Table of Contents INTRODUCTION...........................................................................................................................4 MAIN BODY...................................................................................................................................4 1. Presenting the data in table format..........................................................................................4 2. Pictorial representation of the data.........................................................................................4 3. Calculation and analysation of total number of passengers exited the clock house station for 10 years.......................................................................................................................................6 4. Linear forecasting model for predicting the Clock House station usage for 12 and 15 years7 CONCLUSION...............................................................................................................................9 REFERENCES..............................................................................................................................10
INTRODUCTION Collection of numerical data and its analysis with the application of tools and techniques of statistics could largely benefit in drawing out the most meaningful information from the data. Statistical data analysis is the method which is concerned with the collection and scrutiny of data sample thoroughly. It basically summarises the data into such a form which could be used for taking effective decisions (statistical analysis,2019). In the present report, data regarding the station usage of Clock House will be collected for the period of 10 years and presented by the medium of tables and charts. After which the sample data will be analysed by applying descriptive statistical techniques so as to determine the trends and pattern of the data. Lastly, the forecasting of the station usage will be done with the help of linear regression model for 12 and 15 years. MAIN BODY 1. Presenting the data in table format Station usage data of Clock House for the 10 years was collected which was related to total number of exits in each year. The data shows the figures that how drastically it changed over the period of 10 years. It can be seen that number of passengers exiting was reduced after the year 2015-16. YearsTotal number of exits 2008 -200912 2009 - 201014 2010- 201111 2011 - 201271 2012 - 201352 2013- 201448 2014-201551 2015-20168 2016-201715
2017-2018317 2. Pictorial representation of the data Column chart Bar chart 2008 -2009 2009 - 2010 2010- 2011 2011 - 2012 2012 - 2013 2013- 2014 2014-2015 2015-2016 2016-2017 2017-2018 0 50 100 150 200 250 300 350 Total number of exits 2008 -2009 2009 - 2010 2010- 2011 2011 - 2012 2012 - 2013 2013- 2014 2014-2015 2015-2016 2016-2017 2017-2018 050100150200250300350 12 14 11 71 52 48 51 8 15 317 Total number of exits
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Interpretation :The above graphs are the pictorial representation of the number of passengers exited theClock House station every year. It can be noticed that numbers fell tremendously after the year 2015-16. In the year 2015-16, the total number of passengers exiting the station was 577097 whereas it decreased in the next year to 302068. The numbers were stable till 2015 after that it started fluctuating. 3. Calculation and analysation of total number of passengers exited the clock house station for 10 years For the purpose of analysing the data, descriptive statistics is the efficient tool which could help in drawing out a pattern out of the data. This is a tool of statistics which has several components such as mean, median, mode which are measures of central tendency and range, variance and standard deviation which are the measures of dispersion (Muñoz and et.al., 2018.). For evaluating and interpreting the currently collected, the implication of descriptive statistics is as follows: Total number of entries Mean59.9 Standard Error29.44 Median31.5
Mode#N/A Standard Deviation93.1 Sample Variance8667.65 Range309 Minimum8 Maximum317 Mean :Mean can be referred to as the sum of all the values divided by the number of observations in a data sample. Being a measure of central tendency, it represents the average of all the values (Zhang, 2016). The mean of the data collected related to total number of passengers leaving the station was 59.9. Median :This term denotes the quantity that exists at the midpoint of the data sample's frequency distribution in such a way that an equal probability is occurs of falling beneath or above it. From the calculation table, the median of the collected data is 31.5 Mode :This word signifies a quantity that occurs for maximum number of times in the given set of data sample. In the present study, mode of the station usage data is 0. This shows that there is no value in the data which is repeating or occurring again and again. Range :It can be called as the variation between the lowest and highest value in the data. It is a measure of variability which focuses on measuring the degree to which the variables in a data set differentiates from one another. The range of station usage data is 309 Standard deviation :It is one of the variability measure that determines the degree of deviation between two variables in the sample population or entire population (Grzegorzewski, 2018). The standard deviation for the station usage data of Clock House was calculated to be 93.1 4. Linear forecasting model for predicting the Clock House station usage for 12 and 15 years Linear forecasting is one of the measure of foretelling the values of the variables for the future. It is a time series method which employs statistical tools for projecting the future values of the given data (Dudek,2016). There is an equation through which the forecasting is done which is as follow :
y= mx+c Calculation of m :This term denotes the slope of linear regression and the formula for calculating the same is : m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2 Calculation of c :c represents the interception of the y axis in this forecasting model. This is calculated with the help of following formula : c=Σy -mΣx / N 12 and 15 years of Clock House usage forecasting YearsTotal number of entries (x)(y)(xy)x^2 13173171 214284 311339 47128416 55226025 64828836 75135749 886464 91513581 103173170100 559044936385 m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2 n = 10
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Σx = 55 Σy =904 Σxy =4936 Σx^2 = 385 m = (10*904- 55*4936)/ (10*385 - 3025) m = −318.10 c = Σy - mΣx / N = 904-(−318.10)*55/10 c = 2653.55 12 years forecasting of Clock House station usage Y = mX + c =−318.10*12+2653.55 =−1163.65 15 years forecasting of Clock House station usage Y = mX + c =−318.10*15+ 2653.55 = −2117.95 CONCLUSION From the above study, it can be summarised that descriptive statistical tools and techniques are of great help for the purpose of evaluating and analysing the data. Its aim is to let the user to conclude meaningful information from the data so that better understanding could be formed of the data so collected. In the study, measures of central tendency and measures of dispersion were calculated for the purpose of analysing of Clock House station usage data. Forecasting for the periods of 12 &15 was also done through linear regression in which the total passengers for 12 years is estimated−1163.65and for 15 years it is−2117.95.
REFERENCES Books and Journals Dudek,G.,2016.Pattern-basedlocallinearregressionmodelsforshort-termload forecasting.Electric Power Systems Research.130.pp.139-147. Grzegorzewski, P., 2018, September. Measures of Dispersion for Interval Data. InInternational Conference Series on Soft Methods in Probability and Statistics(pp. 91-98). Springer, Cham. Muñoz,A.Mandet.al.,2018.ComparisonofDescriptiveAnalysisMethods.Descriptive Analysis in Sensory Evaluation.pp.679-709. Zhang, Z., 2016. Univariate description and bivariate statistical inference: the first step delving into data.Annals of translational medicine.4(5). Online statisticalanalysis.2019.[online].Availablethrough <https://whatis.techtarget.com/definition/statistical-analysis>