Back To Course

Contemporary Math: Help and Review20 chapters | 228 lessons

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:
*Beverly Maitland-Frett*

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

Statistics is a major mathematical component of our world that some depend on and others hardly give a passing glance. Statistics has significant value and is used in areas from government to big business. This lesson gives a brief introduction to this broad field.

Timmy is a pizza shop manager and he has two locations picked for a possible new location. He decides to conduct a mini-study to decide based on a variety of factors. Location A is smaller, and he notices that there is a high school two blocks away, some business offices close by, and a laundromat next door. Location B is larger and next to a supermarket with some business offices scattered around the area, amidst several vacant lots. If you were Timmy, which would you choose?

You are a statistician in many ways. **Statistics** is the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data. Being a statistician at an elementary level may simply mean noticing patterns in daily circumstances and drawing conclusions about those patterns. On a grander scale, statisticians may spend months or years conducting a study before they can produce meaningful analysis of information. Statistics is its own community, with rules, procedures, and policies all built on simple mathematical principles.

The statistical process guides genuine study, and statisticians are exacting in their methodologies. The major steps of statistics are explained in a simplistic form as follows:

__Planning a study:__There must be a subject that requires investigation. Planning entails deciding what instruments (interviews, surveys, etc.) to use, who to speak with, and how to analyze findings.**Instruments**, in this case, are tools used in conducting a study like surveys, interviews, etc. Do you remember Timmy? In this stage, he plans to interview shoppers and count people.__Organizing the data:__The best way to obtain the valid answers is to organize the information effectively to help expose patterns and other significant relationships. There are a variety of software programs that can help with this step. Once Timmy has gathered data, he could perform calculations of the mean, mode, and median visitors.__Interpreting the data:__This is the heartbeat of statistics. Interpretations can have lasting repercussions, and it's important to make sure they are valid assumptions and supported by mathematical reasoning. Timmy, based on his interpretations of the numbers, could make plans to have special sales on days with the most traffic.__Presenting the data:__The methods you chose to present the data can make findings more interesting or powerful. People use graphs, tables, and various diagrams to show relationships between data. With this information, Timmy could present compelling arguments using his analysis so that he and his business partners can discuss the most profitable possibilities for the pizza shop.

Other than individuals and small businesses owners like Timmy who conducted their own studies, there are some entities who thrive on statistics. Here are a few major examples.

The government uses statistics to make decisions about populations, health, education, etc. It may conduct research on education to check the progress of high schools students using a specific curriculum or collect characteristic information about the population using a census.

The medical field would be far less effective without research to see which medicines or interventions work best and how the human bodies react to treatment. Medical professionals also perform studies by race, age, or nationality to see the effect of these characteristics on health.

Although this is attached to both the science and medical field, success in psychology would be impossible without the systematic study of human behavior, often analyzing results statistically.

Teachers are encouraged to be researchers in their classrooms, to see what teaching methods work on which students and understand why. They also should evaluate test items to determine if students are performing in a statistically expected way. At all levels of education and testing there are statistical reports about student performance, from kindergarten to an SAT or GRE.

Every large company employs its own statistical research divisions or firms to research issues related to products, employees, customer service, etc. Business success relies on knowing what is working and what isn't.

In many cases, basic statistical analysis can be done by using three main concepts: the mean, the median, and the mode.

The **mean** is the mathematical average. For example, a laundromat may conduct a study to see how many people use a machine each day, then calculate the average for each week.

- Sun: 105
- Mon: 50
- Tues: 40
- Wed: 50
- Thurs: 70
- Fri: 80
- Sat: 95

The mean is the sum of the items divided by the number of items. In this case, we have seven items, so: mean = (105 + 50 + 40 + 50 + 70 + 80 + 95) / 7 = 70 people

The **mode** is the number that occurs most frequently in the data set. If we first organize the data in ascending order we get: 40, 50, 50, 70, 80, 95, 105. You can see 50 is the mode because it occurs twice while every other number occurs just once.

The **median** is found by organizing the data and then taking note of the number(s) that is in the middle. If we consider our data set again (40, 50, 50, 70, 80, 95, 105), you can see 70 is the number in the middle.

In data sets with an odd number of items, you simply select the middle item. In data sets with an even number of items, you must average the value of the two middle items to find the median.

Some of the main concerns with statistics are:

__Data interpretation__: Many people can interpret the same data differently. For example, if a report explains that 80% of high school students are left handed, it is easy to think that teenagers these days are mostly left handed. However, if you find that this is based on a population of students at Left Handed High, your opinion would change. When reading statistics, it is important to ask: what data was really captured and how was it interpreted?

__Data validity?__: **Validity** is a common term in the statistics world and it refers to whether the study is true or false. A study could be inaccurate, for example, if researchers pressured participants to answer a certain way. All factors must be representative of the real world to create a valid study.

Statistical studies are extremely important in our everyday life. **Statistics** are the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data.

Every human, at some level, is a statistician. We observe trends, sort out information, and then draw conclusions. This is similar to the actual process of gathering statistics, which begins with **planning a study**, which involves deciding what instruments to use, who to speak with, and how to analyze findings. **Instruments** are tools used in conducting a study like surveys, etc. From there, you **collect data**, when the instruments you selected are used, **organize the data**, putting the information together effectively to help expose patterns and other significant relationships. **Interpret the data**, valid assumptions supported by mathematical reasoning and finally, **present the data**, graphs, tables, and various diagrams are used to show relationships between data.

The **mean**, **median** and **mode**, the average, The middle-valued number(s), and the most common number, respectively are all calculated during the organization process, while **validity**, whether the study is true or false, is a common concern that is analyzed during the entire process.

Many major entities do more advanced and larger statistical analysis. Some major areas relying on statistics include government, education, science, and large companies. By doing more and better statistical analysis, we are able to understand the world around us, appreciate the value of analysis, and we are less deceived by numbers.

**Statistics** - the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data

**Instruments** - tools used in conducting a study like surveys, interviews, etc.

**Mean** - the mathematical average of a set of data

**Mode** - the number that occurs most frequently in the data set

**Median** - the middle number of an ordered data set

**Validity** - whether the study is true or false

After viewing this lesson, you should be able to:

- Restate various fields in which statistics are used
- Report the major steps of statistics
- Calculate the mean, mode, and median of a set of data
- Recognize how you adapt statistical instruments to everyday scenarios

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
28 in chapter 3 of the course:

Back To Course

Contemporary Math: Help and Review20 chapters | 228 lessons

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- What is Random Sampling? - Definition, Conditions & Measures 5:55
- Simple Random Samples: Definition & Examples 5:10
- Stratified Random Samples: Definition, Characteristics & Examples 6:25
- Cluster Random Samples: Definition, Selection & Examples 6:44
- Systematic Random Samples: Definition, Formula & Advantages 8:37
- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Mean, Median, Mode & Range: Practice Problems 7:13
- Population & Sample Variance: Definition, Formula & Examples 9:34
- Calculating the Standard Deviation 13:05
- 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
- Frequency & Relative Frequency Tables: Definition & Examples 4:48
- Cumulative Frequency Tables: Definition, Uses & Examples 5:17
- How to Calculate Percent Increase with Relative & Cumulative Frequency Tables 5:47
- Creating & Interpreting Histograms: Process & Examples 5:43
- Degrees of Freedom: Definition, Formula & Example 5:12
- Restriction of Range: Definition & Examples 4:09
- Linear Regression Model: Definition, Equation & Example
- Misleading Graphs: Definition & Examples 3:46
- Misleading Statistics: Definition & Examples 4:39
- Poisson Distribution: Definition, Formula & Examples 4:26
- Population Variance: Definition, Formula & Example
- Sample Variance: Definition, Formula & Example
- What is Data Distribution? - Definition & Types 4:21
- Application of Statistics in Daily Life 8:11
- Go to Statistics Overview: Help and Review

- 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

- What is Deadlock? - Definition, Examples & Avoidance
- El Hombre que se Convirtio en Perro: Author, Summary & Theme
- Achilles in The Iliad: Character Analysis & Description
- A Wrinkle in Time Chapter 5 Summary
- Roald Dahl Project Ideas
- Media Literacy Activities for High School
- Letter M Activities
- Quiz & Worksheet - Shang Dynasty Religion & Culture
- Quiz & Worksheet - Alternative Assessment Types
- Quiz & Worksheet - Population Composition
- Quiz & Worksheet - Minimalist Painters
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Math Worksheets | Printable Math Worksheets for Teachers
- Social and Emotional Learning | Self-Management

- CHSPE: Practice & Study Guide
- MTEL Foundations of Reading (90): Study Guide & Prep
- Freak the Mighty Study Guide
- Smarter Balanced Assessments - ELA Grade 11: Test Prep & Practice
- TCI History Alive The United States Through Industrialism: Online Textbook Help
- AP Physics 2: Magnetic Fields
- Works by African American Writers
- Quiz & Worksheet - Kinds of Employees
- Quiz & Worksheet - Strategic Human Resource Planning
- Quiz & Worksheet - Employee Engagement
- Quiz & Worksheet - Geotropism
- Quiz & Worksheet - Fundamental Attribution Error

- What is Project Cost Management? - Definition & Importance
- Stem Cells Lesson for Kids
- Resources for Speech Education
- How to Pass the California Bar Exam
- New Careers for Teachers
- Rainy Day Activities for Kids
- How to Ace a Phone Interview
- Earth Day Lesson Plan
- Inertia Experiments for Kids
- Resources for Speech Education
- Michigan Associations for Speech & Speech Education
- Letter Writing Lesson Plan

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

Browse by subject