Unit 6 Statistics

Warm Up Mom has just baked a batch of cookies. The kids run into the kitchen to get them while they are hot. Jill, the oldest, grabs 12 cookies, Amanda gets 8, Rod gets 4, and Alex, the baby doesn’t get any. So of course Alex starts crying. Mom has to fix it. What should she do? Draw a picture to represent what each child should get if everyone gets their fair share of cookies.

KEY STANDARDS   MCC6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. MCC6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Essential Questions: How can I describe the center of a set of data? How can I describe the spread of a set of data? How can I use data to compare different groups? What conclusions can be drawn from data?

The mean and the median are both ways to measure the ____________ for a set of data. Measures of Center

The “average” or “fair share” value for the data The “average” or “fair share” value for the data. It is also the balance point of the corresponding data distribution. Mean

The range and the mean absolute deviation are both common ways to measure the ___________ for a set of data. Measures of Spread

Mean Absolute Deviation the average distance of each data value from the MEAN; how different the data values are from the mean value Mean Absolute Deviation

A plot where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits). Stem & Leaf Plot

the number of times an item, number, or event occurs in a set of data Frequency

How many people are in your Family? Use the interlocking cubes to “build” your family. Also, write the number of family members on the sticky note. 7

How many people are in your Family? X = 1 family 2 3 4 5 6 7 8 9 10 11 Number of people in my family

How many people are in your Family? Working in groups of 2 or 3, come up with a distribution on your number line that would yield a mean family size of 5. Be creative with your answer and check your answer for accuracy.

How many people are in your Family? What does each “X” represent in this line plot? Is there much variation in the data?

How many people are in your Family? What method did you use to come up with 9 numbers that averaged to 5? Explain in detail.

How many people are in your Family? Display all of the distributions on the board. Look at the different distributions displayed. Discuss the limitations of only knowing the mean family size, instead of the actual data pieces. Only knowing the mean of a data set limits our knowledge on each individual piece of data in the set. Look at the data sets displayed. The mean of ALL of the data sets is 5.

How many people are in your Family? Looking at the data sets, which one seems to differ the least from the mean? Explain why you chose this data set.

How many people are in your Family? Which seems to differ the most from the mean? Explain why you chose this data set.

How many people are in your Family? With your group, put all of the data sets in order from “Differs Least” from the mean to “Differs Most” from the mean. How did you come up with this list?

How many people are in your Family? As a class, decide on the “best” order for all of the data sets varying least from the mean to greatest from the mean.

How many people are in your Family? One way to describe how far a value is from the mean is called the “deviation” from the mean. Deviation= Value - Mean Below is a display of the deviations for a distribution:

How many people are in your Family? Since the sum of all deviations from the mean equals zero, let’s look at the distance each value is away from zero (the absolute value of each individual data piece). Let’s look at the Distribution. Determine each value’s distance away from zero

How many people are in your Family? If I were to ask you “on average” how different the data values are away from the mean, you can use the Mean Absolute Deviation to find this. Total up the distances away from the mean, and then find the “average” of these by dividing by the total number of values in the distribution.

How many people are in your Family? A large MAD means that the values vary greatly from the mean.

How many people are in your Family? A small MAD means that the values do not vary much from the mean. Find the MAD of the Distribution. First find the distances each value is from the mean. Total the distances, then divide by 9 (the number of values).

How many people are in your Family? A small MAD means that the values do not vary much from the mean. Find the MAD of the Distribution. First find the distances each value is from the mean. Total the distances, then divide by 9 (the number of values).

How many people are in your Family? 3 + 3 + 3 + 2 + 1 + 1 + 3 + 4 + 6 9 = 2.89

How many people are in your Family? 3 + 3 + 3 + 2 + 1 + 1 + 3 + 4 + 6 9 Do the values vary much from the mean? What does this tell you about the data? = 2.89

Work Session: Find the MAD for each data distribution

Closing Steps for finding MAD: 1. Find the ________. 2. Find the ____________ between each data value and the mean (absolute value). 3. Find the average of those __________. Word Bank: differences, mean, distance