Back To Course

Introduction to Psychology: Homework Help Resource13 chapters | 236 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Chevette Alston*

Dr. Alston has taught intro psychology, child psychology, and developmental psychology at 2-year and 4-year schools.

Standard deviations are scores around the mean of a distribution. It measures how much a set of scores is dispersed around an average measure of variability. Deviations around the mean can be calculated to express it as a variance or a standard deviation.

A **standard deviation** is a statistic that is calculated as the square root of a variance, or a data set calculated by taking the mean of the squared differences between each value and the mean value. Because the differences are squared, units of variance are not units of data. This is why a standard deviation is the square root of the variance. The points or units plotted from the variance becomes the data set. Standard deviations and variances are common measures of dispersion.

Ïƒ = standard deviation |
Ïƒ ² = variance |

A standard deviation is how a set of data is plotted around the mean (average) of a set of data. It is how a data set compares to a calculated norm or standard. The further the data spreads from the mean, the greater the deviation from the norm. Likewise, the closer the data are to the mean, the closer the data are to the norm, which creates a steep curve. The standard deviation of a data set that equals zero indicates all values in the set are the same.

Standard deviation data sets are plotted and dispersed around a **bell curve**. A bell curve is a symmetrical curve that represents the distribution, values, and frequencies in a set of data. From the middle point at the top, it slopes in a downward arc on both sides. The top middle point is the mean value or the maximum probability. Probability is likelihood of occurrence.

As the probability decreases, the slope of the bell curve falls away from the mean. This explains why a wide deviation indicates a greater deviation from the mean. A **normal distribution** of data means that the numbers in the standard deviation's data set are close to the mean.

Units are plotted on the x-axis, or the horizontal line, in relation to how this information aligns with the frequency for each value on the y-axis, or the vertical line. For example, on the y-axis, salary, range may be from $50,000 to $200,000, with an average salary of $200,000 (top of the bell curve). Let's say we plot the salaries of 30 people, or units, on the x-axis. The x-axis would reflect where each worker's salary would be plotted according to how much each person made. To the right of the median average, the worker would make more than $200,000, and to the left of the median average, he or she would make less than $200,000.

One standard deviation from the mean (red area) on the x-axis usually accounts for about 68% of the data set. Two standard deviations from the mean (green area) usually accounts for about 95% of the data set. Likewise, three standard deviations from the mean (blue area) usually accounts for about 99% of the data set. Lastly, four deviations from the mean would be the white area.

Using the example given, the further from the average salary of $200,000 earned (slope top), the greater the deviation from the mean (average). Also notice that the number of data sets would decrease with each standard deviation. Again, large standard deviation could reveal that not too many people are averaging $200,000 in earnings. A small standard deviation may be revealing that there are many who are averaging earnings around the norm for the 30 people plotted. Depending upon the size of the bell curve, another interpretation could be that everyone averages around the norm (a steep curve) or that not too many people are averaging $200,000 (a flatter slope).

A **standard deviation** is a statistic that is calculated as the square root of a variance, or a data set calculated by taking the mean of the squared differences between each value and the mean value. Because the differences are squared, units of variance are not units of data. This is why a standard deviation is the square root of the variance. The points or units plotted from the variance become the data set. Standard deviations and variances are common measures of dispersion.

A standard deviation is how a set of data is plotted around the mean (average) of a set of data. It is how a data set compares to a calculated norm or standard. Standard deviation data sets are plotted and dispersed around a **bell curve**, which is a symmetrical curve that represents the distribution, values, and frequencies in a set of data. A **normal distribution** of data means that the numbers in the standard deviation's data set are close to the mean.

One standard deviation from the mean (red area) on the x-axis usually accounts for about 68% of the data set. Two standard deviations from the mean (green area) usually accounts for about 95% of the data set. Likewise, three standard deviations from the mean (blue area) usually accounts for about 99% of the data set. Lastly, four deviations from the mean would be the white area.

Knowing the contents of this lesson could enable you to do the following:

- Define standard deviation, bell curve and normal distribution
- Explain why a standard deviation is the square root of the variance
- Plot and interpret standard deviation around a bell curve

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
10 in chapter 13 of the course:

Back To Course

Introduction to Psychology: Homework Help Resource13 chapters | 236 lessons

- Introduction to Research Design & Statistical Analysis for Psychology 4:52
- Types of Research Designs in Psychology 7:11
- Reliability & Validity in Psychology: Definitions & Differences 4:07
- Statistical Analysis for Psychology: Descriptive & Inferential Statistics 4:55
- Experimental Group: Definition & Explanation 4:01
- Experimental Research in Psychology: Methods, Studies & Definition 9:06
- Normal Distribution of Data: Examples, Definition & Characteristics 4:43
- Outlier in Statistics: Definition & Explanation 5:50
- Raw Score: Definition & Explanation 3:30
- Standard Deviation in Psychology: Formula & Definition 5:33
- Validity in Psychology: Types & Definition 6:06
- Variable Interval and the Schedule of Reinforcement: Examples & Overview 4:08
- Go to Statistics, Tests and Measurement: Homework Help

- Drama 101: Intro to Dramatic Art
- Team Briefing Basics for Supervisors
- Communications 104: Intro to Mass Communications I
- Art 104: History of Western Art II
- Inclusion in Recruitment, Interviews & Hiring
- Origins of Theatre
- Western Theatre from Renaissance to Realism
- Theatre as Activism
- Introduction to the Dramatic Arts
- Contemporary Theatre
- Study.com FTCE Scholarship: Application Form & Information
- Study.com CLEP Scholarship: Application Form & Information
- List of FTCE Tests
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits

- Dislocated Ribs: Symptoms & Treatment
- What is Air Resistance? - Lesson for Kids
- The IRAC Method
- What is an Absolute Phrase? - Definition & Example
- Constructed Textiles Designers
- Linear vs. Branched Silanes
- Healthcare Breaches of Contract: Examples & Remedies
- Kinematics in Physics Activities
- Quiz & Worksheet - Themes in Dracula
- Quiz & Worksheet - Subsequent Events on Balance Sheets
- Quiz & Worksheet - I/O Psych Data Collection
- Quiz & Worksheet - Noise Pollution Causes & Examples
- Quiz & Worksheet - Efficiency, Equity & Voice in Business
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- Quantitative Analysis: Tutoring Solution
- Middle School World History: Homeschool Curriculum
- High School Precalculus: Homeschool Curriculum
- Educational Psychology Textbook
- Human Growth & Development Studies for Teachers: Professional Development
- CSET Science: Heat Transfer and Thermodynamics
- CSET Business - Leadership
- Quiz & Worksheet - Factors Impacting Developmental Genes
- Quiz & Worksheet - Salary & Benefits for Veterinary Offices
- Quiz & Worksheet - What's Your Learning Style?
- Quiz & Worksheet - Lycidas by Milton
- Quiz & Worksheet - Scansion in Poetry

- Dramatic Irony in Julius Caesar: Example & Analysis
- Sequencing of Music Instruction
- Alliteration Lesson Plan
- Response to Intervention Training
- What is the PSAT 8/9? - Information, Structure & Scoring
- Conjunctions Lesson Plan
- GMAT Test Dates
- Texas Real Estate Licensing & Continuing Education
- How to Use the GED Math Prep Course
- What are the NBPTS Standards?
- Iowa Science Standards & Benchmarks
- TExES School Counselor Exam Dates

Browse by subject