uantitative Marketing Methods Assignment # 1 Purpose: To gain a better understanding of descriptive statistics and how they are a component of inferential statistics. Throughout lecture, and several of your classes here at GUST, you have had to calculate several descriptive statistics. Most likely, these descriptive statistics were the sample mean and standard deviation. In some cases, you may have been asked to calculate the coefficient of variation or the median. As you are probably aware, descriptive statistics are quantitative descriptions to describe the nature of a sample (and in some cases the term descriptive statistics refers to the nature of a population as well). Inferential statistics use probability to make statements about how well a sample statistic depicts a population parameter. Descriptive statistics are an integral component of inferential statistics. To help ensure that you understand the concepts of sample statistics and population parameters and how descriptive statistics are a component of inferential statistics, we will calculate a number of descriptive statistics and in some cases we will attempt to quantify the uncertainty associated with how well our sample statistic depicts the population parameter. Remember, due to sampling error, that our sample statistic will rarely equal the population parameter. Thus, we want to not only know the value of a statistic but how likely it is that the statistic represents the value of the parameter we are estimating. One. For the following population of Sierra Marketing Company sales data, calculate the mean, median, mode, and standard deviation using R software package. State all units of measure and attach the R codes used to your answer sheet. Observation Sales ($000) 1 62 2 65 3 135 4 120 5 145 6 61 7 133 8 160 9 75 10 121 11 140 12 103 13 116 14 160 15 120 16 133 17 82 18 108 19 60 20 115 21 95 22 128 23 145 24 133 25 130 26 160 27 107 28 76 29 137 30 144 31 95 32 129 33 81 34 143 35 153 36 71 Mean ____________________ Median ______________________ Mode ____________________ Standard deviation ____________________ Two. Use R to draw a boxplot, a histogram and a stem and leaf plot. Comment on the shape of the distribution. Note graphs MUST be in color with clear legends. Attach graphs to your answer sheet. Three. Explain, in your own words, what the population mean is, express in mathematical notation how to calculate the sample mean Four. Explain, in your own words, what the population standard deviation is, express in mathematical notation how to calculate the sample standard deviation? In this part of the assignment we will now repeatedly randomly sample from our population using random number generation based on Microsoft Excel algorithms. I want to make sure that you understand the difference between population measures of central tendency and dispersion and sample measures of central tendency and dispersion. There is a total of 36 observations in our population, lets assume for some reason, that we cannot measure all 36 sales data and thus we will use some sort of sampling technique. For this example, we will only sample 10 sales data points. I want you to develop several sample datasets (10 different data sets) of a sample size of 10 from this population using Microsoft Excel. If you set this process up in Excel correctly, you can quickly repeatedly randomly sample from the population and calculate measures of central tendency and dispersion. I will help you conduct these random samples in Excel. First, you need to type or paste all total sales in the far upper left corner of an Excel sheet (cells A2 to B37 of the spreadsheet). Make sure the observations are ordered by observation number and not by total sales volume. In cell C2, type the phrase =rand(). This phrase causes Excel to generate random numbers from 0 to 1. Drag all the way down to C11. In D2, multiple the contents of C2 times 36 (=c2*36). Drag all the way down to D11. In E2, type the phrase =round(D2, 0). Drag all the way down to E11. We now have ten numbers that have been randomly generated from 1 to 36 (due to problems with Excel, we need to change the observation numbers from 1 to 36 to 0 to 35; respectively). We now need to select the sales data to be sampled from our population. To do this in Excel, in cell F2, type the phrase =Vlookup(E2, $A$2:$B$37, 2). Can you understand what is occurring? We can now calculate summary statistics of our sample as we did for our population. Five. Is each of the 10 samples that we will calculate a valid estimate of the population mean? Six. Why do the 10 sample means differ, what causes this to occur? Seven. In practice, if we were to actually sample 10 sales data, how many times would conduct the sample of 10 sales data points