by inferential statistics. “Shortcomings, weaknesses, and limitations are admitted when the arguments are presented. Dealing with both the positive and the negative suggests objectivity”.
- Kenneth F.Harling(2009), Writing a Managerial report, The Maple leaf conference, [Online]. Available at http://info.wlu.ca/~wwwsbe/MapleLeaf/Report_Writing_c.html [Accessed: 18th April 2009]
- Kenney J F and Keeping E S, “Linear Regression and Correlation”. Ch.15 in “Mathematics of Statistics”, Pt.1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 252 – 285, 1962.
- Weisstein, Eric W., “Mean” From Mathworld – A Wolfram Web resource. [Online]. Available at http://mathworld.wolfram.com/Mean.html [Accessed: 19th April 2009]
- Weisstein, Eric W. “Standard Deviation.” From the Math world – A Wolfram Web Resource. [Online] Available at http://mathworld.com/StandardDeviation.html [Accessed: 19th April 2009]