1. Common Core Math I Unit 6 One-Variable Statistics Introduction

2. Two Main Uses of Statistics
TO DESCRIBE (Data Analysis) TO PREDICT (Statistical Inference)

3. Data Population Sample Element
What do they mean?
You want to study the GPA for NC State graduates.
Match the appropriate vocabulary words to the below descriptions, then write your own definition.
Data Population Sample Element
The GPA of all NC State graduates.
A collection of the GPA’s of NC State graduates.
The GPA of your brother who graduated from NC State.
The GPA for fifty NC State graduates.
You can have the students do this individually, then Think-Pair-Share with a group/partner. You can also have them collaborate with a team. Once they have their definitions, you can call on specific groups to share their definition, then have the class compare and contrast their definition to the actual definition.

4. Data Population Sample Element
What do they mean?
Data Population Sample Element
The GPA of all NC State graduates.

5. Data Population Sample Element
What do they mean?
Data Population Sample Element
The GPA of all NC State graduates.
Population: A set of all elements that we wish to describe and/or make predictions about.

6. Data Population Sample Element
What do they mean?
Data Population Sample Element
2. A collection of the GPA’s of NC State graduates.

7. Data Population Sample Element
What do they mean?
Data Population Sample Element
2. A collection of the GPA’s of NC State graduates.
Data: A collection of information in context.

8. Data Population Sample Element
What do they mean?
Data Population Sample Element
3. The GPA of your brother who graduated from NC State.

9. Data Population Sample Element
What do they mean?
Data Population Sample Element
3. The GPA of your brother who graduated from NC State.
Element: One specific item from the data.

10. Data Population Sample Element
What do they mean?
Data Population Sample Element
4. The GPA for fifty NC State graduates.

11. Data Population Sample Element
What do they mean?
Data Population Sample Element
4. The GPA for fifty NC State graduates.
Sample: A subset of the population that data is collected from.

12. In this unit, we will mainly focus on
Types of Data
Categorical Data: data that records or names qualities/characteristics about an object; such as gender or eye color.
Quantitative Data: data that measures a numerical value/characteristics about an object; such as height, weight, or age.
In this unit, we will mainly focus on
quantitative data.
When describing categorical vs. quantitative, explain that sometimes numerical data is categorical. Think of quantitative data as “How many?” For example, when classifying a zip code as categorical or quantitative, you would ask, “What is your zip code?” not, “How many….zip code?”

13. What type of data is it? Categorical Quantitative
Go over the Collect student data worksheet and discuss which type of data each one is.

14. Categorical or Quantitative Data?
Birth month
Categorical
Length of hair in inches
Quantitative
Amount of time (in minutes) of your ride to school
Year & model of the car you drive
Predicted letter grade of your first Math 1 test

15. Describing Data Graphically
Graphically illustrates distribution of data
Histogram
Displays data and the data’s frequency
Bars touch to show intervals
Boxplot
Breaks data into
quartiles

16. Describing Data Numerically
Measures of Center
mean
median
Measures of Spread
range
interquartile range
standard deviation

17. What is the typical value?
Measures of Center
What is the typical value?
Note: Images came from

18. How do outliers affect these? We’ll find out!
Measures of Spread
How much do values typically vary from the center?
Range
Interquartile Range (IQR)
Standard Deviation
How do outliers affect these? We’ll find out!

19. Describing Distributions
Shape
Center
Spread
Outliers
In order to describe a distribution, we address the following things: the shape of the distribution, the center or most typical value, how spread out the data is, and if there are outliers, we note them.

20. Shape Mound shaped & symmetrical Skewed left (extreme low values)
Skewed right (extreme high values)
Uniform
Go over 4 types of shapes.

21. Center
If you don’t know the exact data shown in the distribution, the center can be “eyeballed” However, if you DO know the exact data, the center should be “calculated” Remember, you are trying to answer the question: “What is the most typical value?”
When first discussing how to interpret graphs, have students give an eyeball estimate of the center of the distribution. Then formalize with the numerical calculations later on in the unit.
What is the approximate center, or typical value, for the number of links put together in one minute?

22. Spread BE SURE TO STATE EVERYTHING IN CONTEXT!!
Range is best to approximate when you don’t know the exact data.
Interquartile Range is best to use when data is present as boxplot
Standard Deviation is best to use when you know the exact data.
Remember, you are trying to answer the question:
“How much do values typically vary from the center?”
BE SURE TO STATE EVERYTHING IN CONTEXT!!
Again, when first describing distributions, we do not need to go into the numerical calculations of the interquartile range or the standard deviation – just focus on the max and min values and use the range to describe the distribution of the data.
What was our max number of links? Our min number? So what is the range?

23. Outliers Outliers a data value that does not fit the overall pattern.
There could be more than
one outlier!
At this point, we are identifying
potential outliers. We will learn
how to actually calculate outliers
later in the unit.
Remember, you are trying to answer the question:
“What value(s) fall outside the rest of the data?”
BE SURE TO STATE EVERYTHING IN CONTEXT!!
Do we have any apparent outliers? (What is an outlier? An informal definition is fine – a data value that does not fit the overall pattern.)
Have students write a one to two sentence summary describing the shape, center, spread, and outliers – in context!

24. Describing Distributions
Shape
Symmetrical
Center
Between a score
of 40-50
Spread
100 points (100-0)
Outliers
No potential outliers
Be sure students are stating this information in terms of the context of the data.

25. Describing Distributions
Shape
Skewed left
Center
Between a
score of 40-43
Spread
50 points
(50-0)
Outliers
Potential outliers between a score 0-15
Be sure students are stating this information in terms of the context of the data.