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You should sign this sheet to show that you comply with these regulations. Student’s Signature Date Acknowledgement I take this chance to thank Miss. M. PriyanthimalaWho helped me to improve and developed this particular project. She explained well about the project and sacrificed her most of the time to explain and also made sure that all the students understood. She was ready to help out in any time and gave her full support for this particular project.
I finally would like to thank my parents, friends and others for helping to do this project.
Thank you TASKS| PAGE NO| Task 01| 04| Task 02| 09| Task 03| 14| Task 04| 16| Task 05| 24| Task 06| 27| Task 07| 31| Task 08| 32| Task 09| 34| Task 10| 35| Task 11| 38| Task 12| 43| Task 13| 44| Task 14| 47| Task 15| 49| Reference | 51| Task 1 T 1. 1 Difference between a sample and a population Population| Sample| * Population is the area in which you are trying to get information from. * This meaning of population is also used in survey research, but this is only one of many possible definitions of population.
Examples: Cedar Crest students; trees in North America; automobiles with four wheels; people who consume olive oil. | * Sample is a section of your population that you are actually going to survey. It is important to have a sample that will represent your entire population in order to minimize biases.
Survey research is based on sampling, which involves getting information from only some members of the population. * Samples can be drawn in several different ways, such as probability samples, quota samples, purposive samples, and volunteer samples. Examples assuming the populations stated above: 47 Cedar Crest students chosen randomly; 8463 trees randomly selected in North America; 20 sample autos from each make (e.
g. , GM, Ford, Toyota, Honda, etc. ); 1% of the oil consuming population per country| T 1. 2 Describe the advantages of sampling * Sampling saves money as it is much cheaper to collect the desired information from a small sample than from the whole population. * Sampling saves a lot of time and energy as the needed data are collected and processed much faster than census information.
And this is a very important consideration in all types of investigations or surveys. * Sampling provides information that is almost as accurate as that obtained from a complete census; rather a properly designed and carefully executed sample survey will provide more accurate results. Moreover, owing to the reduced volume of work, persons of higher caliber and properly trained can be employed to analyze the data. * Sampling makes it possible to obtain more detailed information from each unit of the sample as collecting data from a few units of the population (i. e. ample) can be more complete and thorough. * Sampling is essential to obtaining the data when the measurement process physically damages or destroys the sampling unit under investigation. For example, in order to measure the average lifetime of light bulbs, the measurement process destroys the sampling units, i. e. the bulbs, as they are used until they burn out.
A manufacturer will therefore use only a sample of light bulbs for this purpose and will not burn out all the bulbs produced. Similarly, the whole pot of soup cannot be tasted to determine if it has an acceptable flavor. Sampling may be the only means available for obtaining the needed information when the population appears to be infinite or is inaccessible such as the population of mountainous or thickly forested areas. In such cases, taking $ complete census to collect data would neither be physically possible nor practically feasible. * Sampling has much smaller “non-response”, following up of which is much easier. The term non-response means the no availability of information from some sampling units included in the sample for any reason such as failure to locate or measure some of the units, refusals, not-at-home, etc. Sampling is extensively used to obtain some of the census information. * The most important advantage of sampling is that it provides a valid measure of reliability for the sample estimates and this is one of the two basic purposes of sampling. * Reliability: If we collect the information about all the units of population, the collected information may be true. But we are never sure about it. We do not know whether the information is true or is completely false. Thus we cannot say anything with confidence about the quality of information. We say that the reliability is not possible.
This is a very important advantage of sampling. The inference about the population parameters is possible only when the sample data is collected from the selected sample. * Sometimes the experiments are done on sample basis. The fertilizers, the seeds and the medicines are initially tested on samples and if found useful, then they are applied on large scale. Most of the research work is done on the samples. * Sample data is also used to check the accuracy of the census data. T 1. 3 Difference between primary data and secondary data T1. 4 Difference between a statistic and a parameter
Parameter is any characteristic of the population. Statistic on the other hand is a characteristic of the sample. Statistic is used to estimate the value of the parameter. Note that the value of statistic changes from one sample to the next which leads to a study of the sampling distribution of statistic. When we draw a sample from a population, it is just one of many samples that might have been drawn and, therefore, observations made on any one sample are likely to be different from the ‘true value’ in the population (although some will be the same).
Imagine we were to draw an infinite (or very large) number of samples of individuals and calculate a statistic, say the arithmetic mean, on each one of these samples and that we then plotted the mean value obtained from each sample on a histogram (a chart using bars to represent the number of times a particular value occurred). This would represent the sampling distribution of the arithmetic mean. T1. 5 Define sampling errors with example? Sampling error is an error that occurs when using samples to make inferences about the populations from which they are drawn.
There are two kinds of sampling error: random error and bias. Random error is a pattern of errors that tend to cancel one another out so that the overall result still accurately reflects the true value. Every sample design will generate a certain amount of random error. Bias, on the other hand, is more serious because the pattern of errors is loaded in one direction or another and therefore do not balance each other out, producing a true distortion. These are the errors which occur due to the nature of sampling.
The sample selected from the population is one of all possible samples. Any value calculated from the sample is based on the sample data and is called sample statistic. Task 2 T2. 1 Advantages and disadvantages of arithmetic mean. Advantages * Fast and easy to calculate- As the most basic measure in statistics, arithmetic average is very easy to calculate. For a small data set, you can calculate the arithmetic mean quickly in your head or on a piece of paper. In computer programs like Excel, the arithmetic average is always one of the most basic and best known functions.
Here you can see the basics of arithmetic average calculation. * Easy to work with and use in further analysis- Because its calculation is straightforward and its meaning known to everybody, arithmetic average is also more comfortable to use as input to further analyses and calculations. When you work in a team of more people, the others will much more likely be familiar with arithmetic average than geometric average or mode. Disadvantages * Sensitive to extreme values- Arithmetic average is extremely sensitive to extreme values.
Therefore, arithmetic average is not the best measure to use with data sets containing a few extreme values or with more dispersed (volatile) data sets in general. Median can be a better alternative in such cases. * Not suitable for time series type of data- Arithmetic average is perfect for measuring central tendency when you’re working with data sets of independent values taken at one point of time. There was an example of this in one of the previous articles, when we were year. However, in finance you often work with percentage returns over a series of multiple time periods.
For calculating average percentage return over multiple periods of time, arithmetic average is useless; as it fails to take the different basis in every year into consideration (100% equals a different price or portfolio value at the beginning of each year). The more volatile the returns are, the more significant this weakness of arithmetic average is. Here you can see the example and reason why arithmetic average fails when measuring average percentage returns over time. * Works only when all values are equally important- Arithmetic average treats all the individual observations equally.
In finance and investing, you often need to work with unequal weights. For example, you have a portfolio of stocks and it is highly unlikely that all stocks will have the same weight and therefore the same impact on the total performance of the portfolio. Calculating the average performance of the total portfolio or a basket of stocks is a typical case when arithmetic average is not suitable and it is better to use weighted average instead. You can find more details and an example here: Why you need weighted average for calculating total portfolio return. T2. 2 Comparative picture of median, mode, mean The Median
The Median is the ‘middle value’ in your list. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order. When the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. Thus, remember to line up your values, the middle number is the median! Be sure to remember the odd and even rule.
That is, if the data is in meters, the standard deviation is in meters as well. The variance is in meters2, which is more difficult to interpret. Neither the standard deviation nor the variance is robust to outliers. A data value that is separate from the body of the data can increase the value of the statistics by an arbitrarily large amount. The mean absolute deviation (MAD) is also sensitive to outliers. But the MAD does not move quite as much as the standard deviation or variance in response to bad data. The interquartile range (IQR) is the difference between the 75th and 25th percentile of the data.
Since only the middle 50% of the data affects this measure, it is robust to outliers. T3. 2 What are the different characteristics of the following measures of dispersion. The range is the simplest measure of dispersion. The range can be thought of in two ways. 1. As a quantity: the difference between the highest and lowest scores in a distribution. 2. As an interval; the lowest and highest scores may be reported as the range. By far the most commonly used measures of dispersion in the social sciences are variance and standard deviation. Variance is the average squared difference of scores from the mean score of a distribution.
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