Back To Course

Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Log in here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Cathryn Jackson*

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Finding the center in a data set can sometimes be a little confusing. This lesson will help you determine the correct method for finding the center in a data set, and when you are finished, test your knowledge with a short quiz!

Elizabeth is working on a science project. She is testing the effectiveness of bleach on certain types of stains. After trying the bleach on each stain five times, Elizabeth records how many times the bleach removes the stain completely. Check out this chart to see how the project turned out.

Elizabeth has a data set of 4, 2, 5, 4, 1, 2 and 3. She wants to find a way to summarize the information. Elizabeth needs to find the **center of data**, a single number that summarizes the entire data set. You can find the center of data using either the mean or the median of the data set.

The **mean** is the sum of the numbers in a data set divided by the total number of values in the data set. The mean is also commonly known as the average. The mean can be used to get an overall idea or big picture of the data set. Mean is best used for a data set with numbers that are closer together.

Since all of Elizabeth's numbers are close together, she can use mean to find the center of her data set. Simply add all of the numbers together and divide by how many numbers there are in the data set: 4 + 2 + 5 + 4 + 1 + 2 + 3 = 21 / 7 = 3. Elizabeth's center of data for this data set is 3. She can summarize that, on average, bleach will effectively remove a stain 3 out of 5 times.

Elizabeth is now experimenting with the effectiveness of plain soap on stains. After trying the soap on stains eight times, Elizabeth records how many times the soap removes the stain completely. Check out the chart she has made showing the effectiveness of soap on the stains.

From this chart you can see that our data set is 6, 7, 8, 8, 6, 0 and 7. You might notice that we have several numbers that are close together and one number that is a bit off. This number is referred to as the **outlier**. An outlier is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set. Because we have an outlier in this data set, we need to use the median to find the center of the data set.

The **median** is the midpoint value of a data set, where the values are arranged in ascending or descending order. The median can be used to get an idea of what values fall above the midpoint and what values fall below the midpoint. There is equal likelihood that the values in the data set will fall either above or below the median. Median is best used for a data set with numbers that have a few larger or smaller numbers and several numbers close together. One large or small number might skew the mean, but the median can often give you a better idea of the data.

We can find the median of this data set by first arranging the numbers in ascending order: 0, 6, 6, 7, 7, 8, 8.

Now eliminate numbers from each side of the data set. That leaves us with 7 as the center of our data set. That means we can summarize this data by saying roughly 7 out of 8 times the soap will remove a stain. If we were to find the mean of this data set, we would have 6. You can see that the 0 in the data set would skew the center of data by a full number lower.

It is important for Elizabeth to be able to summarize her data for her science project. You can summarize data in different ways by finding the center of data. The **center of data** is a single number that summarizes the entire data set. It is important to use the correct method for finding the center of data so you can accurately summarize the data set. You can do this by using either the mean or the median.

The **mean** is the sum of the numbers in a data set divided by the total number of values in the data set. The mean can be used to find the center of data when the numbers in the data set are fairly close together.

The **median** is the midpoint value of a data set, where the values are arranged in ascending or descending order. The median can be used to find the center of data when the numbers in the data set contain one or more outliers. An **outlier** is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set. Make sure you examine your data carefully before deciding which method to use to find your center of data.

Once you have finished reviewing this lesson, you should be able to:

- Understand what the center of data is and how to find it
- Discuss when it is better to use either the mean or the median

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

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Log in here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 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
1 in chapter 2 of the course:

Back To Course

Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

- What is the Center in a Data Set? - Definition & Options 5:08
- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Mean, Median, Mode & Range: Practice Problems 7:13
- Visual Representations of a Data Set: Shape, Symmetry & Skewness 5:22
- Unimodal & Bimodal Distributions: Definition & Examples 5:29
- The Mean vs the Median: Differences & Uses 6:30
- Spread in Data Sets: Definition & Example 7:51
- Maximums, Minimums & Outliers in a Data Set 4:40
- Quartiles & the Interquartile Range: Definition, Formulate & Examples 8:00
- Finding Percentiles in a Data Set: Formula & Examples 8:25
- Calculating the Standard Deviation 13:05
- The Effect of Linear Transformations on Measures of Center & Spread 6:16
- Population & Sample Variance: Definition, Formula & Examples 9:34
- Ordering & Ranking Data: Process & Example 6:54
- Go to Summarizing Data

- Go to Probability

- Go to Sampling

- SIE Exam Study Guide
- Indiana Real Estate Broker Exam Study Guide
- Grammar & Sentence Structure Lesson Plans
- Foundations of Science Lesson Plans
- Career, Life, & Technical Skills Lesson Plans
- Business Costs, Taxes & Inventory Valuations
- Using Math for Financial Analysis
- Assessments in Health Education Programs
- Governmental Health Regulations
- Understanding Health Education Programs
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- Curt Lemon in The Things They Carried
- Religion in Jane Eyre: Analysis & Examples
- Intrapreneurship in the Hospitality Industry
- Saadat Hasan Manto: Biography & Works
- Using File-Carving & Scalpel Techniques to Recover Android Device Data
- Functional Text Activities for Middle School
- A Midsummer Night's Dream Fairies Role & Analysis: Peaseblossom, Cobweb, Moth & Mustardseed
- Quiz & Worksheet - Assessing Nutritional & GI Status
- Quiz & Worksheet - Achievements of President Jackson
- Quiz & Worksheet - Agile Environments
- Quiz & Worksheet - State & Federal Rights in the Civil War
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- 9th Grade Math Worksheets & Printables
- Precalculus Worksheets

- AP Physics 1: Exam Prep
- Workplace Harassment Training for Employees
- American Government Syllabus Resource & Lesson Plans
- Introduction to Criminal Justice Syllabus Resource & Lesson Plans
- Workplace Harassment Training for Supervisors
- Organization of Written Works
- COOP Exam: Data Analysis & Statistics
- Quiz & Worksheet - Marginal Tax Rate
- Quiz & Worksheet - Calculus Integration Problems
- Quiz & Worksheet - Economic Incentives
- Quiz & Worksheet - Biography of Louis XIV
- Quiz & Worksheet - War of 1812 Causes & Effects

- Double Angle: Properties, Rules, Formula & Examples
- Legacy of the New Deal Lesson Plan
- Alcohol Awareness Activities
- What Are the Best Online SAT Prep Courses?
- Finding Continuing Education Grants for Teachers
- Best Books to Learn Spanish
- Alphabet Games for Kids
- How to Learn Accounting
- How to Pass the Living Environment Regents Exam
- Addition Math Games
- How to Pass the Real Estate Exam
- How to Prep for the NYS English Regents Exam

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject