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Concept

Describing Data Collected From a Sample | |
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Calculating the measures of center | Mean, median, and mode |

Calculating the measures of spread | Range, interquartile range, mean absolute deviation, standard deviation, and variance |

Representing data graphically | Bar chart, pie chart, histogram, frequency polygon, and box plot |

Describing the sample probability distribution | Represented by tables, equations, and graphs |

The other branch of statistics is called inferential statistics. This involves making one or multiple hypothesis, predictions, inferences, or drawing conclusions and making generalizations about a population. Data collected from samples make this possible. The following are the main areas of inferential statistics.

Making Predictions or Generalizations About a Population | |
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Estimating Parameters | Using a statistics from sample data (e.g. the sample mean) to make an estimation about a population parameter (e.g. the population mean). Estimations are commonly presented as confidence intervals. |

Hypothesis Tests | Using sample data to test if a claim about the mean of a population is true or false. |

A few weeks before a city's election for its next mayor, a company surveyed $1000$ randomly-selected residents. The residents were asked which candidate they plan to vote into office. The results are represented in the following pie chart.

The chart shows that more than half of the sample participants plan to vote for Candidate A. This analysis meets the criteria for descriptive statistics. Additionally, based on the sample, it can be inferred that more than half of residents of the city will vote for Candidate A. This is an inference, and therefore, it is an inferential statistic.

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