Data Analysis and Forecasting Report: Sleep Hours Prediction

This report presents a comprehensive data analysis and forecasting study based on sleep hours data collected over ten consecutive days. The analysis begins with a table summarizing the data, followed by graphical representations using line and pie charts to visualize the sleep patterns. The core of the report involves calculating and discussing various statistical measures, including mean, median, mode, range, and standard deviation, to identify patterns and trends within the data. Furthermore, a linear forecasting model is applied to predict sleep hours for upcoming days, providing insights into potential future sleep patterns. The report concludes with the application of the linear forecasting model, which allows for the prediction of sleep hours for the 11th and 15th days, demonstrating the practical application of statistical methods in making informed predictions. References to relevant books and journals are also provided to support the analysis and findings presented in this report.

Data Analysis and
Forecasting

Table of Contents
INTRODUCTION...........................................................................................................................1
Main Body.......................................................................................................................................1
1. Table Format......................................................................................................................1
2. Graphical representation of data.........................................................................................2
3. Calculation and discussion of data pattern.........................................................................4
4. Liner-forecasting model.....................................................................................................7
REFERENCES................................................................................................................................9

INTRODUCTION
Data analysis is one of the important process which is used for identifying a particular
pattern in a specific information, then put the same for making predictions for future (Little and
Rubin, 2019). To analyse this concept, a data based on sleeping hours for ten consecutive days is
taken, then a report is prepared for forecasting upcoming days. For this purpose, some statistical
method has applied like mean, median, mode, range, standard deviations and linear forecasting
model.
Main Body
1. Table Format
Sleeping hours per day:
Days
Sleep
hours per
day
01/04/20 9
02/04/20 11
03/04/20 8
04/04/20 12
05/04/20 11
06/04/20 8
07/04/20 10
08/04/20 8
09/04/20 7
10/04/20 10
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2. Graphical representation of data
Sleeping hours per day:
Days
Sleep
hours per
day
01/04/20 9
02/04/20 11
03/04/20 8
04/04/20 12
05/04/20 11
06/04/20 8
07/04/20 10
08/04/20 8
09/04/20 7
10/04/20 10
1. Line Chart of sleep hours per day
2

2. Pie Chart of sleep hours per day
3

3. Calculation and discussion of data pattern
In order to predicate sleep hours for upcoming days, it is essential to identify the pattern of
data, which can only be done by using statistical methods, as given below –
Mean: This method shows the average of certain data, by using below formula –
Mean = sum of total observation
total number of observation
Median: It shows the number that divides entire statistical data into two half parts equally,
where it is essential to rearranging the data in term of ascending order before segmenting, by
using below formula –
Median = (No. of total observation + 1) if number is odd, else
2
= No. of observation
2
Mode: It provides highest occurrence of observation i.e. data which repeat most times
Range: It illustrates difference between highest observations to lower one:
Range = Maximum observation – Minimum Observation
Standard Deviations: It is equal to square root of variance
Standard Deviation =√ (variance)
Variance2 = {∑ (x – mean) / N} 2
Calculation:
Days
Sleep
hours
per
day
1/4/2020 9
2/4/2020 11
3/4/2020 8
4/4/2020 12
5/4/2020 11
6/4/2020 8
7/4/2020 10
8/4/2020 8
9/4/2020 7
10/4/2020 10
Total 9.4
4

Mean 94
Median 9.5
Mode 8
Mean = (Sum of Observation) / Number of observation
= 94 / 10
= 9.4 hours
Median = 10 / 2
= 5th Observation
= ½ (11 + 8) = 9.5 hours
Mode = 8 (repeated three times)
Range = Max – Min
= 12 – 7
= 5 hours
For present data, variance and standard deviation of dispersed data is calculated by using
given information
Days
Sleep
hours
per
day
(x-
mean) (x-mean)2
1 9 -0.4 0.16
2 11 1.6 2.56
3 8 -1.4 1.96
4 12 2.6 6.76
5 11 1.6 2.56
6 8 -1.4 1.96
7 10 0.6 0.36
8 8 -1.4 1.96
9 7 -2.4 5.76
10 10 0.6 0.36
Mean
= 9.4 24.4
Variance = [ ∑(x – mean) 2 / N ]
= 24.4 / 10 = 2.44
Std Dev. = √variance
5

=√ 2.44 = 1.56
6

4. Liner-forecasting model
For predicting the data of coming days, linear forecasting model can be applied in
following way –
y = mx + c
where, given linear equation indicates slope of a line as m and c as a constant -
m = Change in Y
Change in X
Days Sleep hours
per day (Y)
X2
∑XY
1 9 1 9
2 11 4 22
3 8 9 24
4 12 16 48
5 11 25 55
6 8 36 48
7 10 49 70
8 8 64 64
9 7 81 63
10 10 100 100
55 94 385 503
1. m using above table can be calculated by using given formula-
m = N * ∑XY - ∑X * ∑Y
N * ∑X2 - (∑X)2
= 10 * 503 – 55 * 94
10 * 385 – (55)2
= 5030 – 5170 / 3850 – 3025
= -140/ 825 = -0.17 approx.
Similarly,
c = (∑Y – m ∑x) / N
= 94 – (-0.17) * 55 / 10
= 10.3 approx.
7

So, sleep hours for 11th and 15th day of same month, can be predicted as –
For 11th day -
Y = m x + c
= (-0.17) * 11 + 10.3
= 8.4 hours approx.
While for 15th day, it is
Y = m x + c
= (-0.17) * 15 + 10.3
= 7.8 hours approx.
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REFERENCES
Books and Journals
Little, R. J. and Rubin, D. B., 2019. Statistical analysis with missing data (Vol. 793). Wiley.
Silverman, B. W., 2018. Density estimation for statistics and data analysis. Routledge.
Washington, S. and et. al., 2020. Statistical and econometric methods for transportation data
analysis. CRC press.
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