Mean and Standard Deviation Distributions
What Are Mean and Standard Deviation Distributions? Understanding the concepts of statistics is crucial in mathematics as the applications of these extend even in everyday life. The concepts of mean, median, mode, standard deviation, and variance help companies record data and provide invaluable insight into it. Mean is the basic concept which we usually refer to as the average. Mean is the average value of the entire data. To calculate the mean, we have to divide the sum of all values with the total number of values in the data. Mean = x = (Σx)/n However, to know how spread out the data is, we use the standard deviation. It is the measure of how tightly packed or widely spread the data is and is denoted by sigma. To calculate the standard deviation, we need to calculate variance. Standard deviation is the square root of variance. Variance is the squared difference from the mean. The first step is to calculate the mean. Once you have calculated the mean, you subtract each data from the mean and square the result. After you have found all the squared differences, you then find out the average of the squared differences. Find the square root of the result, and you get the standard deviation. Students can use these worksheets and lessons to learn how to calculate the common forms of deviation found within data sets.
Aligned Standard: HSS-ID.A.4
- Three Data Sets Step-by-step Lesson- This is a great overall activity it lends it self to comparing groups.
- Guided Lesson - I like to use frequency tables to help this make more sense.
- Guided Lesson Explanation - It is neat how you can calculate levels of deviation between groups of data.
- Practice Worksheet - I really like this one, it feels like an obstacle course focused on this skill.
- Matching Worksheet - Somewhat of a weird sheet. I don't even remember putting this one together.
- Central Tendency and Dispersion Five Pack - This is basically what you would have to do to begin to make a box and whisker plot.
- Answer Keys - These are for all the unlocked materials above.
We give you a lot of data to manage.
- Homework 1 - Calculate the mean of each data set.
- Homework 2 - Calculate the standard deviation of each data set.
- Homework 3 - Determine and compare both forms of deviation.
We start to circle back towards more word problems here.
- Practice 1 - The frequency table is shown below display the number of students in classes.
- Practice 2 - Each floor of the office building commutes into work together. Tom was monitoring how many cars it took for the people to travel.
- Practice 3 - The police chief was tracking the number of phones. 5 groups of suspects were caught with phones.
Math Skill Quizzes
This is a mix of data sets and word problems.
- Quiz 1 - 5 groups of people go to the town pool. The chart shows the number of people in the group that go swimming.
- Quiz 2 - The frequency table shows the number of girls that wear dresses regularly.
- Quiz 3 - The frequency table shows the number of chocolates won by children at a carnival.
What Do These Measures Tell Us About a Data Set?
In many different situations you will perform experiments or observations to better understand a system or environment. To make sense of all the data that you collect it often helpful to understand the mean or average of the data. This provides us with a sense of the center. We then want to understand how far from the center did other observations fare. This helps us understand if the average is a good representative of observations. For example, if you had three quarterbacks on your football team that average 125 passing yards a game, that would not get you so thrilled. If you knew that average was based on averaging a quarterback that throws for 250+ yards and another who throws for less than 20 yards a game, you can quickly understand that your average is not representative of the individual data points. What the standard deviation does for you when applied to any data set is tell you how well the average reflects the overall data set. A good sports analogy would be you may have a good team with few huge standout players. You can also have a bad team with many great standouts. The standard deviation helps you make assessment of the players on team in respect to the average.