Assignment Sample on ACC01169 Quantitative Methods
Introduction
Quantitative method calculations are one of the important parts to understand different statistical interpretations. The project focuses on providing detailed statistical knowledge. The study also helps to understand the workability of excel. It shows the formulas which can be used in excel to calculate different quantitative problems. The project mainly focuses on the concept related to probability distribution, frequency-related problems, and hypothesis testing. The study has been divided into 4 parts and these fourth parts have been further divided into multiple subparts to demonstrate the relative knowledge.
Question 1
1A.
1) Frequency distribution
| Year | Return | Low range |
Highest range |
Frequency | ||
| 1993 | 46.21% | From | -50 | To | -30 | 1 |
| 1994 | -6.18% | More than | -30 | To | -10 | 1 |
| 1995 | 8.04% | More than | -10 | To | 10 | 3 |
| 1996 | 22.87% | More than | 10 | To | 30 | 3 |
| 1997 | 45.90% | More than | 30 | To | 50 | 2 |
| 1998 | 20.32% | Total 10 | ||||
| 1999 | 41.20% | |||||
| 2000 | -9.53% | |||||
| 2001 | -17.75% | |||||
| 2002 | -43.06% | |||||
Table 1: Frequency distribution
(Source: MS-Excel)
2) Cumulative frequency and relative frequency
| Year | Return | Low range | highest range | Frequencies | Relative frequency( Frequency/Total) | Cumulative relative frequency | ||
| 1993 | 46.21% | From | -50 | To | -30 | 1 | 0.1 | 0.1 |
| 1994 | -6.18% | More than | -30 | To | -10 | 1 | 0.1 | 0.2 |
| 1995 | 8.04% | More than | -10 | To | 10 | 3 | 0.3 | 0.5 |
| 1996 | 22.87% | More than | 10 | To | 30 | 3 | 0.3 | 0.8 |
| 1997 | 45.90% | More than | 30 | To | 50 | 2 | 0.2 | 1 |
| 1998 | 20.32% | Total | 10 | |||||
| 1999 | 41.20% | |||||||
| 2000 | -9.53% | |||||||
| 2001 | -17.75% | |||||||
| 2002 | -43.06% | |||||||
Table 2: Cumulative frequency and relative frequency
(Source: MS-Excel)
3) Systematic or unsystematic frequency
From the above, it can be seen that the frequency does not crate a graph that starts and ends at the same level. The curvature of the graph is also not the same. From this, it can be said that frequency distribution is systematic in nature (Sablan, 2019). The basic character of asymmetrical frequency is that it does not create a pattern. It is considered to be a natural and unbiased frequency.
1B.
1) Sample mean return
| Year | Return | Low range |
Highest range |
Frequencies | Mean | ||
| 1993 | 46.21% | From | -50 | To | -30 | 1 | 10.80% |
| 1994 | -6.18% | More than | -30 | To | -10 | 1 | |
| 1995 | 8.04% | More than | -10 | To | 10 | 3 | |
| 1996 | 22.87% | More than | 10 | To | 30 | 3 | |
| 1997 | 45.90% | More than | 30 | To | 50 | 2 | |
| 1998 | 20.32% | ||||||
| 1999 | 41.20% | ||||||
| 2000 | -9.53% | ||||||
| 2001 | -17.75% | ||||||
| 2002 | -43.06% | ||||||
Table 3: Sample mean return
(Source: MS-Excel)
2) Median return
| Year | Return | median |
| 1993 | 46.21% | 14.18% |
| 1994 | -6.18% | |
| 1995 | 8.04% | |
| 1996 | 22.87% | |
| 1997 | 45.90% | |
| 1998 | 20.32% | |
| 1999 | 41.20% | |
| 2000 | -9.53% | |
| 2001 | -17.75% | |
| 2002 | -43.06% |
Table4: median return
(Source: MS-Excel)
3) Intervals
| Year | Return | Low range | highest range | Friquence | Modal interval | ||
| 1993 | 46.21% | From | -50 | To | -30 | 1 | 1 |
| 1994 | -6.18% | More than | -30 | To | -10 | 1 | |
| 1995 | 8.04% | More than | -10 | To | 10 | 3 | |
| 1996 | 22.87% | More than | 10 | To | 30 | 3 | |
| 1997 | 45.90% | More than | 30 | To | 50 | 2 | |
| 1998 | 20.32% | ||||||
| 1999 | 41.20% | ||||||
| 2000 | -9.53% | ||||||
| 2001 | -17.75% | ||||||
| 2002 | -43.06% | ||||||
Table 5: Intervals
(Source: MS-Excel)
1C.
1) Geometric Mean and compound rate
Compound rate
The formula that is used to calculate the compound rate is as follows
These formulas are used in the case where the principal time increases over time.
Geometric Mean
| Year | Return | Return as a positive form | Geometric mean (0GEMEAN(Range 1:Range n)) |
| 1993 | 0.4621 | 0.4621 | 7.10% |
| 1994 | -0.0618 | 0.01 | |
| 1995 | 0.0804 | 0.0804 | |
| 1996 | 0.2287 | 0.2287 | |
| 1997 | 0.459 | 0.459 | |
| 1998 | 0.2032 | 0.2032 | |
| 1999 | 0.412 | 0.412 | |
| 2000 | -0.0953 | 0.01 | |
| 2001 | -0.1775 | 0.01 | |
| 2002 | -0.4306 | 0.01 |
Table 6: Geometric mean
(Source: MS-Excel)
2) Percentile
| percentile | value |
| 30 | -16.871 |
Table 7: percentile
(Source: MS-Excel)
1D.
1) Range
| Year | Return | range(max value-minimum value) |
| 1993 | 46.21% | 89.27% |
| 1994 | -6.18% | |
| 1995 | 8.04% | |
| 1996 | 22.87% | |
| 1997 | 45.90% | |
| 1998 | 20.32% | |
| 1999 | 41.20% | |
| 2000 | -9.53% | |
| 2001 | -17.75% | |
| 2002 | -43.06% |
Table 8: range
(Source: MS-Excel)
2) Mean absolute deviation
| Year | Return | Mean deviation |
| 1993 | 46.21% | 24% |
| 1994 | -6.18% | |
| 1995 | 8.04% | |
| 1996 | 22.87% | |
| 1997 | 45.90% | |
| 1998 | 20.32% | |
| 1999 | 41.20% | |
| 2000 | -9.53% | |
| 2001 | -17.75% | |
| 2002 | -43.06% |
Table 9: Mean absolute deviation
(Source: MS-Excel)
3) Variance
| Year | Return | Variance (=VAR(Range 1: Range n)) |
| 1993 | 46.21% | 8.97% |
| 1994 | -6.18% | |
| 1995 | 8.04% | |
| 1996 | 22.87% | |
| 1997 | 45.90% | |
| 1998 | 20.32% | |
| 1999 | 41.20% | |
| 2000 | -9.53% | |
| 2001 | -17.75% | |
| 2002 | -43.06% |
Table 10: variance
(Source: MS-Excel)
4) Standard deviation
| Year | Return | Standard deviation (=STEDV(Range1: Range n) |
| 1993 | 46.21% | 29.95% |
| 1994 | -6.18% | |
| 1995 | 8.04% | |
| 1996 | 22.87% | |
| 1997 | 45.90% | |
| 1998 | 20.32% | |
| 1999 | 41.20% | |
| 2000 | -9.53% | |
| 2001 | -17.75% | |
| 2002 | -43.06% |
Table 11: Standard deviation
(Source: MS-Excel)
Question 2
1. Graph
2. Correlation
| Income | Sales(Y) | Correlation coefficient | |
| 1 | 2450 | 162 | 0.64 |
| 2 | 3254 | 120 | |
| 3 | 3802 | 223 | |
| 4 | 2838 | 131 | |
| 5 | 2347 | 67 | |
| 6 | 3782 | 169 | |
| 7 | 3008 | 81 | |
| 8 | 2450 | 192 | |
| 9 | 2137 | 116 | |
| 10 | 2560 | 55 | |
| 11 | 4020 | 252 | |
| 12 | 4427 | 232 | |
| 13 | 2660 | 144 | |
| 14 | 2088 | 103 | |
| 15 | 2605 | 212 |
Table 12: Correlation
(Source: MS-Excel)
3. Regression equation
| Items | Income(X) | Sales(Y) | XY | X^2 | Y^2 |
| 2450 | 162 | 396900 | 6002500 | 26244 | |
| 3254 | 120 | 390480 | 10588516 | 14400 | |
| 3802 | 223 | 847846 | 14455204 | 49729 | |
| 2838 | 131 | 371778 | 8054244 | 17161 | |
| 2347 | 67 | 157249 | 5508409 | 4489 | |
| 3782 | 169 | 639158 | 14303524 | 28561 | |
| 3008 | 81 | 243648 | 9048064 | 6561 | |
| 2450 | 192 | 470400 | 6002500 | 36864 | |
| 2137 | 116 | 247892 | 4566769 | 13456 | |
| 2560 | 55 | 140800 | 6553600 | 3025 | |
| 4020 | 252 | 1013040 | 16160400 | 63504 | |
| 4427 | 232 | 1027064 | 19598329 | 53824 | |
| 2660 | 144 | 383040 | 7075600 | 20736 | |
| 2088 | 103 | 215064 | 4359744 | 10609 | |
| 2605 | 212 | 552260 | 6786025 | 44944 | |
| Summations | 44428 | 2259 | 7096619 | 139063428 | 394107 |
| an (intercept) | -0.59 | ||||
| b (Slope) | 0.003 | ||||
| Hence the regression line | Y=a+bX
Y=-0.59+0.003*X |
||||
Table 13: Regression equation
(Source: MS-Excel)
4. Interpretation of regression equation
The regression equation follows a straight line. From this, it can be seen that the slope of the line is 0.003. The line intersects with each other at the point of “-0.59”.
Question 3
1. Simple index number
| Average search engine rates (£) per 1000 total visits of social media traffic source. | Number of search engine advertisements per 1000 users of search engine traffic source | Average social media rates (£) per 1000 users of social media traffic source | Average social media rates (£) per 1000 users of social media traffic source | Simple Index | |
| 0 | 184 | 35 | 395 | 40 | #N/A |
| 1 | 200 | 32 | 406 | 40 | |
| 2 | 326 | 30 | 450 | 28 | |
| 3 | 326 | 30 | 450 | 25 | |
| 4 | 346 | 25 | 530 | 18 | |
| 5 | 372 | 14 | 540 | 13 | |
| 6 | 392 | 10 | 580 | 12 | |
| 7 | 395 | 8 | 640 | 12 | |
| 8 | 395 | 8 | 660 | 7 | |
| 9 | 456 | 8 | 660 | 6 | |
| 10 | 516 | 5 | 670 | 5 | |
| 11 | 526 | 3 | 670 | 4 |
Table 14: Simple index number
(Source: MS-Excel)
2) Unweighted index
| Average search engine rates (£) per 1000 total visits of social media traffic source. | Unweighted average | Number of search engine advertisements per 1000 users of search engine traffic source | Unweighted average | Average social media rates (£) per 1000 users of social media traffic source | Unweighted average | Average social media rates (£) per 1000 users of social media traffic source | Unweighted average |
| 184 | 4% | 35 | 17% | 395 | 6% | 40 | 19% |
| 200 | 5% | 32 | 15% | 406 | 6% | 40 | 19% |
| 326 | 7% | 30 | 14% | 450 | 7% | 28 | 13% |
| 326 | 7% | 30 | 14% | 450 | 7% | 25 | 12% |
| 346 | 8% | 25 | 12% | 530 | 8% | 18 | 9% |
| 372 | 8% | 14 | 7% | 540 | 8% | 13 | 6% |
| 392 | 9% | 10 | 5% | 580 | 9% | 12 | 6% |
| 395 | 9% | 8 | 4% | 640 | 10% | 12 | 6% |
| 395 | 9% | 8 | 4% | 660 | 10% | 7 | 3% |
| 456 | 10% | 8 | 4% | 660 | 10% | 6 | 3% |
| 516 | 12% | 5 | 2% | 670 | 10% | 5 | 2% |
| 526 | 12% | 3 | 1% | 670 | 10% | 4 | 2% |
| 4434 | 208 | 6651 | 210 |
Table 15: Unweighted Index
(Source: MS-Excel)
3) Laspeyres index
| Laspeyres index |
| 21.32 |
Table 16: Laspeyres index
(Source: MS-Excel)
4) Paasche index
| Paasche index |
| 0.666667 |
Table 17: Paasche Index
(Source: MS-Excel)
Question 4
4A.
1) Probability distribution
| Average starting income | 40000 |
| Standard deviation | 5000 |
| Sample size | 80 |
| Standard value | 40000 |
| Probability Distribution | -7 |
Table 18: Probability distribution
(Source: MS-Excel)
2) Probability of sample mean over 41000
| Probability of sample mean over 41000 | 0.013 |
Table 19: Probability of sample mean
(Source: MS-Excel)
3) Probability of sample mean below 39000
| Probability of sample mean below 39000 | 0.012 |
Table 20: Probability of sample mean
(Source: MS-Excel)
4) Is sample size was 20
4B.
1) Hypothesis testing
| Mean | 36.5 |
| Standard Error | 3.5 |
| Median | 36.5 |
| Mode | #N/A |
| Standard Deviation | 4.949747468 |
| Sample Variance | 24.5 |
| Kurtosis | #DIV/0! |
| Skewness | #DIV/0! |
| Range | 7 |
| Minimum | 33 |
| Maximum | 40 |
| Sum | 73 |
| Count | 2 |
Table 21: Hypothesis testing
(Source: MS-Excel)
2) Confidence interval method
| Confidence Level (95.0%) | 44.47171657 |
| Upper CI (%) | 80.97171657 |
| Lower CI (%) | -7.971716569 |
Table 22: Confidence interval method
(Source: MS-Excel)
Conclusion
The report shows that statistical analysis is one of the best ways to interpret datas. It helps to understand whether a particular sample size has any hidden relation with individual sample elements or not. It also helps to subtract or sort data’s from a sample file. Sorting important data is one of the important processes of any research process. It helps researchers to identify the required important information from the sea of data available in different sources. The probability section also helps to identify the likelihood of events. This helps researchers understand the significance of their research.
Reference List
Journals
Auerbach, D., 2018. ‘A cannon’s burst discharged against a ruinated wall’: A Critique of Quantitative Methods in Shakespearean Authorial Attribution. Authorship, 7(2).
Auerbach, D., 2018. ‘A cannon’s burst discharged against a ruinated wall’: A Critique of Quantitative Methods in Shakespearean Authorial Attribution. Authorship, 7(2).
Blackstone, A., 2018. Principles of sociological inquiry: Qualitative and quantitative methods.
Johnston, R., Harris, R., Jones, K., Manley, D., Wang, W.W. and Wolf, L., 2019. Quantitative methods I: The world we have lost–or where we started from. Progress in Human Geography, 43(6), pp.1133-1142.
Jürgens, U., 2018. ‘Real’versus ‘mental’food deserts from the consumer perspective–concepts and quantitative methods applied to rural areas of Germany. DIE ERDE–Journal of the Geographical Society of Berlin, 149(1), pp.25-43.
King, K.M., Pullmann, M.D., Lyon, A.R., Dorsey, S. and Lewis, C.C., 2019. Using implementation science to close the gap between the optimal and typical practice of quantitative methods in clinical science. Journal of abnormal psychology, 128(6), p.547.
Korauš, A., Gombár, M., Kelemen, P. and Backa, S., 2019. Using quantitative methods to identify insecurity due to unusual business operations. Entrepreneurship and Sustainability Issues, 6(3), p.1101.
Moats, D. and Borra, E., 2018. Quali-quantitative methods beyond networks: Studying information diffusion on Twitter with the Modulation Sequencer. Big Data & Society, 5(1), p.2053951718772137.
Sablan, J.R., 2019. Can you really measure that? Combining critical race theory and quantitative methods. American Educational Research Journal, 56(1), pp.178-203.
Srivastava, A.B., Kobeissy, F.H. and Gold, M.S., 2019. Qualitative vs. Quantitative Methods in Psychiatric Research: Updated. Psychiatric Disorders, pp.23-37.
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