Back To Course

Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

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:
*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.

Calculating the mean, median, mode, and range of a data set is a fundamental part of learning statistics. Use this video to practice your skills and then test your knowledge with a short quiz.

The **mean** is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by how many numbers there are. The **median** is the middle number in a data set when the numbers are listed in either ascending or descending order. The **mode** is the value that occurs the most often in a data set, and the **range** is the difference between the highest and lowest values in a data set.

During this video, we will be looking at practice problems to help you find the mean, median, mode, and range of a data set. Since these are practice problems, feel free to pause the video during each example and try to work out the problems on your own. Then, play the video to check your answers.

According to the U.S. Bureau of Labor Statistics, the gas prices for each month of the year in 2000 were as follows, rounded to the nearest hundredth of a decimal:

1.30, 1.37, 1.54, 1.51, 1.50, 1.62, 1.59, 1.51, 1.58, 1.56, 1.56, 1.49.

Let's start with the mean. Pause the video here to see if you can find the mean of this data set. The **mean** of a data set tells us on average how much gas cost in the year 2000. We can find the mean by adding all of the numbers up and dividing by 12, which is the number of months in the year and how many numbers we have in this data set.

1.30 + 1.37 + 1.54 + 1.51 + 1.50 + 1.62 + 1.59 + 1.51 + 1.58 + 1.56 + 1.56 + 1.49 = 18.13 / 12 = 1.51

1.51 is the mean for this data set. This number tells us on average the price of gas for the entire year. You will notice that 1.51 appears in the data set. Sometimes you will have an average that does not appear in the data set, but will still show you the big picture of the numbers given.

Okay, let's move on to median. Pause the video here to see if you can find the median of this data set. The **median** of a data set tells us what number falls directly in the middle. This is useful if you have one or two numbers that are greatly larger or smaller than the rest of the numbers in the data set. If the numbers are all pretty close together, then the mean and the median will be very close to the same number.

First, arrange the numbers in either ascending or descending order.

1.30, 1.37, 1.49, 1.50, 1.51, 1.51, 1.54, 1.56, 1.56, 1.58, 1.59, 1.62

Now, eliminate each number until you are down to the middle. I like to take one number from each end like this:

So we are left with 1.51 and 1.54 with five numbers crossed out on each side. Sometimes you will have data sets that have an odd amount of numbers. When this happens you are left with one number as a median. In this case, we have two numbers because our data set has an even amount of numbers. When you are left with two numbers as the median, you need to find the average by adding the two numbers and dividing by 2.

1.51 + 1.54 = 3.05 / 2 = 1.53

I rounded this number to the nearest hundredth. The median is 1.53 and this tells us that exactly half of the data set is greater than 1.53 and exactly half of the data set is less than 1.53. Although it isn't the same number, the mean and the median for this set of numbers is very close, meaning that the numbers in the data set are very close together.

Now let's find the mode in this set of data. The **mode** is the number you will see the most in the data set. While mean and median give you a big picture idea, the mode gives you an idea of what number you are most likely to encounter. Let's look at some numbers that repeat in the data set. I see two 1.51 numbers and two 1.56 numbers. In this data set, there are no other numbers that repeat. So in this case, we have two modes: 1.51 and 1.56.

Our last practice problem is finding range. You can find the **range** in the data set by taking the largest number and subtracting the smallest number. This will show you the spread in the numbers and how much difference there is between them. In this data set, our largest number is 1.62 and our smallest number is 1.30. Subtract those numbers.

1.62 - 1.30 = .32

This is our range. So now we know that over the course of the year 2000, the price in gas fluctuated a total of 32 cents.

Remember, the **mean** is the arithmetic average of a data set. You can find the mean by adding the numbers in a data set and dividing by how many numbers there are. The **median** is the middle number in a data set when the numbers are listed in either ascending or descending order, and the **mode** is the value that occurs the most often in a data set. The mode can tell you what numbers are most likely to come across in the data set. The **range** is the difference between the highest and lowest values in a data set. The range can tell you how much the data set fluctuates.

By the end of this lesson you should be able to explain and calculate the mean, median, mode, and range for a data set.

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 160 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
4 in chapter 2 of the course:

Back To Course

Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- What is the Center in a Data Set? - Definition & Options 5:08
- Mean, Median & Mode: Measures of Central Tendency 6:00
- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Mean, Median, Mode & Range: Practice Problems 7:13
- 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

- MTLE Pedagogy - Secondary (Grades 5-12): Study Guide & Practice
- MTLE Pedagogy - Elementary (Grades K-6): Study Guide & Practice
- Computer Science 113: Programming in Python
- DSST Information Guide
- GACE Early Childhood Special Education General Curriculum: Practice & Study Guide
- Required Assignments for Communications 301
- Required Assignments for Psychology 306
- Computing with Numbers
- Introduction to Python Programming
- Object-Oriented Programming
- CBEST Passing Rate
- What is the CTEL Exam?
- How to Prepare for the CTEL
- CTEL Test Score Information
- CTEL Test Accommodations
- CTEL Test Retake Policy
- CSET Test Day Preparation

- Bradford Protein Assay: Principle, Protocol & Calculations
- Menelaus vs. Paris in The Iliad
- Strategies for Teaching ELL Students with Interrupted Formal Education
- Double Slit Experiment: Explanation & Equation
- Global Equity Portfolio: Definition & Strategies
- Crystal Twinning: Definition & Symmetry
- Logo Imagery in Visual Storytelling
- CPG Companies Brand Value Case Studies
- Quiz & Worksheet - Civil War Border States
- Quiz & Worksheet - Literacy Development Research
- Quiz & Worksheet - Role of ELL Teachers
- Quiz & Worksheet - Life & Works of Stephen Krashen
- Quiz & Worksheet - The New Right Movement
- Flashcards - Introduction to Research Methods in Psychology
- Flashcards - Clinical Assessment in Psychology

- Prentice Hall Algebra 1: Online Textbook Help
- CSET English: Study Guide & Test Prep
- Chemistry: High School
- Information Systems for Teachers: Professional Development
- High School Algebra II: Homework Help Resource
- Researching the Speech Lesson Plans
- Praxis Environmental Education: Climate Variations & Weather Patterns
- Quiz & Worksheet - Expressed vs. Implied Contracts
- Quiz & Worksheet - How to Express Rational Functions
- Quiz & Worksheet - Using Anemometers & Wind Vanes
- Quiz & Worksheet - Features of No Child Left Behind
- Quiz & Worksheet - Mutual Assent & Objective Standard in Contract Law

- How to Write the Equation of a Parabola in Standard Form
- Gaius Marius: Biography & Quotes
- Good Persuasive Writing Topics for Kids
- Reading Food Labels Lesson Plan
- Supply and Demand Activities for Kids
- Inertia Experiments for Kids
- Persuasive Writing Prompts: 3rd Grade
- Renaissance Lesson Plan
- Albert Einstein Experiments for Kids
- Air Pressure Experiments for Kids
- Study.com's Bachelor's Degree in Business: Degree Plan
- Chemical Change Experiments for Kids

Browse by subject