# Understanding Analytics and Statistics: Key Concepts and Definitions

Classified in Mathematics

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## 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.