This document provides an overview of data analysis and forecasting techniques. It covers the calculations of mean, median, mode, range, and standard deviation. The importance of statistics in business management is also discussed.
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Data Analysis and Forecasting
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Table of Contents INTRODUCTION...........................................................................................................................3 Data Arrangement.......................................................................................................................4 Preparation of Charts...................................................................................................................4 Calculations.................................................................................................................................4 Mean............................................................................................................................................4 Median.........................................................................................................................................5 Mode...........................................................................................................................................6 Range...........................................................................................................................................6 Standard Deviation......................................................................................................................7 Forecasting.................................................................................................................................8 CONCLUSION................................................................................................................................9 REFERENCES................................................................................................................................9
INTRODUCTION The file represents data analysis and forecasting as the study. The data collected of expenditure of various months is used for calculating statistics which help in forecasting the future trends and decision-making. Businesses get help in budget forecasting and also in anticipating the expenses over a period of time. The statistics calculation and interpretation has been discussed to show their relevance. Data Arrangement MonthsExpenditure 117 210 39 43 525 630 725 88 915 105 Preparation of Charts The data recorded can be presented in form of chart as below:
Calculations Mean MonthsExpenditure 117 210 39 43 521
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630 725 88 915 105 Total expenditure(∑x)143 Total observations(n)10 Mean(∑x/n)14.3 Interpretation: The calculation done by dividing total expenditure by observations is 14.3 or 14 which is the mean here. It can be thus said that average expenditure done in a month is around 14. The mean serves as a yardstick for all observations and is mostly used as a general indicator of data. It is an important tool used in computing statistical data (Ribeiro and et.al., 2017). Median These are the two steps that need to be performed in order to calculate the median value. Step 1: Arranging data in ascending order: S.no.MonthsExpenses 143 2105 388 439 5210 6915 7117 8521
9725 10630 Step 2: Implementing the formula (n+1)/2 to obtain median value: Total no. of observations10 Median value=(10+1)/25.5 Median=(10+15)/212.5 Interpretation: The median value that was obtained was 5.5 but as it does not indicate a definitive position, the average of 5thand 6thvalue was taken through which the middle value of these two was obtained which came out to be 12.5. Therefore, the median value of 10 observations is 12.5 indicating the median expenditure. Median is considered to be the best representative of central location of data. It gives the idea of the distribution of data set (Ribeiro, and et.al., 2017). Mode MonthsExpenditure 117 210 39 43 521 630 725
88 915 105 Mode: The value is indicated by the frequently repeated value in the observation data which has been collected together. Here, it can be seen that no value has repeated itself but it is actually the repeating value in the observations which is identified as mode. It is a measure of central tendency when examining categorical data (Moray, 2020). Range Largest Observation30 Smallest Observation3 Range=Largest-Smallest27 Interpretation: Range value means the difference between highest and lowest values in the observations where the maximum and minimum values oscillate. Here, the range has been identified as 27 which is derived as subtraction of highest value minus lowest value. It is an indicator of statistical dispersion around the central tendency or degree of data spread. There are many methods to indicate range but often it is reported as a single number. Standard Deviation MonthsExpenses(X)X2 117289 210100 3981 439 521441
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630900 725625 8864 915225 10525 Total1432759 The formula of standard deviation is as below: Standard Deviation=SQRT [(∑X2/ N) – (∑X / N)2] =SQRT[(2794/10)-(143/10)^2] =8.65. Interpretation: By use of the formula above, the value of standard deviation was calculated which indicates the standard deviation to be 8.65 points. This actually indicates the overall deviation that has occurred in the observations from the mean i.e. average value point. Standard deviation is measure of amount of variation or dispersion occurring in a set of values. A lower standard deviation is an indicator of the values being close to the mean of set, while a higher standard deviation means that the values have been spread over a wide range (Silvestre and Meireles, 2020). Forecasting Forecasting is a process of making predictions of future based on previous as well as present data. Forecasting is done to reduce risks in future by making use of data for estimations and making judgments. It can also be said that forecasting helps in decision-making and also making management of an organization aware of the rectifiable measures to be taken to avoid losses which can occur if measures are bot taken in advance (Moray, 2020). The relevant values can be calculated as follows: MonthsXExpenses(y)x*yx2
111717289 221020400 33927729 44312144 552110511025 663018032400 772517530625 888644096 991513518225 10105502500 Total55143785100433 I.) Calculating m m = [(n*Σxy) – (Σx*Σy)] / [(n*Σx2) – (Σx)2] -15 m= [(10*785)-(55*143)]/[(10*3025)- 3025] m= -0.00055. ii) Calculating c c= [Σy – (m * Σx)] / n c=[143-(-0.00055*55)]/10=14.30 Forecasting for 11thand 12thmonth The linear forecasting equation of y=mx+c is used in order to obtain the values of 11thand 12th month in order to forecast their expenditures. Forecastingexpenseson 11th month y=mx+cHere, x=11 y=-0.00055(11)+14.30 y=14.2939
Forecasting on 12thmonthy=mx+cHere, x=12 y=-0.00055(12)+14.30 y=14.2934 CONCLUSION The research done in the report indicates different parameters used with different results but with a common goal in forecasting. The results are interpreted to lead to help in forecasting measures. REFERENCES Books and Journals Ribeiro, V. and et.al.,2017, August. Importance of statistics for data mining and data science. In2017 5th International Conference on Future Internet of Things and Cloud Workshops (FiCloudW)(pp. 156-163). IEEE. Moray, R., 2020. Role and Importance of Statistics in Business Management.FOUNDED 1998, p.175. Fries, F. and et.al.,2020, March. The importance of statistics for photoluminescence quantum yieldmeasurements(ConferencePresentation).InOrganicPhotonicMaterialsand Devices XXII(Vol. 11277, p. 1127708). International Society for Optics and Photonics.
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Silvestre, C. and Meireles, A., 2020, October. Statistics for communication students. InProgram and Book of Abstracts XXVII Meeting of the Portuguese Association for Classification and Data Analysis (CLAD)(p. 73).