StatisticsLesson 2 of 2 in the course Descriptive Statistics

Standard Deviation: Calculation, Interpretation, and Related Rules

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

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Summary

This lesson introduces variation, or spread, and explains how standard deviation describes the distance of data values from their mean. Understanding spread helps you compare data sets that may have the same average but very different patterns.

A data set's mean describes its center, but it does not tell us whether the values are tightly clustered or widely scattered. Variation describes how much the data values differ from one another and from the mean.

All flashcards

Deviation
The difference between a data value and the relevant mean.
Grouped-data standard deviation
An estimate based on class midpoints and their frequencies.
Z-score
A value's signed distance from its mean, measured in standard deviations.
Standard error of the mean
The standard deviation of the sampling distribution of sample means.
Degrees-of-freedom adjustment
Using n − 1 in the sample variance denominator to estimate population variance.

Quiz questions

  1. For a sample of n observations, which denominator is used to calculate sample variance from squared deviations?Answer: n − 1
  2. A value is 14, the mean is 10, and the standard deviation is 2. What is the value's z-score?Answer: 2
  3. When the population standard deviation is known, how is the standard error of the sample mean calculated?Answer: Divide the population standard deviation by the square root of the sample size.
  4. According to Chebyshev's Rule, at least what proportion of values lie within two standard deviations of the mean?Answer: 75%
  5. What does a standard error describe?Answer: Variation in a statistic across repeated samples.

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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