Selection of Lead Balls Based on Their Masses from Three Sources - Assignment Example

Student Name: Topic: SIMPLE DATA ANALYSIS AND COMPARISON Course: Tutor: Institution: Date Due: Running Head: Selection of lead balls based on their masses from three sources EXECUTIVE SUMMARY In this work, data sets of masses of iron from three sources to be used in engineering class experiments on iron casting were used in performing various statistical analyses. Each data set comprised of 150 pieces whose masses were determined and recorded in an Excel sheet. The Microsoft Excel tools were used for determination of descriptive statistics which involved the following parameters was carried out; median, mean, min, max, mode, standard deviation, kurtosis and skewness. The parameters from descriptive statistics were tabulated for each data set and for all the variables in the data sets jointly. The data was further described using histograms, and the 25th, median (50th) and 75th quartile were calculated and tabulated and used in the plotting of box plots for all the three data sets. The distribution of the variables in the data sets was examined by use of normal probability plots. Data set three had the highest range and the standard deviations compared with data sets 1 and 2. The data sets are all skewed, whereby data set 1 and 2 are skewed towards the left hand side and data set 3 towards the left hand side. These results are summarized in different tables and rendered appropriately in figures in this report. INTRODUCTION In this work, three data sets provided were analyzed singly and jointly using various statistical methods to test their distribution, dispersion and how they compared with each other. Simple statistical parameters such as mean, median, min, max, quartiles, kurtosis and skewness among others were determined by use of Microsoft Excel software 2010. These parameters generally show the distribution of the variables in a data set. The three measures of central tendency and dispersions; that is mean, mode and median were used to describe and compare data sets. The distribution of the data sets was described by the kurtosis and skewness and the data was rendered in histograms and box plots. Histograms, box, mean, and percentile plot were used to show a visual summary and statistics such as the mean, standard deviation, and median and percentiles. This type of data and analysis can be generated from measurement of masses of materials used in an engineering project. These materials were obtained from three different sources as represented by the three data sets. The three sources were compared in terms of the masses and their distributions and variations of 150 materials masses derived from three different sources. Measures of dispersions and comparisons will help the engineer to decide which material could act as a replacement in case one of the materials is missing or the supply is inadequate. The histograms and box plots would help one to decide which materials are closely related by having a visual presentation of the readings. PROJECT WORK Data collection In this project, the masses of 150 pieces of lead masses to be used in designing experimental electrodes for an Engineering class were weighed by top bar balance to 2 decimal places and the results recorded as data set 1-3 in Excel sheet. The different masses were obtained from three sources by approximately cutting equal sizes by visual inspection and then taking the masses. The materials from the three sources were to be compared to establish if they could be blended together for the production of the electrodes without compromising the quality. It was assumed that for the materials to blend properly their masses should be comparable and should be normally distributed. Analysis Procedure The source of the lead balls were designated data set 1, 2 and 3. In each data set, the masses were determined and recorded appropriately. The masses were taken in grams. From each data set the descriptive statistics were carried out by use of Microsoft Excel tools to determine, the mean, mode, min, max, range and the standard deviations of each data set and all the masses put together (Bowman & Robinson, 1987). Furthermore, the masses were displayed in histograms for each data set and also by use of normal probability distribution plots. For the median, first and 3rd quartiles box plots were also used to display these features for all the data sets and also for the data sets analyzed jointly. The summary of the lead masses analyses are shown tables 1-3 and figures 1-4 in this report. Results and Discussions Descriptive statistics For each data set there are 150 masses of lead balls making up the total to be 450 balls in the three data sets. The minimum mass was in data set 3 with 0.020692, while the maximum was 99.977. The means for the three data sets are; 11.01354267, 11.11486333 and 19.79446193 for the data sets 1, 2 and 3, respectively. Skewness is a measure of symmetry of data. For the data to be normal the skewness should be zero. However, this does not exist in reality. For a normal distribution of the variables (masses) kurtosis which is a measure of flatness is approximately 3. This shows that the distribution of data in set 3 approaches normal distribution. Looking at the variation of the masses the data set in set 3 are widely distributed with a large distribution margin and large standard deviations compared with other masses. This is summarised in table 1 and figures 1-3. Table 1: The descriptive statistics for each data set, separately. Parameters Data set 1 Data set 2 Data set 3 Min 8.971 9.0713 0.20692 Max 13.134 12.97 99.977 Median 11.0045 11.242 11.0455 Range 13.134 - 8.971 12.97 - 9.0713 99.977 - 0.20692 mean 11.01354267 11.11486333 19.79446193 Stdev 0.909919679 1.165818494 19.91471993 Mode 11.372 #N/A #N/A Kurtosis -0.47431792 -1.2210128 2.204513397 Skewness -0.064321878 -0.135658672 1.577565636 Table 2: The descriptive statistics for all the data sets jointly Parameters Values Min 0.20692 Max 99.977 Median 11.087 Range 99.977 - 0.20692 Mean 13.97428931 Stdev 12.21933937 Mode 10.688 Kurtosis 14.53605015 Skewness 3.534811694 After combining all the masses in the three sources, there were 450 variables, and the mean was 13.9742831. Other parameters are summarised in table 2. The positive value of skewness is an indication that most of the variables (masses of the lead balls) are above the mean side of the data sets, and the tail is more stretched on this side than on the side below the mean. Therefore, it can be concluded that most of the masses (variables) had masses stretched on the side above mean, compared to those below the mean. Positive skewness indicates that the distribution is asymmetrical and the tail extends toward more positive values. In the data sets, all the variables are positive and this is demonstrated further by the positive skewness. See table 3. Histograms The histogram is a vertical bar chart that depicts the distribution the distribution of a set of data. From the visual inspection of the histograms, data sets 1 and 2, the masses tends to have minimal variations and their masses are clustered near the mean, compared to data set 3 in which the masses are widely scattered. This is shown in figures 1-3. Figure 1: Histogram of the masses of 150 lead balls in data set 1 Figure 2: Histogram of the masses of 150 lead balls in data set 2 Figure 3: Histogram of the masses of 150 lead balls in data set 3 Quartiles Table 3: The first, second and third quartiles for the three data sets and all the data sets jointly Quartiles Data Set 1 Data Set 2 Data Set 3 All the Data Sets Jointly Q1 (25th quartile) 10.40375 10.08425 5.97215 9.884275 Q2(50th quartile) 11.0045 11.242 11.0455 11.087 Q3 (75th quartile) 11.63625 12.09925 28.086 12.30975 Max 13.134 12.97 99.977 99.977 Box plots The box plots in shows the first, second and third quartiles and the maximum masses. It is a summary of the variables in table 3. Figure 4: A box plot of data sets 1, 2 and 3 and all the three data sets combined The box plots shows the data graphically. It can be interpreted from the visual inspections of the box plots that the data sets 1 and 2 are shorter compared to data sets 3 and all data sets which are much stretched. This shows that there is high variations in data sets 3 and all data sets because the box plots are taller than those of 1 and 2. A normal probability plot is a statistical tool that is used to determine if values of a set of variables are derived from a normal distribution. Figure 5: A normal probability plot for the data series 1 Figure 6: The normal probability plot for series data 2 Figure 7: The normal probability plot for series data 2 Conclusions In conclusion, the masses are well distributed and the data for the masses, their means, standard deviations, median, and quartiles have been computed for the data sets to be able to examine whether the masses are comparable for the experiment. However, student t test which could have shown whether the means are statistically different or comparable was not comparable. The parameters obtained from the analysis are rendered in histograms, box-plots and normal distributions and by use of tables. References Bowman, A. W, & Robinson, D. R. (1987). Introduction to Statistics. London: Oxford University Press. Read More