Descriptive Statistics for Nonparametric Models By Experts

Question: Discuss about the Descriptive Statistics for Nonparametric Models. Answer: Introduction In this report a coffee roasting and producing firm named Sublime coffee is taken for the purpose of comparing the sales figure across various outlets. The company has been started by David Geoffs as a coffee roasting and coffee supplying company. In about eighteen months, the company has grown into a mid-level capacity and now operates in three different outlets: coffee sold to the external customers, coffee sold by mobile carts and coffee sold by internally owned vehicles. There are mainly three types of coffee sold by the firm, namely, sublime delight, mocha delight and expresso delight. The different sales figures for each of the 17 different factory outlet, three mobile carts, and coffee sold from internal carts are given for each month of the year. Various methods of descriptive statistics have been used to analyze the sales figures.The measure of central tendency that has been used are: Arithmetic mean: It is calculated by the formula, Xbar=1/n* Median: It is the middle most observation from the set of observations. Geometric Mean: Geometric mean is the weighted average of the log of the observations( Courvoisier and Renaud 2015). In any dataset, the values of the variable have a tendency to cluster around a central value. The measures of central tendency give this fundamental value of the sales figures.After calculating the mean value, one has to check how much the values are dispersed from the core value. For this one needs to calculate the dispersion among the variables(Bickel and Lehmann 2012). The most common measures of dispersion are: Standard Deviation: It is the root of the sum of the square of deviation of the values from the original value.The following formula gives it: Range: Range is the difference between the smallest and largest observations. It only provides an idea about the spread of the dataset(Gelade, Verardi, and Vermandele 2015). Interquartile range: Sometimes a measure called interquartile range is calculated which is the difference between first and the third quartile of the observations. In general, 90 % of the dataset is expected to lie within the IQR(Weiss and Weiss 2012). After getting an idea about the dispersion of the dataset, one would like to know how much the distribution deviates from a normal distribution. That is whether the distribution is negatively skewed or positivily skewed. The following formula gives a measure of skewness: b1= where denotes the third order raw moment and s^3 is the cube of the standard deviation. After calculating skewness of the distribution, one would like to know about the peakedness of the distribution. To measure peakedness one has to measure kurtosis. The measure of kurtosis is given by the square of second order raw moment divided by fourth order rare moment. From the given dataset on 11 months sales figure for the year 2015, the arithmetic mean is least from sales to external customers and highest for sales from internal carts. The sales figure from the mobile van is moderate among the three. The median value is also highest for sales from internal carts, second largest for sales from mobile vans and least for sales from sales to external customers.The same result is also correct for geometric mean.So the measure of central tendency reveals highest sales from internal carts and lowest to external clients.( Samuels, Witmer and Schaffner 2012). Standard deviation is calculated for the measure of dispersion. The values of dispersion for the three outlets are 12.41121 for sales to external customers, 14.23982 for sales from internal carts and 10.61553 for sales from mobile vans. Although the value of central tendency is highest for sales from internal carts, the standard deviation is also greatest for this particular area. This means that the sales from an internal vehicle are very high, but the sales figures fluctuate very much. The standard deviation is second largest for sales to external customers and least for sales to internal carts. The range and interquartile range values also indicate the sales for external clients and internal carts are widely scattered(Lomaxand Hahs-Vaughn 2013). Kurtosis is greater than zero for external customers and less than zero for internal carts and mobile vans. Kurtosis less than zero means the distribution is platykurtic, that is, the distribution is less peaked while a value more than one indicates a peaked or leptokurtic distribution(Blanca et al. 2013). Skewness measure values are 1.335949, 0.416119, 0.32686 respectively. The skewness values for internal carts and mobile vans are almost approaching towards zero that means unimodal distribution while external customers have a positively skewed distribution(Ho and Carol 2015). So descriptive statistics measures indicate sales from internal carts to be highest followed by mobile vans and lowest to external customers. References: Bickel, P.J. and Lehmann, E.L., 2012. Descriptive statistics for nonparametric models IV. Spread. InSelected Works of EL Lehmann(pp. 519-526). Springer US. Blanca, M.J., Arnau, J., Lpez-Montiel, D., Bono, R. and Bendayan, R., 2013. Skewness and kurtosis in real data samples.Methodology. Courvoisier, D.S. and Renaud, O., 2015. Robust analysis of the central tendency, simple and multiple regression and ANOVA: A step by step tutorial.International Journal of Psychological Research,3(1), pp.78-87. Gelade, W., Verardi, V. and Vermandele, C., 2015. SQN: Stata module to estimate Rousseeuw and Croux (1993) robust measure of dispersion.Statistical Software Components. Ho, A.D. and Carol, C.Y., 2015. Descriptive Statistics for Modern Test Score Distributions Skewness, Kurtosis, Discreteness, and Ceiling Effects.Educational and Psychological Measurement,75(3), pp.365-388. Lomax, R.G. and Hahs-Vaughn, D.L., 2013.An introduction to statistical concepts. Routledge. Samuels, M.L., Witmer, J.A. and Schaffner, A., 2012.Statistics for the life sciences. Pearson education. Weiss, N.A. and Weiss, C.A., 2012.Introductory statistics. London: Pearson Education.