An average tells us where the center or most common outcome lies within a data set. Regardless of the type of data you are recording the average value gives you a good indication of what to expect from your next data point. The more data you collect, the more accurate that the average becomes. As a result, the more reliable and valid your data becomes. Averages are often used to track or rate performance in all walks of life. You will first come across the concept to understand how well you are doing in school or a particular course. If you are a sporting fan or athlete, you are very familiar with this based on the statistics that best indicates the output of an individual. Our medicine and the effectiveness of drugs and vaccines are focused on this concept. In the business world, company leaders use this fundamental statistic to not only understand how well their company is doing, but if they need to hire or let go of some employees. These worksheets will help us begin to make sense of the use and concept of averages.
- Working with Averages Step-by-step Lesson- At the Acme Rubber Band factory, the manager was asked the average number of hours her part time workers were putting in each week. She has amassed all the hours of the part time employees, below, over the last week. Determine the average number of hours her part time employees put in last week.
- Guided Lesson - Gabby was a talented basketball player that was coming back from an injury. She got better in every game she played in. In her first game she scored 22 points. In every one of her next 5 games she scored 3 more points than the last game she played. In her seventh game she scored 45 points. What was the average number of points per game that Gabby scored over her seven games?
- Guided Lesson Explanation - To find the average of any data set, we follow this equation: sum of all terms ÷ number of terms.
- Practice Worksheet - Find the averages for each set of data. Round answers to the nearest hundredth.
- Word Problems Worksheet - You will work your way through all of the word problems that are presented to you.
- Answer Keys - These are for all the unlocked materials above.
There is a nice mix of all the skills that we explore provided in this selection of homework sheets.
- Homework 1 - You will have a selection of data provided to you. Find the central point within it.
- Homework 2 - We review both techniques that you may want to use here.
- Homework 3 - Example: Tyler swam 4 laps in the morning, 11 laps at lunch. After school he swam 10 laps then did his homework. When he finished homework he swam 15 more laps. How many laps did he swim on average each time?
- Homework 4 - Example: Max practices gymnastics for 2 hours one day, 3 hours the next day, 8 hours on Saturday, and 7 hours on Sunday. What is the average number of hours he practices?
- Homework 5 - We pull algebra in with this concept.
We follow the same progress with the concept explored in different ways.
- Practice 1 - Crunch this data inside to help make sense of it all.
- Practice 2 - These are nice and simple values to work with.
- Practice 3 - Sample: Sam is a glassblower. On Monday he made 3 bowls, On Tuesday he made 6 vases, and on Wednesday he made 6 glasses. What is the average number of objects Sam made per day?
- Practice 4 - You will make sense of math sentences to find an end value.
Math Skill Quizzes
Time to see if you have put everything together for your team.
- Quiz 1 - Flat data sets for you to find the central point for.
- Quiz 2 - Sample: Timothy ran five days in a row. He ran 5 miles on Monday, 2 miles on Tuesday, 3 miles on Wednesday, 5 on Thursday, and 6 miles on Friday. How many miles did he average over the week?
- Quiz 3 - Example: Matthew watches TV for 2 hours on Monday, 3 hours on Tuesday, 1 hour on Wednesday, 2 hours on Thursday, and 2 hour on Friday. What is the average number of hours Matthew watched TV?
- Quiz 4 - We squeeze out our last drop of algebra with this topic.
Averages as a Data Point
In today's data driven decision making we are often looking for the key statistics that we should use to make our decision. Using the concept of average or formally called the statistical mean is very attractive, but definitely not always the best choice. There are many advantages and disadvantages of this data point. Let's take a quick peek at the advantages and disadvantages of it:
1. It is very easy to compute. Simply add up all the data and divide by number of pieces of data that you used to find that sum.
2. It is a true measure of central tendency because it takes every single piece of data into account, including outliers.
3. It is a reliable statistic. It will not vary too much from one population to the next as long as all variables are taken into account.
1. You actually need to do the math it cannot be done by spot checking or graphically. This is not a big deal when you have a few pieces of data, but this can become cumbersome when you are working with pools of data.
2. You need complete data in order to process this statistic. It is the only measure of central tendency that always requires a complete data set.
3. When you are dealing with data that is very lop-sided this is not a measure you want to count it. That is because it takes all of the values into account and skews the measures. It is a double-edged sword that way.