Numeracy and Data Analysis: Sleep Hours, Statistics, and Predictions

This assignment delves into the realm of numeracy and data analysis, presenting a comprehensive analysis of sleep hours data. The solution begins by organizing the data in a clear table format, followed by a graphical presentation using both bar and line graphs to visualize the trends. The core of the assignment involves the computation of descriptive statistics, including the mean, median, mode, range, and standard deviation, providing a detailed interpretation of each. Furthermore, the assignment applies linear forecasting techniques to predict sleep hours for the 12th and 14th days, showcasing the practical application of statistical methods. The assignment concludes with a reference list of the resources used. This assignment is a great example for students to learn and understand data analysis and statistical concepts.

NUMERACY AND DATA
ANALYSIS

TABLE OF CONTENTS
TABLE OF CONTENTS................................................................................................................2
MAIN BODY..................................................................................................................................1
1. Arrangement of data in table format........................................................................................1
2. Graphical Presentation.............................................................................................................1
3. Computation of descriptive statistics.......................................................................................2
4. Liner forecasting for prediction of values for 12th and 14th day..............................................5
REFERENCES................................................................................................................................7

MAIN BODY
1. Arrangement of data in table format.
Sr. No. Date
Sleep hours
per day
1 1st may 2020 8
2 2nd may 2020 9
3 3rd may 2020 6
4 4th may 2020 10
5 5th may 2020 5
6 6th may 2020 8
7 7th may 2020 6
8 8th may 2020 9
9 9th may 2020 12
10 10th may 2020 8
2. Graphical Presentation
Bar Graph
1st
may
2020
2nd
may
2020
3rd
may
2020
4th
may
2020
5th
may
2020
6th
may
2020
7th
may
2020
8th
may
2020
9th
may
2020
10th
may
2020
0
2
4
6
8
10
12
Sleep Hours per day
Sleep Hours per day
1

Line Graph
1st
may
2020
2nd
may
2020
3rd
may
2020
4th
may
2020
5th
may
2020
6th
may
2020
7th
may
2020
8th
may
2020
9th
may
2020
10th
may
2020
0
2
4
6
8
10
12
14
Sleep Hours per day
Sleep Hours per day
3. Computation of descriptive statistics
Mean
Sr. No. Date
Sleep hours
per day
1 1st may 2020 8
2 2nd may 2020 9
3 3rd may 2020 6
4 4th may 2020 10
5 5th may 2020 5
6 6th may 2020 8
7 7th may 2020 6
8 8th may 2020 9
9 9th may 2020 12
10 10th may 2020 8
Sum total of bill
payment 81
No. of observation 10
Mean 8.1
Interpretation- The results generated indicates that mean value for sleep hours per day
for past 10 days equating as 8.1. It is been calculated by making average of 10 days data by
dividing the total of the data attained as 81 with total number of observation that is 10.
Median
2

Sr. No. Date
Data in
relation to
Sleep hours
per day
1 1st may 2020 8
2 2nd may 2020 9
3 3rd may 2020 6
4 4th may 2020 10
5 5th may 2020 5
6 6th may 2020 8
7 7th may 2020 6
8 8th may 2020 9
9 9th may 2020 12
10 10th may 2020 8
No. of
observation 81
M= (10+1)/2 5.5
M= (400+300)/2 6.5
Interpretation- The assessment depicts that value of median equated to 6.5 in respect of
sleep hours per day data of last ten days. It is computed by applying formula of median i.e.
(n+1)/2 where n is stated as the no. of observation (Ho and Yu, 2015). It is considered as the
mid value of an entire data.
Mode
Date Sleep Hours
1st may 2020 8
2nd may 2020 9
3rd may 2020 6
4th may 2020 10
5th may 2020 5
6th may 2020 8
7th may 2020 6
8th may 2020 9
9th may 2020 12
10th may 2020 8
Mode = 8
3

Interpretation- From the analysis it is analyzed that value of mode is 400. Mode is
depicted as the value that occurs more number of times or the highest repeated value in the data
(Norman, Mello and Choi, 2016).
Range
Particulars Formula Amount
Maximum 12
Minimum 5
Range
Largest value-Smallest
value 7
Interpretation- The results shows the range value as 7 which is been calculated by
subtracting the lowest value that is 5 from the highest value equating to 12. Range is described as
difference between the maximum & minimum value in data (Sarstedt and Mooi, 2019).
Standard deviation
Date
Sleep
Hours (X) X^2
1st may 2020 8 64
2nd may 2020 9 81
3rd may 2020 6 36
4th may 2020 10 100
5th may 2020 5 25
6th may 2020 8 64
7th may 2020 6 36
8th may 2020 9 81
9th may 2020 12 144
10th may 2020 8 64
Total 81 695
Standard deviation= Square root of ∑x^2 / N – (∑x / n) ^ 2
= SQRT of (695 / 81) – (81 / 10) ^ 2
= SQRT of 8.5802 – 65.61
= SQRT of 57.0298
= 7.55
4

Interpretation- The analysis shows that the standard deviation is 7.55. It reflects that
dispersion from mean is 7.55. It is worked out by mean value and reducing it by the squaring
result.
4. Liner forecasting for prediction of values for 12th and 14th day.
Date X Sleep Hours
(Y)
X*Y X^2
1st march 2020 1 8 8 1
2nd march 2020 2 9 18 4
3rd march 2020 3 6 18 9
4th march 2020 4 10 40 16
5th march 2020 5 5 25 25
6th march 2020 6 8 48 36
7th march 2020 7 6 42 49
8th march 2020 8 9 72 64
9th march 2020 9 12 108 81
10th march 2020 10 8 80 100
Total 55 81 459 385
i) Calculation of m values
m = NΣxy – Σx Σy / NΣ x^2 – (Σx)^2
Y = mX + c
m = 10 (459) - (55 * 81) / (10 * 385) – (55)^2
m = (4590 – 4455) / (3850 – 3025)
m = 135 / 825
m = 0.16
ii) Calculation of c values
c = Σy – m Σx / N
c = 81 – (0.16 * 55) / 10
c = (81 – 9) / 10
5

c = 72 / 10
c = 7.2
iii) Computing value of Y by making use of m and c value
For 11th day -
Y = mX + c
= 0.16 * (11) + (7.2)
= 1.76 + 7.2
= 8.96 = 9 hours approx
For 15th day -
Y = mX + c
= 0.16 * (15) + (7.2)
= 2.4 + 7.2
= 9.6 = 10 hours approx
Interpretation- The above analysis shows that sleep for 11th day will be 9 and for 15th day
will be 10. The values are computed by multiplying values of m with x and adding them to c.
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REFERENCES
Books and Journals
Ho, A. D. and Yu, C. C., 2015. Descriptive statistics for modern test score distributions:
Skewness, kurtosis, discreteness, and ceiling effects. Educational and Psychological
Measurement. 75(3). pp.365-388.
Norman, C., Mello, M. and Choi, B., 2016. Identifying frequent users of an urban emergency
medical service using descriptive statistics and regression analyses. Western Journal of
Emergency Medicine. 17(1). p.39.
Sarstedt, M. and Mooi, E., 2019. Descriptive Statistics. In A Concise Guide to Market
Research (pp. 91-150). Springer, Berlin, Heidelberg.
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