The Measure of Center of Data Sets
When we want to make sense of any figures at all, we need to have some foundational knowledge as to what is normal and what is not. This helps understand if there is so form of error that may exist or a calculation that perhaps went very wrong. To do this when looking into a new data set, we will often start by finding the measure of center. This helps understand which data fits the pattern and which may be way out there. We will work through the most common measures that are used to determine this center. These worksheets and lessons will show students how to do this from scratch and explain how to interpret these values.
Aligned Standard: Grade 6 Statistics - 6.SP.A.3
- 7 Pieces of Data Step-by-step Lesson- From just 7 simple pieces of data we find a how bunch of answers to questions.
- Guided Lesson - Launching web sites, shopping for LCDs, and bananas for everybody. How fun!
- Guided Lesson Explanation - You should find these pretty easy to follow and understand.
- Practice Worksheet - This one is a whole lot of data to sift through and make sense of.
- Matching Worksheet - Great for a quick wrap up or "remember me" worksheet.
- Answer Keys - These are for all the unlocked materials above.
Time to get critical about the data that we see here.
- Homework 1 - Jerry sold burgers. He sold the following number of burgers over the last 7 days: 21, 33, 50, 42, 52, 20, 30.
- Homework 2 - In the past five days, John recorded the number of daily visitors to his website: 45, 46, 63, 112, and 95.
- Homework 3 - Mrs. Smith has an ice cream shop. She sold this many ice creams over the last 9 days. 20, 32, 35, 40, 25, 45, 50, 55, 60. What is range of the data set?
These get progressively easier. I didn't intend for that to happen; it just did.
- Practice 1 - Some children compared how many chocolates were in their pockets.
- Practice 2 - Find the mean of the data set.
- Practice 3 - Jolly compared how many sweets she purchased over the last 5 weeks.
Math Skill Quizzes
There is a visual problem section with these problems.
- Quiz 1 - What was the median amount of juice available?
- Quiz 2 - The owner of a super market recorded the number of customers who came into his store each day.
- Quiz 3 - The owner of a store recorded the number of TVs sold over 6 days.
How to Measure the Center of Data Sets
At some point in your life, you will come across a huge stream of data that you will need to make sense of, whether it be a sports statistic, medical test, or science problem. When analyzing data sets, one of the most important quantities that you must calculate is the center of data sets. The center of the data is a way to describe a location in the data set and give an audience an understanding of what normal or common is for this stream of data. There are two generally used measures of centers of data sets, including mean and median.
Mean is also widely referred to as the average value of the data. Kids can refer to average as the arithmetic mean. Both of these terms represent the same value. To measure the mean, you must add all the values in the data set and divide the sum of these values by the total number of values.
Mean = (Sum of all values) / (Total number of values)
Median is the second center that we can measure in a data set. As compared to mean, the median is a better measure of center and is used all as the data set center all around the world. The calculating median is simple; you find out the term number and locate the median. You can use this value to better understand how many outliers (abnormal measures) you are looking at. It can also be used in a pinch to get a generally understanding if you are working with valid data. This gauge is not exact, but it can give you feeling of where you are headed.
Median = (Total number of terms) / 2
The overall goal with both of these measures is to help the audience, which may even be yourself, gauge what is regular and what is special. For example, if it is your first day living in a much warmer climate than you were used to. You really would not have an understanding if the weather that day were warm or cold for that relative location. If you took your time and evaluated the temperature of the last 30 days, you would have a good idea.