Descriptive Statistics

Understanding Descriptive Statistics and Analysis

Descriptive statistics is a term used to refer to the analysis used to describe and summarize data in a more meaningful manner such that patterns and trends that were previously not noticeable emerge from the data. Descriptive statistics analysis is mostly utilized with quantitative data or other forms of collective information. Descriptive statistics is commonly broken down to; - measures of frequency-count, percent and frequency, measures of central tendency - mean, median and the mode, measures of variation - range, standard deviation and variance, measures of position- IQR, percentile ranks and quartile ranks

1. Measures of location
   Measures of location are commonly referred to as the measures of central tendency. A measure of central tendency is any single value of measure that gives an effort to describe a set of data by indicating the central position within that data set. Due to their universal utility of location, they are deemed summary statistics. The mean also known as the average is the most likely measure of central location that is widely used and other such as the median and the mode.
2. Mean (average)
   This is the most popular of all measure of central location. It is used on both discrete and continuous data. It is the equal to the sum of all the values in the data set divided by the number of values in the data set. That is; if we have n values and variables x1,x2,.....xn we can assume that the mean is; = x1+x2....x3/n
   Thus, the mean is essentially the value that is most common. The mean has a relationship to the data because the more dispersed the data to the top the higher the mean thus it cannot be the best statistics to measure data in a skewed distribution or data that has many outliers. For our case since our data is susceptible to very high amounts for certain counties and very small amounts for other counties, the mean for this case is not the best statistic to measure central tendency.
3. Median
   The median is the middle value of any data arranged in the order of their magnitude. The median unlike the mean is less affected by outliers and skewed data. When calculating the median, the values are arranged in order of their magnitude from the least to the maximum. Then the central value is taken as the median, as the word goes (middle).
4. Mode
   The mode is the most frequents score in the data set being analyzed. On a histogram it represents the highest bar in the graphical representation thus we can make a deduction that the mode is the most frequent and popular variable and value in the data being analyzed
   Bearing that the mode describes the most popular variable, the mode becomes problematic when the most popular variables are shared across multiple variables in a graphical representation thus making it a non-unique indicator of popularity. Another weakness of the data is the fact that it cannot be used as a good measure of central location and tendency where the most popular mark and value is very far away from rest of the data thus making it an outlier that depicts biased results.
5. Measures of variability
   In statistics the measures of variability are an important aspect of analysis. The most important measures of variability often called the spread is the standard deviation and range measures. The standard deviation measures depict the spread of the data in relation to the mean or the average score. i.e the number of values that exist between variables and the mean. On the other hand, the range is another important measure of variability or spread. It is computed as the difference between the largest and smallest value of the data being analyzed.
6. Measures of shape
   When describing a variable, an important aspect is the shape. The shape describes the frequency of values from different rages of the values. Mostly known as the distribution in approximation to the normal distribution. There are two important measures of shape, skewness and the Kurtosis.
7. Skewness
   Skewness is the measure of the distribution asymmetry. For a normal distribution the skewness is equal to zero and its graphical representation forms a curved bell shape with the highest values in the middle and the least to its left- and right-hand side. A distribution with a positive skewness has a tail to the right-hand side i.e., the highest values comes first as they progress downwards to the right making skewness a dimensionless quantity.
8. Kurtosis
   Another measure of shape is the kurtosis. Kurtosis is the degree to which a distribution is peaked. It is usually in connection to the normality of the distribution. The peak effect indicates that there is an excess frequency at the middle of the distribution. Positive values of the kurtosis indicate that the tails are longer and thicker while a negative kurtosis is indicated by shorter thinner tail

Essay Experts is Canada's premier essay writing and research service. We help undergraduate and graduate students with their essays, research papers, theses and dissertations. Our statisticians are standing by to help. Simply email us your question, requirements or assignment and we'll get back to you with a quote. Our statisticians all possess advanced degrees and have experience in helping students succeeed in statistical writing and analysis.