StatisticsLesson 5 of 8 in the course Descriptive Statistics

Measures of Center, Sampling Statistics, and Grouped-Data Means

5 flashcards · 4 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Measures of center describe the location of a typical value in a data set. This lesson introduces the mean, median, and mode, explains how to calculate them, and shows how to choose a measure that suits the data.

xˉ=sum of the data valuesn\bar{x}=\frac{\text{sum of the data values}}{n}

The population mean is represented by the Greek letter μ\mu. A sample mean can estimate a population mean; taking a truly random sample helps make that estimate useful.

All flashcards

Arithmetic mean
The sum of all numerical values divided by their count; the sample mean is written as xˉ\bar{x}.
Median
The middle value in ordered data, or the average of the two middle values when the count is even.
Mode
The value or category that occurs most frequently.
Grouped-data mean estimate
An estimate calculated by weighting each interval midpoint by its frequency and dividing by the total frequency.
Sampling distribution
The distribution of a statistic's values across many samples.

Quiz questions

  1. In statistics, what is a statistic?Answer: A numerical summary calculated from sample data.
  2. What does a sampling distribution describe?Answer: How a statistic varies across many samples.
  3. According to the Law of Large Numbers, what tends to happen as random sample sizes increase?Answer: Sample means are more likely to be close to the population mean.
  4. Why is random selection useful when estimating a population value from a sample?Answer: It helps the sample represent the population.

Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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