Numeracy and Data Analysis (Coursework Sample)

Numeracy and Data Analysis Table of Contents TOC \o "1-3" \h \z \u Introduction PAGEREF _Toc123825462 \h 3Arrangement of data PAGEREF _Toc123825463 \h 4Visualisation of data PAGEREF _Toc123825464 \h 5Calculation PAGEREF _Toc123825465 \h 6Linear Forecasting model PAGEREF _Toc123825466 \h 10Conclusion PAGEREF _Toc123825467 \h 12References PAGEREF _Toc123825468 \h 13 Introduction In this report, the data will be analysed in excel. At first, the data of the wind speed will be considered for ten consecutive days in Manchester, UK. Then it will be visualised in chart format. Then the descriptive statistics will be calculated. Then, using the Linear Forecasting model the data for the 11th day and the 12th will be predicted. Arrangement of data Date 25/12/2022 26/12/2022 27/12/2022 28/12/2022 29/12/2022 30/12/2022 31/12/2022 01/01/2023 02/01/2023 03/01/2023 Wind speed (“Km/hr”) 11 19 11 13 24 17 4 9 11 11 Table 1: Arrangement of data in tabular form (Source: Created by the learner) For the data, the wind speed for Manchester, England, United Kingdom was considered from the website https://www.timeanddate.com. From, table 1, the wind speed can be observed for ten consecutive days, from 25th December 2022 to 3rd January 2023. For this case, the wind speed is taken at 11:50 am for the respective days. Visualisation of data Chart 1: Line chart for wind speed (Source: Created by the learner) Chart 2: Bar chart for wind speed (Source: Created by the learner) Calculation Mean In the mean, the summation of all the data is divided with the number of items in the set (Cooksey, 2020). With the help of the mean, the central tendency of the set of data is observed. Formula: Here, µ = “Mean”, ∑ = “Sum of / Total”, x = “Individual data value”, N = “Number of items” ∑x = 11+19+11+13+24+17+4+9+11+11 Total terms = 10, Thus, N = 10 Thus, mean = 130 / 10 = 13 “Km/hr” Median In the median, the central value of the sorted data is observed. Through this, the value in the middle of the database is observed (Cooksey, 2020). Serial number Wind speed (Km/hr) 1 4 2 9 3 11 4 11 5 11 6 11 7 13 8 17 9 19 10 24 Table 2: Arrangement of wind speed in ascending order (Source: Created by the learner) Formula: Here, N = “Number of items” Thus, Median = [5th term + 6th term]/2 = (11+11)/2 = 22/2 = 11 Thus, the median windspeed is 11 “Km/hr” Mode In the mode, the value which has the highest number of occurrence in the dataset is observed (Cleff, 2019). Wind speed (Km/hr) Frequency 4 1 9 1 11 4 13 1 17 1 19 1 24 1 Table 3: Wind speed frequency table (Source: Created by the learner) From table 3, 11 has the highest frequency. Thus, the mode is 11 “Km/hr”. Range In the range, the variation of the data between the highest point and lowest point is observed (Cleff, 2019). The highest windspeed is 24 “Km/hr”, and the lowest windspeed is 4 “Km/hr”. Highest windspeed - Lowest windspeed = 24 “Km/hr” - 4 “Km/hr” Thus, the range is 20 “Km/hr”. Standard Deviation In the standard deviation, the square root of the variance is calculated. It provides the dispersion of the values from the mean. Formula: Here, σ = “Standard deviation”, µ = “Mean”, ∑ = “Sum of / Total”, x = “Individual data value’, N = “Number of items”. x 11 19 11 13 24 17 4 9 11 11 x-µ -2 6 -2 0 11 4 -9 -4 -2 -2 (x-µ)^2 4 36 4 0 121 16 81 16 4 4 ∑(x-µ)^2 286 Table 4: Standard deviation calculation (Source: Created by the learner) From table 4, ∑(x-µ)^2 = 286 Thus, ∑(x-µ)^2/ 10 = 286 /10 = 28.6 Then, √(∑(x-µ)^2/ 10) = 5.35 Hence, the standard deviation is 5.35. Linear Forecasting model Linear forecasting helps in determining the future values from the present values. It uses the linear function (Oluwa, 2019). In this model, the value of an unknown variable is calculated with the help of a known variable. With the help of this forecasting, the demand can be predicted (Oluwa, 2019). Assumption: For the calculation, it has been assumed that is a dependence of wind speed on temperature. So, the wind speed in “Km/hr” is taken as the “y” variable, the dependent variable. And the temperature in Celsius is taken as the “x” variable, the independent variable Wind speed (Km/hr) 11 19 11 13 24 17 4 9 11 11 ∑y 130 Temperature (Celsius) 9 6 6 10 7 9 9 8 5 9 ∑x 78 x^2 81 36 36 100 49 81 81 64 25 81 ∑(x^2) 634 xy 99 114 66 130 168 153 36 72 55 99 ∑xy 992 Table 5: Forecasting model calculation (Source: Created by the learner) i) Fo...