Statistical Analysis of Mainland Electricity Frequencies - Assignment Example

Statistical analysis of mainland power system. Name: Institution: Professor: Course: Unit code: Date: Mainland electricity has been always seen as stable but a deeper look into frequencies shows that there are major discrepancies in the output frequencies. The frequency change is a major bond of contention and this call for deeper analysis to gain a deeper understanding of the severity of the situation. There are many causes for this discrepancies but analysis and visual impression of the changes can help the management and the authorities to understand the solution and mitigation of problems associated to it. The values in consideration are as shown below. Summary of values to be used in the statistical analysis. Time Frequency. 09-Jul-17 23:24:00 49.96 09-Jul-17 23:24:04 49.96 09-Jul-17 23:24:08 49.97 09-Jul-17 23:24:12 49.97 09-Jul-17 23:24:16 49.97 09-Jul-17 23:24:20 49.97 09-Jul-17 23:24:24 49.98 09-Jul-17 23:24:28 49.98 09-Jul-17 23:24:32 49.98 09-Jul-17 23:24:36 49.98 09-Jul-17 23:24:40 49.99 09-Jul-17 23:24:44 49.99 09-Jul-17 23:24:48 50.00 09-Jul-17 23:24:52 50.01 09-Jul-17 23:24:56 50.01 09-Jul-17 23:25:00 50.00 09-Jul-17 23:25:04 50.00 09-Jul-17 23:25:08 49.99 09-Jul-17 23:25:12 49.99 09-Jul-17 23:25:16 49.98 09-Jul-17 23:25:20 49.99 09-Jul-17 23:25:24 50.00 09-Jul-17 23:25:28 50.00 09-Jul-17 23:25:32 50.00 09-Jul-17 23:25:36 50.00 09-Jul-17 23:25:40 49.99 09-Jul-17 23:25:44 49.99 09-Jul-17 23:25:48 49.99 09-Jul-17 23:25:52 49.98 09-Jul-17 23:25:56 49.98 09-Jul-17 23:26:00 49.99 09-Jul-17 23:26:04 50.00 09-Jul-17 23:26:08 50.00 09-Jul-17 23:26:12 50.00 09-Jul-17 23:26:16 50.00 09-Jul-17 23:26:20 49.99 09-Jul-17 23:26:24 49.98 09-Jul-17 23:26:28 49.98 09-Jul-17 23:26:32 49.99 09-Jul-17 23:26:36 50.00 09-Jul-17 23:26:40 50.00 09-Jul-17 23:26:44 50.01 09-Jul-17 23:26:48 50.01 09-Jul-17 23:26:52 50.02 09-Jul-17 23:26:56 50.03 09-Jul-17 23:27:00 50.03 09-Jul-17 23:27:04 50.04 09-Jul-17 23:27:08 50.04 09-Jul-17 23:27:12 50.02 09-Jul-17 23:27:16 50.02 09-Jul-17 23:27:20 50.03 09-Jul-17 23:27:24 50.04 09-Jul-17 23:27:28 50.04 09-Jul-17 23:27:32 50.04 09-Jul-17 23:27:36 50.04 09-Jul-17 23:27:40 50.05 09-Jul-17 23:27:44 50.04 09-Jul-17 23:27:48 50.02 09-Jul-17 23:27:52 50.01 09-Jul-17 23:27:56 50.03 09-Jul-17 23:28:00 50.02 09-Jul-17 23:28:04 50.01 09-Jul-17 23:28:08 50.03 09-Jul-17 23:28:12 50.02 09-Jul-17 23:28:16 50.00 09-Jul-17 23:28:20 49.99 09-Jul-17 23:28:24 50.00 09-Jul-17 23:28:28 50.01 09-Jul-17 23:28:32 50.01 09-Jul-17 23:28:36 50.00 09-Jul-17 23:28:40 50.00 09-Jul-17 23:28:44 50.00 09-Jul-17 23:28:48 50.00 09-Jul-17 23:28:52 50.02 09-Jul-17 23:28:56 50.01 09-Jul-17 23:29:00 50.00 09-Jul-17 23:29:04 50.00 09-Jul-17 23:29:08 50.01 09-Jul-17 23:29:12 50.00 09-Jul-17 23:29:16 50.00 09-Jul-17 23:29:20 50.00 09-Jul-17 23:29:24 50.00 09-Jul-17 23:29:28 50.00 09-Jul-17 23:29:32 49.97 09-Jul-17 23:29:36 49.96 09-Jul-17 23:29:40 49.96 09-Jul-17 23:29:44 49.96 09-Jul-17 23:29:48 49.95 09-Jul-17 23:29:52 49.96 09-Jul-17 23:29:56 49.96 09-Jul-17 23:30:00 49.97 09-Jul-17 23:30:04 49.96 09-Jul-17 23:30:08 49.94 09-Jul-17 23:30:12 49.92 09-Jul-17 23:30:16 49.92 09-Jul-17 23:30:20 49.91 09-Jul-17 23:30:24 49.90 09-Jul-17 23:30:28 49.90 09-Jul-17 23:30:32 49.89 09-Jul-17 23:30:36 49.88 09-Jul-17 23:30:40 49.86 09-Jul-17 23:30:44 49.84 09-Jul-17 23:30:48 49.85 09-Jul-17 23:30:52 49.86 09-Jul-17 23:30:56 49.86 09-Jul-17 23:31:00 49.87 09-Jul-17 23:31:04 49.88 09-Jul-17 23:31:08 49.89 09-Jul-17 23:31:12 49.88 09-Jul-17 23:31:16 49.87 09-Jul-17 23:31:20 49.88 09-Jul-17 23:31:24 49.88 09-Jul-17 23:31:28 49.89 09-Jul-17 23:31:32 49.91 09-Jul-17 23:31:36 49.90 09-Jul-17 23:31:40 49.89 09-Jul-17 23:31:44 49.89 09-Jul-17 23:31:48 49.89 09-Jul-17 23:31:52 49.90 09-Jul-17 23:31:56 49.90 09-Jul-17 23:32:00 49.89 09-Jul-17 23:32:04 49.88 09-Jul-17 23:32:08 49.90 09-Jul-17 23:32:12 49.91 09-Jul-17 23:32:16 49.92 09-Jul-17 23:32:20 49.92 09-Jul-17 23:32:24 49.92 09-Jul-17 23:32:28 49.92 09-Jul-17 23:32:32 49.92 09-Jul-17 23:32:36 49.94 09-Jul-17 23:32:40 49.96 09-Jul-17 23:32:44 49.97 09-Jul-17 23:32:48 49.97 09-Jul-17 23:32:52 49.96 09-Jul-17 23:32:56 49.97 09-Jul-17 23:33:00 49.96 09-Jul-17 23:33:04 49.95 09-Jul-17 23:33:08 49.96 09-Jul-17 23:33:12 49.97 09-Jul-17 23:33:16 49.99 09-Jul-17 23:33:20 49.99 09-Jul-17 23:33:24 49.98 09-Jul-17 23:33:28 49.98 09-Jul-17 23:33:32 50.00 09-Jul-17 23:33:36 50.01 09-Jul-17 23:33:40 50.02 09-Jul-17 23:33:44 50.04 09-Jul-17 23:33:48 50.06 09-Jul-17 23:33:52 50.08 09-Jul-17 23:33:56 50.08 09-Jul-17 23:34:00 50.07 09-Jul-17 23:34:04 50.07 09-Jul-17 23:34:08 50.07 09-Jul-17 23:34:12 50.08 09-Jul-17 23:34:16 50.09 09-Jul-17 23:34:20 50.10 09-Jul-17 23:34:24 50.11 09-Jul-17 23:34:28 50.09 09-Jul-17 23:34:32 50.09 09-Jul-17 23:34:36 50.10 09-Jul-17 23:34:40 50.10 09-Jul-17 23:34:44 50.10 09-Jul-17 23:34:48 50.10 09-Jul-17 23:34:52 50.09 09-Jul-17 23:34:56 50.10 09-Jul-17 23:35:00 50.10 09-Jul-17 23:35:04 50.10 09-Jul-17 23:35:08 50.10 09-Jul-17 23:35:12 50.10 09-Jul-17 23:35:16 50.10 09-Jul-17 23:35:20 50.09 09-Jul-17 23:35:24 50.09 09-Jul-17 23:35:28 50.09 09-Jul-17 23:35:32 50.08 09-Jul-17 23:35:36 50.09 09-Jul-17 23:35:40 50.11 09-Jul-17 23:35:44 50.12 09-Jul-17 23:35:48 50.13 09-Jul-17 23:35:52 50.13 09-Jul-17 23:35:56 50.13 09-Jul-17 23:36:00 50.12 09-Jul-17 23:36:04 50.12 09-Jul-17 23:36:08 50.11 09-Jul-17 23:36:12 50.12 09-Jul-17 23:36:16 50.12 09-Jul-17 23:36:20 50.12 09-Jul-17 23:36:24 50.12 09-Jul-17 23:36:28 50.13 09-Jul-17 23:36:32 50.12 09-Jul-17 23:36:36 50.11 09-Jul-17 23:36:40 50.12 09-Jul-17 23:36:44 50.11 09-Jul-17 23:36:48 50.12 09-Jul-17 23:36:52 50.12 09-Jul-17 23:36:56 50.11 09-Jul-17 23:37:00 50.10 09-Jul-17 23:37:04 50.10 09-Jul-17 23:37:08 50.11 09-Jul-17 23:37:12 50.10 09-Jul-17 23:37:16 50.11 09-Jul-17 23:37:20 50.10 09-Jul-17 23:37:24 50.11 09-Jul-17 23:37:28 50.11 09-Jul-17 23:37:32 50.09 09-Jul-17 23:37:36 50.09 09-Jul-17 23:37:40 50.10 09-Jul-17 23:37:44 50.11 09-Jul-17 23:37:48 50.11 09-Jul-17 23:37:52 50.11 09-Jul-17 23:37:56 50.10 09-Jul-17 23:38:00 50.09 09-Jul-17 23:38:04 50.10 09-Jul-17 23:38:08 50.10 09-Jul-17 23:38:12 50.11 09-Jul-17 23:38:16 50.11 09-Jul-17 23:38:20 50.10 09-Jul-17 23:38:24 50.10 09-Jul-17 23:38:28 50.09 09-Jul-17 23:38:32 50.10 09-Jul-17 23:38:36 50.11 09-Jul-17 23:38:40 50.11 09-Jul-17 23:38:44 50.11 09-Jul-17 23:38:48 50.11 09-Jul-17 23:38:52 50.12 09-Jul-17 23:38:56 50.12 09-Jul-17 23:39:00 50.11 09-Jul-17 23:39:04 50.10 09-Jul-17 23:39:08 50.10 09-Jul-17 23:39:12 50.10 09-Jul-17 23:39:16 50.10 09-Jul-17 23:39:20 50.09 09-Jul-17 23:39:24 50.08 09-Jul-17 23:39:28 50.09 09-Jul-17 23:39:32 50.10 09-Jul-17 23:39:36 50.10 09-Jul-17 23:39:40 50.09 09-Jul-17 23:39:44 50.09 09-Jul-17 23:39:48 50.09 09-Jul-17 23:39:52 50.09 09-Jul-17 23:39:56 50.09 09-Jul-17 23:40:00 50.08 09-Jul-17 23:40:04 50.07 09-Jul-17 23:40:08 50.08 09-Jul-17 23:40:12 50.09 09-Jul-17 23:40:16 50.10 09-Jul-17 23:40:20 50.10 09-Jul-17 23:40:24 50.11 09-Jul-17 23:40:28 50.10 09-Jul-17 23:40:32 50.10 09-Jul-17 23:40:36 50.10 09-Jul-17 23:40:40 50.09 09-Jul-17 23:40:44 50.08 09-Jul-17 23:40:48 50.05 09-Jul-17 23:40:52 50.06 09-Jul-17 23:40:56 50.07 09-Jul-17 23:41:00 50.09 09-Jul-17 23:41:04 50.08 09-Jul-17 23:41:08 50.08 09-Jul-17 23:41:12 50.08 09-Jul-17 23:41:16 50.09 09-Jul-17 23:41:20 50.09 09-Jul-17 23:41:24 50.08 09-Jul-17 23:41:28 50.08 09-Jul-17 23:41:32 50.08 09-Jul-17 23:41:36 50.08 09-Jul-17 23:41:40 50.09 09-Jul-17 23:41:44 50.10 09-Jul-17 23:41:48 50.09 09-Jul-17 23:41:52 50.09 09-Jul-17 23:41:56 50.07 09-Jul-17 23:42:00 50.05 09-Jul-17 23:42:04 50.06 09-Jul-17 23:42:08 50.05 09-Jul-17 23:42:12 50.05 09-Jul-17 23:42:16 50.05 09-Jul-17 23:42:20 50.05 09-Jul-17 23:42:24 50.05 09-Jul-17 23:42:28 50.06 09-Jul-17 23:42:32 50.07 09-Jul-17 23:42:36 50.08 09-Jul-17 23:42:40 50.08 09-Jul-17 23:42:44 50.08 09-Jul-17 23:42:48 50.08 09-Jul-17 23:42:52 50.07 09-Jul-17 23:42:56 50.05 09-Jul-17 23:43:00 50.06 09-Jul-17 23:43:04 50.07 09-Jul-17 23:43:08 50.05 09-Jul-17 23:43:12 50.06 09-Jul-17 23:43:16 50.06 09-Jul-17 23:43:20 50.05 09-Jul-17 23:43:24 50.04 09-Jul-17 23:43:28 50.03 09-Jul-17 23:43:32 50.03 09-Jul-17 23:43:36 50.01 09-Jul-17 23:43:40 50.01 09-Jul-17 23:43:44 50.00 09-Jul-17 23:43:48 50.00 09-Jul-17 23:43:52 50.00 09-Jul-17 23:43:56 50.00 09-Jul-17 23:44:00 50.00 09-Jul-17 23:44:04 50.00 09-Jul-17 23:44:08 50.02 09-Jul-17 23:44:12 50.01 09-Jul-17 23:44:16 50.02 09-Jul-17 23:44:20 50.03 09-Jul-17 23:44:24 50.05 09-Jul-17 23:44:28 50.05 09-Jul-17 23:44:32 50.05 09-Jul-17 23:44:36 50.04 09-Jul-17 23:44:40 50.04 09-Jul-17 23:44:44 50.04 09-Jul-17 23:44:48 50.01 09-Jul-17 23:44:52 50.01 09-Jul-17 23:44:56 50.03 09-Jul-17 23:45:00 50.03 09-Jul-17 23:45:04 50.04 09-Jul-17 23:45:08 50.06 09-Jul-17 23:45:12 50.07 09-Jul-17 23:45:16 50.07 09-Jul-17 23:45:20 50.06 09-Jul-17 23:45:24 50.06 09-Jul-17 23:45:28 50.08 09-Jul-17 23:45:32 50.09 09-Jul-17 23:45:36 50.09 09-Jul-17 23:45:40 50.08 09-Jul-17 23:45:44 50.07 09-Jul-17 23:45:48 50.06 09-Jul-17 23:45:52 50.06 09-Jul-17 23:45:56 50.07 09-Jul-17 23:46:00 50.05 09-Jul-17 23:46:04 50.05 09-Jul-17 23:46:08 50.04 09-Jul-17 23:46:12 50.05 09-Jul-17 23:46:16 50.04 09-Jul-17 23:46:20 50.03 09-Jul-17 23:46:24 50.05 09-Jul-17 23:46:28 50.05 09-Jul-17 23:46:32 50.05 09-Jul-17 23:46:36 50.06 09-Jul-17 23:46:40 50.07 09-Jul-17 23:46:44 50.06 09-Jul-17 23:46:48 50.06 09-Jul-17 23:46:52 50.05 09-Jul-17 23:46:56 50.03 09-Jul-17 23:47:00 50.03 09-Jul-17 23:47:04 50.03 09-Jul-17 23:47:08 50.04 09-Jul-17 23:47:12 50.03 09-Jul-17 23:47:16 50.04 09-Jul-17 23:47:20 50.03 09-Jul-17 23:47:24 50.02 09-Jul-17 23:47:28 50.02 09-Jul-17 23:47:32 50.02 09-Jul-17 23:47:36 50.03 09-Jul-17 23:47:40 50.02 09-Jul-17 23:47:44 50.02 09-Jul-17 23:47:48 50.04 09-Jul-17 23:47:52 50.02 09-Jul-17 23:47:56 50.01 09-Jul-17 23:48:00 50.01 09-Jul-17 23:48:04 50.01 09-Jul-17 23:48:08 50.01 09-Jul-17 23:48:12 50.01 09-Jul-17 23:48:16 50.00 09-Jul-17 23:48:20 49.99 09-Jul-17 23:48:24 50.00 09-Jul-17 23:48:28 49.99 09-Jul-17 23:48:32 49.98 09-Jul-17 23:48:36 49.98 09-Jul-17 23:48:40 49.97 09-Jul-17 23:48:44 49.96 09-Jul-17 23:48:48 49.96 09-Jul-17 23:48:52 49.96 09-Jul-17 23:48:56 49.95 09-Jul-17 23:49:00 49.92 09-Jul-17 23:49:04 49.90 09-Jul-17 23:49:08 49.92 09-Jul-17 23:49:12 49.93 09-Jul-17 23:49:16 49.92 09-Jul-17 23:49:20 49.92 09-Jul-17 23:49:24 49.93 09-Jul-17 23:49:28 49.94 09-Jul-17 23:49:32 49.95 09-Jul-17 23:49:36 49.95 09-Jul-17 23:49:40 49.95 09-Jul-17 23:49:44 49.97 09-Jul-17 23:49:48 49.97 09-Jul-17 23:54:00 49.99 09-Jul-17 23:54:04 49.98 09-Jul-17 23:54:08 49.98 09-Jul-17 23:54:12 49.97 09-Jul-17 23:54:16 49.96 09-Jul-17 23:54:20 49.97 09-Jul-17 23:54:24 49.97 09-Jul-17 23:54:28 49.97 09-Jul-17 23:54:32 49.96 09-Jul-17 23:54:36 49.95 09-Jul-17 23:54:40 49.97 09-Jul-17 23:54:44 49.97 09-Jul-17 23:54:48 49.97 09-Jul-17 23:54:52 49.98 09-Jul-17 23:54:56 50.00 09-Jul-17 23:55:00 50.02 09-Jul-17 23:55:04 50.01 09-Jul-17 23:55:08 50.00 09-Jul-17 23:55:12 49.99 09-Jul-17 23:55:16 49.99 09-Jul-17 23:55:20 49.98 09-Jul-17 23:55:24 49.98 09-Jul-17 23:55:28 49.98 09-Jul-17 23:55:32 49.97 09-Jul-17 23:55:36 49.98 09-Jul-17 23:55:40 49.98 09-Jul-17 23:55:44 49.95 09-Jul-17 23:55:48 49.94 09-Jul-17 23:55:52 49.95 09-Jul-17 23:55:56 49.96 09-Jul-17 23:56:00 49.98 09-Jul-17 23:56:04 49.95 09-Jul-17 23:56:08 49.92 09-Jul-17 23:56:12 49.93 09-Jul-17 23:56:16 49.93 09-Jul-17 23:56:20 49.92 09-Jul-17 23:56:24 49.93 09-Jul-17 23:56:28 49.91 09-Jul-17 23:56:32 49.90 09-Jul-17 23:56:36 49.90 09-Jul-17 23:56:40 49.92 09-Jul-17 23:56:44 49.91 09-Jul-17 23:56:48 49.92 09-Jul-17 23:56:52 49.94 09-Jul-17 23:56:56 49.95 09-Jul-17 23:57:00 49.95 09-Jul-17 23:57:04 49.96 09-Jul-17 23:57:08 49.97 09-Jul-17 23:57:12 49.98 09-Jul-17 23:57:16 49.99 09-Jul-17 23:57:20 49.98 09-Jul-17 23:57:24 49.97 09-Jul-17 23:57:28 49.97 09-Jul-17 23:57:32 49.97 09-Jul-17 23:57:36 49.98 09-Jul-17 23:57:40 50.00 09-Jul-17 23:57:44 50.00 09-Jul-17 23:57:48 50.00 09-Jul-17 23:57:52 50.01 09-Jul-17 23:57:56 50.02 09-Jul-17 23:58:00 50.04 09-Jul-17 23:58:04 50.04 09-Jul-17 23:58:08 50.05 09-Jul-17 23:58:12 50.06 09-Jul-17 23:58:16 50.06 09-Jul-17 23:58:20 50.05 09-Jul-17 23:58:24 50.04 09-Jul-17 23:58:28 50.03 09-Jul-17 23:58:32 50.04 09-Jul-17 23:58:36 50.04 09-Jul-17 23:58:40 50.05 09-Jul-17 23:58:44 50.05 Question one. Plot a chart to illustrate how frequency fluctuated on Mainland Australia, on the 9th July, 2017. Answer: The graph below shows the power frequency fluctuations. Explanation. From the look at the chart, there are slight changes in frequency from the start of the experiment to the end .The difference between the lowest and the highest frequency is 0.35Hz.This shows that there were changes but not as much as those which can give much errors. The variations are also desirable indicators for power instabilities in the mainland. These changes can easily be stabilized by having a strong power production unit which gave give a very stable power production. The fluctuations have been considered as the main source of appliance damages, short-circuits and shocks.The indicators also proofs the reasons why power accidents were reported almost every day in the country. The increase of supply can also act as the agent of stabilizing electricity. The Mainland electricity can also be stabilized by upgrading production machine. Question two. Calculate the mean value of frequency, its standard deviation and the standard deviation of mean on the 9th Jul 2017. Answer: Mean. The mean calculated statistically can give a clear indication of the exact point where the frequency lies in. The formula below is for statistical mean. Statistical mean is different from geometric and harmonic mean and used to give the almost certain answer.Statistical mean is popular because it includes every item in the data set and it can easily be used with other statistical measurements. However, the major disadvantage in using statistical mean is that it can be affected by extreme values in the data set and therefore be biased. From the excel, the formula that we used is In application of the above formula, the result is exactly the same as the one depicted in excel as follows. =Average (B2:B21602) Answer=50.00 Standard deviation. Standard deviation (SD also represented by a Greek symbol as σ) is used to measure the dispersion or the diversion of a quantity from the known mean or mean point. A low standard deviation indicates that the data points tend to be close to the expected value of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values. The standard deviation of a population, group of data, set or any measured quantities is the square root of the variance. Standard deviation takes the units of the data.This property makes data analysis output understandable. There are also other measures of deviation from the norm, including average absolute deviation, which provide different mathematical properties from standard deviation The calculation of extend of variation of the values from the mean is as follows, Function used: =STDEV (B2:B21601) Answer=0.06 This shows that the deviation is really small. The indication here is that the variation cannot be too big to worry about but it exist. In standard of electricity production, this size of deviation is at acceptable limit. The only issue is that there is always a target that excellent call for. That target in mainland electricity seems not to have been achieved. The electricity deviation standards are always published in IEEE journal papers as quantities which must be taken seriously to show extend of performance of stabilizing factors. In excel, the standard deviation is found by selecting a range of cells and taking inside a function =STDEV (RANGE OF CELLS WITH THE DATA).The level of accuracy is admirable since it has been used in many statistical operations for some time.The calculations are also accurate since there are less data entry errors which can easily increase the data integrity in the analysis products. Standard deviation of mean. To measure the dispersion or the diversion of a quantity from the known mean or mean point. A low standard deviation indicates that the data points tend to be close to the expected value of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.The excel software can be used to ease calculations but the standard statistical mead for the standard deviation is as follows. Steps taken to calculate standard deviation is as follows: The first step is to get the average of the numbers by dividing the total by the number of times measurements were done. The average formula is simple and in excel data analysis the answer is accurate because number of decimal places can always can easily be increased to increase precision. In natural calculations, each number is used to subtract the mean and the result is squared. The third stage is to work out the mean of squared differences. Lastly, the square root is calculated for the overall answer. This is simple steps that finding the standard deviation can be followed. Function= STDEV (B2:B21601)/SQRT (COUNT (B2:B21601)) Where Count gives number n of values in consideration =0.00040825. The figure below shows the calculations, answers and some values in consideration. Figure 2:Mean,standard deviation and mean standard deviation. The following table shows various values as they appear in excel document. 09-Jul-17 23:59:32 50.13 09-Jul-17 23:59:36 50.14 09-Jul-17 23:59:40 50.14 09-Jul-17 23:59:44 50.14 09-Jul-17 23:59:48 50.14 09-Jul-17 23:59:52 50.14 09-Jul-17 23:59:56 50.14 10-Jul-17 00:00:00 50.15 Mean 50.00 STANDARD DEVIATION 0.06 Mean standard dev 0.00037920 146.97 50.14 49.80 Question Three: a) Create a bar histogram to plot the number of times each frequency value was observed. The table below shows various values and their frequencies.as used in the histogram. Bin Frequency 49.8 1 49.8024 0 49.80479 0 49.80719 0 49.80959 0 49.81199 2 49.81438 0 49.81678 0 49.81918 0 49.82157 3 49.82397 0 49.82637 0 49.82877 0 49.83116 7 49.83356 0 49.83596 0 49.83836 0 49.84075 12 49.84315 0 49.84555 0 49.84794 0 49.85034 50 49.85274 0 49.85514 0 49.85753 0 49.85993 0 49.86233 76 49.86473 0 49.86712 0 49.86952 0 49.87192 135 49.87431 0 49.87671 0 49.87911 0 49.88151 169 49.8839 0 49.8863 0 49.8887 0 49.8911 292 49.89349 0 49.89589 0 49.89829 0 49.90068 465 49.90308 0 49.90548 0 49.90788 0 49.91027 548 49.91267 0 49.91507 0 49.91747 0 49.91986 0 49.92226 560 49.92466 0 49.92705 0 49.92945 0 49.93185 692 49.93425 0 49.93664 0 49.93904 0 49.94144 735 49.94384 0 49.94623 0 49.94863 0 49.95103 839 49.95342 0 49.95582 0 49.95822 0 49.96062 911 49.96301 0 49.96541 0 49.96781 0 49.97021 1080 49.9726 0 49.975 0 49.9774 0 49.97979 0 49.98219 1202 49.98459 0 49.98699 0 49.98938 0 49.99178 1217 49.99418 0 49.99658 0 49.99897 0 50.00137 2541 50.00377 0 50.00616 0 50.00856 0 50.01096 1385 50.01336 0 50.01575 0 50.01815 0 50.02055 1273 50.02295 0 50.02534 0 50.02774 0 50.03014 1264 50.03254 0 50.03493 0 50.03733 0 50.03973 0 50.04212 1215 50.04452 0 50.04692 0 50.04932 0 50.05171 1099 50.05411 0 50.05651 0 50.05891 0 50.0613 1020 50.0637 0 50.0661 0 50.06849 0 50.07089 859 50.07329 0 50.07569 0 50.07808 0 50.08048 668 50.08288 0 50.08528 0 50.08767 0 50.09007 506 50.09247 0 50.09486 0 50.09726 0 50.09966 0 50.10206 391 50.10445 0 50.10685 0 50.10925 0 50.11165 249 50.11404 0 50.11644 0 50.11884 0 50.12123 99 50.12363 0 50.12603 0 50.12843 0 50.13082 28 50.13322 0 50.13562 0 50.13802 0 50.14041 6 50.14281 0 50.14521 0 50.1476 0 More 1 b) Figure 3: Shows the histogram of number of times each frequency value was observed. c) Create bar histogram to plot the fraction of time each frequency value was observed. Figure 3: Shows the histogram of fraction of times each frequency value was observed. Above is a clear illustration showing frequency at each fraction of time, which led to a linear like graph. The deviation is too minimal to be clearly depicted in the graph. Create a bin histogram to show the fraction of times frequency was observed in various frequency intervals. The bin intervals should be as follows: 49.80-49.82, 49.83-49.85, 49.86-49.88, 49.89-49.91 49.92-49.94, 49.95-49.97, 49.98-50.00, 50.01-50.03 50.04-50.06, 50.07-50.09, 50.10-50.12, 50.13-50.15 Figure 4:Histogram showing fraction of times frequency was observed in various frequency intervals as given in the question four above. The above diagram is obtained by plotting the a chart of frequency against Bin values obtained through data in the table below. Bin Frequency 49.8 1 49.85 74 49.9 672 49.95 3000 50 7790 50.05 6236 50.1 3444 50.15 382 More 1 From the histogram above, the frequency levels rose to the maximum and later fall to the minimum. Maximum frequency being between interval 49.95 and 50.05. Question five. Make a plot of the gauss distribution using the mean and standard deviation values calculated earlier. Can gauss distribution be used as the limiting distribution for the mainland frequency in Australia? Figure 5: Gauss showing the distribution of frequencies in Mainland Australia. References: [1]Dixon, W.J.and Massey frank, J., 1950.Introduction to statistical analysis. McGraw-Hill book Company, Inc.; New York. [2]Anderson, T.W., and mathematician, E.U., 1958.An introduction to multivariate statistical analysis (Vol 2, pp. 5-3) New York: Willey. Read More

In excel, the standard deviation is found by selecting a range of cells and taking inside a function =STDEV (RANGE OF CELLS WITH THE DATA).The level of accuracy is admirable since it has been used in many statistical operations for some time.The calculations are also accurate since there are less data entry errors which can easily increase the data integrity in the analysis products. Standard deviation of mean. To measure the dispersion or the diversion of a quantity from the known mean or mean point.

A low standard deviation indicates that the data points tend to be close to the expected value of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.The excel software can be used to ease calculations but the standard statistical mead for the standard deviation is as follows. Steps taken to calculate standard deviation is as follows: The first step is to get the average of the numbers by dividing the total by the number of times measurements were done.

The average formula is simple and in excel data analysis the answer is accurate because number of decimal places can always can easily be increased to increase precision. In natural calculations, each number is used to subtract the mean and the result is squared. The third stage is to work out the mean of squared differences. Lastly, the square root is calculated for the overall answer. This is simple steps that finding the standard deviation can be followed. Function= STDEV (B2:B21601)/SQRT (COUNT (B2:B21601)) Where Count gives number n of values in consideration =0.00040825. The figure below shows the calculations, answers and some values in consideration.

Figure 2:Mean,standard deviation and mean standard deviation. The following table shows various values as they appear in excel document. 09-Jul-17 23:59:32 50.13 09-Jul-17 23:59:36 50.14 09-Jul-17 23:59:40 50.14 09-Jul-17 23:59:44 50.14 09-Jul-17 23:59:48 50.14 09-Jul-17 23:59:52 50.14 09-Jul-17 23:59:56 50.14 10-Jul-17 00:00:00 50.15 Mean 50.00 STANDARD DEVIATION 0.06 Mean standard dev 0.00037920 146.97 50.14 49.80 Question Three: a) Create a bar histogram to plot the number of times each frequency value was observed.

The table below shows various values and their frequencies.as used in the histogram. Bin Frequency 49.8 1 49.8024 0 49.80479 0 49.80719 0 49.80959 0 49.81199 2 49.81438 0 49.81678 0 49.81918 0 49.82157 3 49.82397 0 49.82637 0 49.82877 0 49.83116 7 49.83356 0 49.83596 0 49.83836 0 49.84075 12 49.84315 0 49.84555 0 49.84794 0 49.85034 50 49.85274 0 49.85514 0 49.85753 0 49.85993 0 49.86233 76 49.86473 0 49.86712 0 49.86952 0 49.87192 135 49.87431 0 49.87671 0 49.87911 0 49.88151 169 49.8839 0 49.8863 0 49.8887 0 49.

8911 292 49.89349 0 49.89589 0 49.89829 0 49.90068 465 49.90308 0 49.90548 0 49.90788 0 49.91027 548 49.91267 0 49.91507 0 49.91747 0 49.91986 0 49.92226 560 49.92466 0 49.92705 0 49.92945 0 49.93185 692 49.93425 0 49.93664 0 49.93904 0 49.94144 735 49.94384 0 49.94623 0 49.94863 0 49.95103 839 49.95342 0 49.95582 0 49.95822 0 49.96062 911 49.96301 0 49.96541 0 49.96781 0 49.97021 1080 49.9726 0 49.975 0 49.9774 0 49.97979 0 49.98219 1202 49.98459 0 49.98699 0 49.98938 0 49.99178 1217 49.99418 0 49.

99658 0 49.99897 0 50.00137 2541 50.00377 0 50.00616 0 50.00856 0 50.01096 1385 50.01336 0 50.01575 0 50.01815 0 50.02055 1273 50.02295 0 50.02534 0 50.02774 0 50.03014 1264 50.03254 0 50.03493 0 50.03733 0 50.03973 0 50.04212 1215 50.04452 0 50.04692 0 50.04932 0 50.05171 1099 50.05411 0 50.05651 0 50.05891 0 50.0613 1020 50.0637 0 50.0661 0 50.06849 0 50.07089 859 50.07329 0 50.07569 0 50.07808 0 50.08048 668 50.08288 0 50.08528 0 50.08767 0 50.09007 506 50.09247 0 50.09486 0 50.09726 0 50.09966 0 50.

10206 391 50.10445 0 50.10685 0 50.10925 0 50.11165 249 50.11404 0 50.11644 0 50.11884 0 50.12123 99 50.12363 0 50.12603 0 50.12843 0 50.13082 28 50.13322 0 50.13562 0 50.13802 0 50.14041 6 50.14281 0 50.14521 0 50.1476 0 More 1 b) Figure 3: Shows the histogram of number of times each frequency value was observed.

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