Question

(1) Briefly elaborate on the idea that the following factors are important belief characteristics of scientists: 1) A realists philosophy 2) Only continuous connected and forward causally, 3) Simplicity, 4) Skepticism, and 5) Quantitative thinking. [8] (2) What is standard deviation? Why is this statistic considered an absolute measure of dispersion? How is standard deviation related to the normal distribution? What percentage of observations are found 1,2, and 3 standard deviations away from a mean in a data set that has a normal distribution? [8] (3) What is a histogram? Explain how they are constructed. How are they different from a cumulative frequency plot? Why are they very important in determining whether it is appropriate to analyze data with other statistical measures and tests? [8] 4) Describe the four scales of measurement used to quantify or qualify data. [8] (5) Describe and define the descriptive statistics mean center and standard distance. [8]

Answer 1

1. A realists philosophy is the main focus of any research a scientist is perusing. The results obtained through the means of the mathematical models should match the ground reality. Since there are certain unknown factors in a research is considered as an outlier that might have a huge impact on the results in the long run as one of the rare events. 2. Continuous connected and forward come to an idea that the world in general works in that way. When all the stuffs in the nature works the way as is, so is our research objectives to meet the realistic predictable models of the events of interest. 3. Simplicity is always what it takes us to think critically about the nothing in anything that is the hidden idea that keeps the system in place. Even a complex system like human beings start with a single cell. The undying basic experimental units in a research is very fundamental in nature, so the mathematical model shall be very simple. But combining the models together to achieve the single most targets is the challenging task before the hands of the scientists. 4. Skeptism drives us to think about the impossibles. Certain things are very hard for an ordinary man to relate to the ground reality that too to put in numbers. Newton doubted about the force or power behind the falling apples and related to the universal phenomena. He went very deeper to reach the nothing in the research objective. It seems like that there is no nothing in the nature or zero in the nature. They are just an another unknown in the history of human beings quest for knowing or understanding the nature better. 5. We need to put the talks and statements of our proposals in numbers to understand the core concept in a phenomena. To master the ins and outs of the concept, knowing the measurement methods of an event of interest and putting it in numbers to analyse it will make us masters of the wisdom about the concept or idea that we are interested.

2. Standard deviation is the spread of the data about the mean. Since the standard deviation is the data with the signs, in the long run this becomes a zero if we sum all the difference from its mean. But in reality, nothing is perfect even if it is repeated by the super computers. So we need to know the variations in the data and the results with the standard deviation measures. Then only we can find out the unknowns in the future. So we can say that the measure of standard deviation is the motivating factor for the scope of the future developments in the concept. For any normally distributed data set, the standard deviation should be more than 0, is the parameter that decides the shape and scale of the bell shaped curve of the normal distribution. Empirically speaking the 68% of the data in a sample will fall within one sigma spread of the process, 95% of the data within mean plus or minus 2 sigma, 99.7% of the data within 3 sigma standard deviations.

3. We can visually present the descriptive statistics using histograms. For example, the mean, median, mode, quartiles, standard deviation, variance in a data set, outliers. It is see to understand the behaviour of the sample data visually using the geometry of the histogram. Histograms are constructed using the following steps: 1. Range of the data calculated as a difference of the maximum value and minimum value of the sample data. 2. Let us divide the range into class intervals, the un-dividable small packets of the data as an unit of same characteristics of having equally likely chance of occurrences. Desired number of number intervals time the the class width is nothing but the range of the data. Then we count the number of events that occurred in each class intervals with non overlapping class limits. The frequency is the summed up to find the total number of such events. Then we plot the class marks(average of the class marks) on the frequency in the x and y plot. This is how frequency histogram is constructed. Cumulative frequency plots are the sums up to 1 from 0. If you are interested in finding the number of events occured atleast or atmost conditions of an interval limits, then the cummulative frequency histogram is very useful. For large data set, this follows the empirical rules for its spread in the histogram. Because the histogram tells us the shape and scale of the distribution of the data, we can find out the normality in the histogram visually, that is very important characteristics of a random sample to model a random phenomena. So to see the normality of the data visually, histogram is the best tool. Then we can explore the data to analysis the core behaviour of the event of interest.

4. Ratio, Interval, Nominal, and ordinal are the four scales of measurements. Ratios are the proportions of the number of event of interest with in an interval in a parameter set. Intervals are measurements of range of values with minimum and maximum values in each interval, it is a continuous data type. Nominal does not have any comparison with other measurements, they are absolute in the mathematical sense that they are unique in nature. Ordinal values are ordered to their values from smallest to largest, or big to small, etc.

5. Mean center means the mean of the mean values of the N independent identical samples of size n. IF we take the repeated measures of the similar data set, on an average within the confidence level, certain specific percentage of means will fall within an interval of the means. Standard distance is the distance of each x value from the mean value of the data set.