Lesson 2 Measures of Center Module 6 Statistics

determine the best measure of center for a set of data and calculate it correctly. I can… On your white board, identify the key vocabulary that you will need to know in order to be successful.

A set of data can be described by its overall shape, measure of center, and measure of variability (spread), Each tells us something important about a set of data. Data Overall Shape Measure of Center Measure of Variability (spread) In this lesson we will focus on overall shape and measures of center.

The overall shape of a graph can be described as normal or skewed. NormalSkewed On your white board describe in words how a normal shape is different from a skewed shape.

Normal Distribution: an arrangement of a data set in which most values are in the middle of the range and the rest taper off evenly toward either end creating a bell shape.

Skewed Distribution: an arrangement of a data set in which most values are gathered at one end of the range creating a tail on the other end.

Practice Complete the practice problems. Be ready to share out with the group. Add any notes that you wish to your study guide question, “What is the difference between a graph with a normal shape and a graph with a skewed shape?” Directions: 1.) Cut out each graph. 2.) Decide if it should go in the Normal or Skewed Column. Be ready to share why. 3.) Wait to paste while we go over the answers.

Summarize on your Study Guide Do you still need help? Form a plan! What is the difference between a graph with a normal shape and a graph with a skewed shape?

What type of distribution does our class graph have? Class Project Step 3: Summarize the data with graphs and numerical summaries.

A measure of center for a data set is one number that describes the middle or average. Helps us to answer our statistical question As you watch the video, write down the measures of center that you hear on your white board.

Mode: The number that appears most often; used with categorical data such as in a vote.

Watch Me:  Find the mode of the following set of data: 39, 42, 41, 38, 39, 39, 42

Help Me:  Find the mode of the following set of data: 83, 90, 98, 96, 88, 98, 95, 97, 96,100

You Try:  Find the mode of the following set of data: 112, 120, 114, 113, 118, 115, 113

Mean : The sum of the values in a data set divided by the number of values in the data set.

Watch Me:  Find the mean of the following set of data: 21, 42, 25, 45, 37, 34, 30

Help Me:  Find the mean of the following set of data: 20, 12, 18, 25, 20

You Try:  Find the mean of the following set of data: 83, 80, 88, 86, 88, 70

Median : The middle value in a data set ordered from least to greatest.

Watch Me:  Find the median of the following set of data: 21, 42, 25, 45, 37, 34, 30

Help Me:  Find the median of the following set of data: 20, 12, 18, 25, 20, 15

You Try:  Find the median of the following set of data: 83, 80, 88, 86, 88, 70

Practice and Pitfalls Measures of Center BINGO As you play the game, keep your study guide in the corner of your desk and add any pitfalls that you come across while working. Calculate the mean Calculate the median

Summarize on your Study Guide Do you still need help? Form a plan! How do I calculate the mean? How do I calculate the median?

John Smith Quiz #1Quiz #2Quiz #3 Quiz #4Quiz #5 Without doing any calculations, what grade do you think summarizes the work this student has done? A measure of center for a data set is one number that describes the middle or average of a data set. It is used to summarize the entire set of data Quiz #6Quiz #7Quiz #8Quiz #9 Quiz #10

Mean  Did you get 86.8?  Do you think this is a fair grade? Why or why not? Is this a fair representation of this students abilities? Why or why not? Now, calculate the mean. Is the mean the best measure of center to summarize this data? Why or why not?

Outlier : A value that is much greater than or much less than the other values in a data set. Based on these pictures, what is an outlier ?

Answer the following questions with your group.  What does the outlier do to the mean?  Is the mean a fair summary of the data when it is skewed? Why or why not?

Now, calculate the median. Median  Did you get 96.5?  Do you think this is a fair grade? Why or why not? Is this a fair representation of this students abilities? Why or why not?

How to answer a statistical question: Data Normal Distribution Mean (best measure of center) Skewed Distribution Median (best measure of center) The mean is the best for data with a normal distribution because the data is equally distributed with most in the center. The median is the best for data with a skewed distribution because the data has one outlier that is too far away from the middle and makes the mean either too high or too low.

What measure of center best summarizes our data? Why? Class Project Step 3: Summarize the data with graphs and numerical summaries.

Summarize on your Study Guide Do you still need help? Form a plan! Why does the shape of the data determine which measure of center to use?