Data Analysis and Forecasting

Data Analysis and Forecasting

Student Name:

Student ID:

Introduction

In this report, main concern will be to analyse a good amount of the knowledge about numeric analysis of data and representation of data in tabular form using an effective tool. This report will cover different aspects of data analysis and then perform calculations accordingly by using standard formulas and linear forecasting.

Table representation of monthly expenses

Data representation is more attractive and understandable when it is in tabular form. Following table is presenting expenses are observed for 10 months from January to October. The tool used for representation is MS excel (Christopher et al., 2021).

Month	Expenses
Jan	30
Feb	10
Mar	40
April	15
May	20
June	5
July	10
Aug	25
Sep	15
Oct	10

Representation of monthly expenses through Chart

Bar Chart

Above bar chart has represented expenses according to month sequence-wise and also showed the difference in the expenses for all months.

Scatter Plot

Scatter plot above is showing variation of the expenses on monthly basis for starting them months by using MS excel tool.

Calculation of Expenses

Mean of Expenses

In the table expenses have given for consecutive 10 months so mean will be calculated for the given data set (Beck et al., 2019).

So for calculating mean formula is-

?Y / N

Where ?Y is representing sum of expenses of all months and N is the number of expenses given in the table.

Now, Mean = = 18

So mean of the expenses will be £18.

Median of Expenses

Calculation of median is done according to number of entries given in the table or number of sets of data given. It also depends upon place values of the data set.

For example, if number of entries of data is in odd number (like 7, 11, etc.) then place values can be calculated by the formula N/2, where N is total number of entries in the table.

If number of data entries is in even numbers (like 10, 12, etc.) then place values will be calculated as (N+1) / 2. In this case possibility of getting decimal values for place, values are very usual which means number before decimal will the first place values, and place value just after that will be considered as second one.

These values only can be calculated when data entries are arranged in ascending or descending order (Higgins, Li, and Deeks, 2019).

Last step of calculating median is to divide this value by 2.

For the given table of expenses, total number of entries is 10, which is an even number.

So, place value = (N+1) /2 = (10+1) / 2 = 11/2 = 5.5

So place values will be 5^th and 6^th.

According to order of the expenses is as following-

5, 10, 10, 10, 15, 15, 20, 25, 30, 40

Now, median = (15+15) / 2 = 30 / 2 = 15

So median expense is £15.

Mode of Expenses

Mode of data entries in the entry that has higher frequency. Mode can be calculated after arranging data entries in ascending or descending order as below-

5, 10, 10, 10, 15, 15, 20, 25, 30, 40

So it is clear that frequency of 10 is highest so mode will be £10.

Range of Expenses

Range of any data represents the difference between highest and lowest value of the table entry and it can be checked easily after arranging data entries in ascending or descending order-

5, 10, 10, 10, 15, 15, 20, 25, 30, 40

So, it is evident that highest value is 40 and lowest value is 5 then range will be calculated as-

Range = (40-5) = £35

Standard Deviation of Expenses

Calculation of standard deviation, first it is required to calculate variance because standard deviation is under root of variance. So for calculating variance and SD table needs to be constructed as below-

Month (X)	Expenses (Y)	Mean (M)	(Y-M)	(Y-M)2
Jan	30	18	12	144
Feb	10	18	-8	64
Mar	40	18	22	484
April	15	18	-3	9
May	20	18	2	4
June	5	18	-13	169
July	10	18	-8	64
Aug	25	18	7	49
Sep	15	18	-3	9
Oct	10	18	-8	64
Sum	180			1060

Because mean is equal to 18.

So variance can be calculated by the following formula-

Variance = {?(Y-M)² / N}^1/2

= {1060 / 10} = 106

So, Standard Deviation = (106)^1/2 = 10.29

So standard deviation of expenses will be £10.29.

Model of Liner Forecasting of Expenses

Linear forecasting is very effective method to calculated missing data so expenses for last two months (11^th and 12^th month) can be calculated by using following formula (Baptista et al., 2018)-

Y = mx + c

Month (X)	Expenses (Y)	(X*Y)	(X)2
Jan (1)	30	30	1
Feb (2)	10	20	4
Mar (3)	40	120	9
April (4)	15	60	16
May (5)	20	100	25
June (6)	5	30	36
July (7)	10	70	49
Aug (8)	25	200	64
Sep (9)	15	135	81
Oct (10)	10	100	100
Sum= 55	180	865	385

So, values are clear by the table above as following-

?X (Sum of months) = 55

?Y (Sum of expenses) = 180

?(X*Y) = 865

?(X)² = 385

Calculation of m for expenses

m = {(10*865 – 55*18) / (10*385 – (55)²)}

m = {7660 / 825}

m = 9.28

Calculation of c for expense

c = (?Y/N - m ?X) / N

c = (18 – 9.28*55) / 10

c = -492.4 / 10 = -49.24

Final forecasting for expenses

Month 11^th (Nov)

Y = mx + c

c = -49.24

x = 11

Y = 9.28*11 + (-49.24)

Y = 102.08 – 49.24

Y = 52.84

So expense for November is £52.84.

Month 12^th (Dec)

Y = 9.28*12 + (-49.24)

Y = 111.36 – 49.24

Y = 62.12

So expense for December is £62.12.

Conclusion

This report has analysed all aspects of data by calculating mean, mode, median, range, standard deviation apart from these calculation report also calculated expense for left months so that better analysis can be performed. This report is an informative source numeric analysis.

References

Baptista, M., Sankararaman, S., de Medeiros, I.P., Nascimento Jr, C., Prendinger, H. and Henriques, E.M., 2018. Forecasting fault events for predictive maintenance using data-driven techniques and ARMA modeling. Computers & Industrial Engineering, 115, pp.41-53.

Beck, R.W., Bergenstal, R.M., Cheng, P., Kollman, C., Carlson, A.L., Johnson, M.L. and Rodbard, D., 2019. The relationships between time in range, hyperglycemia metrics, and HbA1c. Journal of diabetes science and technology, 13(4), pp.614-626.

Christopher, K.L., Patnaik, J.L., Miller, D.C., Lynch, A.M., Taravella, M.J. and Davidson, R.S., 2021. Accuracy of Intraoperative Aberrometry, Barrett True-K With and Without Posterior Cornea Measurements, Shammas-PL, and Haigis-L Formulas After Myopic Refractive Surgery. Journal of Refractive Surgery, 37(1), pp.60-68.

Higgins, J.P., Li, T. and Deeks, J.J., 2019. Choosing effect measures and computing estimates of effect. Cochrane handbook for systematic reviews of interventions, pp.143-176.