Descriptive Statistics Name: Institution:

Introduction Descriptive statistics are coefficients that describe and summarize a specific set of data of either a sample or of a population. The categories of descriptive statistics include the variability, spread and the measures of central tendency. The mode, median and the mean are the examples of the measure of central tendency while variance and the standard deviation are the examples of that gives the measures of variability (Bernstein & Bernstein, 2010, p.67). This document explains the dimension of various descriptive statistics.

Reliability This tool checks the relevance of the data collected as a prerequisite for validity and involves tests such as the inter-rater or inter-observer, test-retest and internal consistency. They check the probabilities of measuring the same phenomena and gives the correlation of results as a reflection of homogeneity of variables.

Reliability conti… This shows the reliability of a certain phenomenon or variable over time.

Validity This statistic gives the extension of the measurement of the statistics in comparison to the real world. Face validity can be used to access the construct on which research is being carried out while formative validity gives information as regards the improvement of a certain program. Sampling validity ensures that there is minimal sample bias while the criterion-related validity is used in the prediction of future performance.

Validity conti… An example is the Pearson’s Correlation Coefficient

Bell Curve Also known as normal distribution, it shows the probabilities of a series of data with an equi-distribution of probable events on a downward sloping line on both sides of the curve. It can be used to show the other descriptive statistics such as the mean and the standard deviation through the study of the dispersion of values.

Bell Curve The picture shows the Normal Distribution showing the mean, median along with the percentile rank.

Mean This is the central value or the average of a set of values and entails the sum of the total observations divided by the number (n) of the observations.

Mean conti… Mean from a lognormal distribution with varied skewness.

Standard Deviation This shows how spread out the numbers is from a specified statistic such as the mean or how far the variables are from the normal. It is given by the following formulae. If the sets of data are far from the mean, then the data set is said to have a higher standard deviation.

Standard Deviation conti… This shows the deviation from the mean which is 112.30.

Standard Scores Also called the z-scores, allows the calculation of a score within the normal distribution and also allows for the comparison of two scores that are from separate normal distributions. It entails the standardization of the normal distribution to get a standard normal distribution (Winkler & Othmar, 2011, p. 78). 

Standard Scores conti… It measures the number of standard deviations there are from the mean of the population to the raw score.

Scaled Scores These are obtained by the statistical adjustment and the conversion of the scores from the data set to a standard score to assess the differences across their forms. In that manner, the statistician only requires a slight change in the questions and gets correct details to get to a particular scaled score.

Scaled Scores conti… This is based on the best practices within a statistical field.

T-Scores These are scores that have been standardized for the particular dimension on every type. Supposing that a score of 60 is mean and a difference of 5 represents one standard deviation. This implies that a score of 70 would be two standard deviations above the mean. This is the criterion in the establishment and attainment of T-Scores.

T-Scores conti… This table shows the Critical Values of the t distribution with the specified degrees of freedom and levels of confidence.

Percentiles This indicates a certain percentage above or below a certain fixed percentage. For example, the 60th percentile can be used to denote the smallest score that is above 60%of the scores of the data. This can be found by getting the percentage of numbers that fall below a certain percentage. In this analysis of the statistic, if one scores 90% then the results implies that he or she scored 90% better than the rest of the individuals who participated in the test. The same case applies to 20% of the data (Bernstein & Bernstein, 2010, p.67). 

Percentiles conti… The figure above shows the 20th percentile with its corresponding percentages of data.

Conclusion Descriptive statistics are coefficients that describe and summarize a specific set of data of either a sample or of a population. The categories of descriptive statistics include the variability, spread and the measures of central tendency. Validity gives the extension of the measurement of the statistics in comparison to the real world. Bell Curve also known as normal distribution, shows the probabilities of a series of data with an equi-distribution of probable events on a downward sloping line on both sides of the curve. Mean is the central value or the average of a set of values and entails the sum of the total observations divided by the number (n) of the observations. Percentiles indicate a certain percentage above or below a certain fixed percentage. All these and other descriptive statistics enhance the accuracy of data analysis.

References Bernstein, S., & Bernstein, R. (2010). Schaum's outline of theory and problems of elements of statistics I: Statistics and probability. New York: McGraw-Hill. Holcomb, Z. C. (2010). Fundamentals of descriptive statistics. Los Angeles, CA: Pyrczak Pub. Winkler, K.M., & Othmar, W.C., (2011). Interpreting Economic and Social Data: A Foundation of Descriptive Statistics. Dordrecht: Springer.