Relationship Between Stock Returns And Volatility Using Symmetric And Asymmetric Models Of The Garch Family

To find the coefficient of skewness (a measure of the degree of skewness), the mean, mode and standard deviation was needed. Due to the large data size, a computer program was used to obtain the necessary information. The data set was inserted into the program (One Variable Analysis by Haese and Harris Publications) which then analysed it and produce the required result. The information collected is displayed below with the result for the mean rounded to 87 from 86.964 and the standard deviation to 8.2 from 8.2375. This was done for convenience however it did reduce the precision of the

The histogram has one spike that shows that high concentration of data values is below this point. This histogram might be representing a seasonal product, which customers are ordering high volume of product until they run out and order one more time. Also it might be showing the histogram of a car brand were less expensive cars are sold frequently, but in average the middle range cars are bringing to the company more capital and high luxury cars are sold more expensive and less frequently.

Descriptive statistics are digits that are used to summarize and describe a given range of data (Klenke, 2008). Basic descriptive data includes, mean, median, mode, variance and standard deviation. The data can be rearranged in an ascending order as follows:

By using the measures of dispersion or central tendency and correlations between sets of data for quantitative interpretation of comparative market data

The variable age is the independent variable and is a ratio level of measurement (Loiselle et al., 2011). The measure of central tendency to describe age are in table 1.2 are the mean of 57.62 which is the average age, the median which is the middle score within the distribution when all scores are organized of 58.5 and the mode of 58 which is the most frequently occurring age (Loiselle et al., 2011). The measures of variability are the range of 69 with a minimum age of 22 and a maximum age of 91, standard deviation which is the average deviation from the sample mean which is a value of 16.26, and the sample variance which is the standard deviation square and the value is 263.46 (Salkind, 2013). The distribution for this sample is described as a negative skew and the value obtained from table 1.2 is -0.22511(Salkind, 2013). A negative skew occurs when the median and the mode value are larger than the mean, within this sample the median is 58.5 the mode is 58 which is greater than the mean of 57.62, the tail would be pointed toward the left (Salkind, 2013). The kurtosis value is -0.65102 and this describes how peak or flat the curve is from the normal distribution curve which is described as mesokurtic (Salkind, 2013). The kurtosis has a large negative value which is representative of a flatter curve also know as playkurtic (Salkind, 2013).

The example below lists the results for numbers 6-10. The measures of central tendency include mean, median, and mode. In this example the measures of central tendency will be calculated based on row B, which indicates the number of months that a particular employee has been with the company. The data being analyzed is the

The summary includes variance, mean, median, mode and standard deviation. As shown in the histogram majority of people in the data pool have a height of 62-68 inches. This is a symmetrical distribution seeing how close the mean and median are to each other.

(60.4.1) Calculate and interpret statistics of variability (e.g., range, mean absolute deviation) and central tendency (e.g., mean, median).

Mean 95% Lower Bound Confidence Upper Bound Interval for Mean 5% Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis Mean 95% Lower Bound Confidence Upper Bound Interval for Mean 5% Trimmed Mean Median Variance Std. Deviation Minimum Maximum Range Interquartile Range Skewness Kurtosis

The key terms and definitions that I will be using are: statistics, mean, median, mode, standard deviation, range, and population standard deviation. Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. The mean of a data set is the sum of the data entries divided by the number of entries. The median of a data set is the value that lies in the middle of the data when the data set is ordered. The mode of a data set is the data entry that occurs with the greatest frequency. Standard deviation is a quantity calculated to indicate the extent of deviation for a group as a whole. The range of a data set is the difference between the maximum and minimum data entries in the set. The population standard deviation of a population data set of N entries is the square root of the population variance (Larson & Farber, 2014).

Percentages and percentile rank are the beginning descriptive data. I am very comfortable with central tendency, normal distribution, variable, frequency distribution, and measures of variability. The mean of any set of numbers is the average and the median is the exact middle of a distribution. The advantage of the mean measure is it captures the full data set but is influenced by outliers. The measures of variability such as range, variance, and standard deviation, tells me how the data is spread out or clumped together.

The mean is the average of all numbers. The Liberal’s mean is 50.76, Conservative’s mean is 38.45 and NDP’s mean is 54.57. The NDP’s mean is higher than Liberal and Conservative. It means that the NDP is more popular than the other two parties and the Conservative, which has the lowest mean, is the less popular party among these three parties. In the data center, means and medians are often tracked over time to spot trends which power cost predictions. The statistical median is the middle number in a sequence of numbers. The median is 56 for Liberal, 38 for conservative and 60 for NDP. As we can see, the mean and the median are related and following each other. When the mean is higher the median is higher too and when the mean is lower the median is lower too. To find the median, organize each number in order by size; the number in the middle is the median. Standard Deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean 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 for Conservative is 31.4 which is higher in relation to the other two parties. The standard deviation for Liberal is 28.4 and for NDP is 27.1. The data points in the conservative party spread out over a wider range of values in relation to the other two parties. The standard

A normal distribution can be regarded as the most important continuous probability distribution in statistics since it can be utilized to model several sets of measurements in business, industry, and nature. For instance, normal distributions can be used to measure the systolic blood pressure of humans, housing costs, and the lifetime of television sets through random variables. Generally, normal distributions can have any mean and positive standard deviation as the two parameters totally determine the shape of the normal curve during evaluation. In this case, the mean determines the location of the symmetry line while the standard deviation defines how much the data are spread out ("Normal Probability Distributions", n.d.).

The above graph shows the income and net worth of households and the percentage of population belonging to each net worth category is depicted using the various data points. One can notice that the percentage of population which is in the net worth category of $0 to $50000 is nearly 12%, while the data points in the distribution is said to be skewed, which can be analyzed in more detail when descriptive statistics for the same is calculated.

As indicated by the case study S&P 500 index was use as a measure of the total return for the stock market. Our standard deviation of the total return was used as a one measure of the risk of an individual stock. Also betas for individual stocks are determined by simple linear regression. The variables were: total return for the stock as the dependent variable and independent variable is the total return for the stock. Since the descriptive statistics were a lot, only the necessary data was selected (below table.)