Understanding Analytics and Statistics: Key Concepts and Definitions

Analytics and Statistics: Key Concepts

Analytics: the scientific process of transforming data into insight for making better decisions. Population: the set of all elements of interest in a particular study. Sample: a subset of the population. Data: the facts and figures collected, analyzed, and summarized for presentation and interpretation. Cross-sectional data: data collected at the same or approximately the same point in time. Statistics: the art and science of collecting, analyzing, presenting and interpreting data. Variable: a characteristic of interest for the elements. Data set: all the data collected in a particular study. Elements: the entities on which data are collected.

Data Summary

1. Cumulative Frequency Distribution: a tabular summary of quantitative data showing the number of data values that are less than or equal to the upper class. 2. Cumulative Percentage: a tabular summary of quantitative data showing the percentage of data values that are less or equal to the upper-class limit of each class. 3. Cumulative Relative Frequency: a tabular summary of quantitative data showing the fraction or proportion of data values that are less than or equal to the upper class limit of each class.

Measurement and Variability

Observation: the set of the measurements obtained for a particular element. Measure of central location: mean, median, mode. Measure of noncentral location: percentiles, quartiles. Measure of variability: range, IQR, variance.

Key Measures

Mean: measure of central location provided computed by summing the data values and dividing by the number of observations. Median: measure of central location provided by the value in the middle when the data are arranged in ascending order. Sample statistic: a numerical value used as a summary measure for a sample. Variance: a measure of variability based on the squared deviations of data values about the mean. Weighted Mean: the mean obtained by assigning each observation a weight that reflects its importance. Range: a measure of variability, defined to be the largest value minus the smallest value. Percentile: a value such that at least p percent of the observations are less than or equal to this value and at least (100-p) percent of the observations are greater than or equal to this value. The 50th percentile is the median. Mode: a measure of location defined as the value that occurs with greatest frequency. Outlier: an unusually small or unusually large data value. IQR: a measure of variability, defined to be the difference between the third and first quartile. Sample space: the set of all experimental outcomes.