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Statistics
TABLE OF CONTENTSINTRODUCTION...........................................................................................................................1(a) Constructing a box plot..........................................................................................................1(b) Constructing a histogram.......................................................................................................3(c) Comparing data characteristics to theoretical properties.......................................................7(b) Constructing a normal probability plot (quantile - quantile plot)........................................15CONCLUSION..............................................................................................................................17REFERENCES..............................................................................................................................18
INTRODUCTIONBusiness statistics may be swerved as a science that facilitates good decision making atthe time of uncertainty. By employing the tool of business statistics analyst can perform financialanalysis and solve issues related to econometrics, auditing, production as well as operations.Further, normal distribution is the main parts of probability which in turn clearly reflects theextent to which values are above or below the average level. Mean and standard deviation is themain elements of such bell curve graph. The present report is based on the data set of domesticbeer which will provide deeper insight about several statistical tools such as box plot, histogramand quantile-quantile (QQ plot).(a) Constructing a box plotBox plot is the standard way of presenting data set on the basis of five key numbers suchas minimum, maximum, Q1, Q3 and median. Hence, box plot method helps in depicting group ofdata graphically through the means of quartiles. Such plots also provide high level of assistancein indicating or showing variability that is outside the upper or lower quartiles (Box or WhiskerPlot, 2017). Further, by using or creating box plots one can present the variations which takeplace in a sample of statistical population without making any assumption of statisticaldistribution. In this, difference which takes place dispersion ofParticularsAlcohol %CaloriesCarbohydratesMedian4.9151.012.1Quartile 14.4129.08.6min0.455.01.9max11.5330.032.1quartile 35.6166.014.6mean5.2154.712.1Alcohol %
0123456Alchol%n= 145BinrangeCalories012345678910Caloriesn= 145BinrangeCarbohydrates
020406080100120140160180200Carbohydratesn= 145BinrangeInterpretation: The above depicted box plot clearly shows that in the case of alcohol%mean and median accounts for 5.2 & 4.9%. Besides this, quartile 1 and 2 of data set implies for4.4% & 5.6%. Range of alcohol % is g 11.1% significant which is the difference of higher andlower value. Referring such box plot, it can be stated that data set does not fall into the categoryof normal standard distribution. Moreover, in the case of normal standard both lower and upperwhisker is equal. Hence, it can be seen in the above box plot that lower whiskers of alcohol % ishigher as compared to upper so it is not considered as normal standard distribution.Along with this, data ofcalories and carbohydrates does not consider as normally standarddistributed. Moreover, box plot of calories presents that lower whisker is longer than the upper one.Descriptive statistics of data set pertaining to calories show that Q1, Q2 and Q3 are 129.0, 121.1 & 166significantly. Further, minimum and maximum value of data set is 55 & 330. On the other side, data set ofcarbohydrates exhibits that minimum and maximum value is 1.9 and 32.1 respectively. Further, it hasassessed from evaluation that average and median value of carbohydrates is similar such as 12.41. Inaddition to this, tabular presentation shows that value of carbohydrates is increased from 1stquarter to the3rdone. Hence, considering the situation of box plot, it can be mentioned that data of calories andcarbohydrate does not have normal standard distribution.(b) Constructing a histogramHistogram is the most effectual tool that presents the distribution of numerical data setand helps in understanding the same. It presents estimated probability distribution of acontinuous variable. For constructing histogram, it is highly required for analyst to determine the
bin values that represents the division of entire range into a series of intervals. Hence, histogramfacilitates structured presentation of large data set and helps in decision making. Symmetric andnon-symmetric are the main two situations that histogram presents on the basis of data set needsto be assessed (Histograms,2017). Under symmetric distribution, two parts of the histogramshows highly perfect representation in relation to each other. On the other, non-symmetricdistribution is also known as skewed one that does not present mirror imaging. Under skeweddistribution, there is one tail that attracted our in relation the next tail.Alcohol %Frequency0.411.302.303.224.1105.0786.0306.977.888.749.7210.62More1