Common Core Math I Unit 2 Day 16 One-Variable Statistics

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

Definitions Data: A collection of information in context. Population: A set of individuals that we wish to describe and/or make predictions about. Sample: A subset of the population that data is collected from. Individual: Member of a population. Variable: Characteristic recorded about each individual in a data set.

Types of Variables Categorical Variable: A variable that records qualities or characteristics of an individual, such as gender or eye color. Quantitative Variable: A variable that measures a characteristic of an individual, such as height, weight, or age. In this unit, we will 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?”

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

Categorical or Quantitative Data? Birth month Number of siblings Height in inches Average amount of time (in minutes) of your ride to school. Number of pets Year & model of the car you drive Age of your youngest parent Predicted letter grade of your first Math 1 test.

1. Brand of vehicle purchased by a customer 2. Price of a CD 3 1. Brand of vehicle purchased by a customer 2. Price of a CD 3. Number of students in a class of 30 who prefer peanut M&Ms over plain M&Ms 4. Phone number of all the students enrolled in school. 5. The height of a 1 year old child. 6. Number of students in a class of 35 who turn in a term paper before the due date. 7. Gender of the next baby born at a particular hospital. 8. Amount of fluid (oz) dispensed by a machine used to fill bottles with soda. 9. Thickness of the gelatin coating of a Vitamin C capsule 10. Brand of computer purchased by a customer 11. State of birth for someone born in the United States. 12. Price of a textbook 13. The phone numbers of everyone in this class. 14. Actual weight of coffee in a one pound can. 15. The length of a rattlesnake.

Describing Data Two ways to describe data: Graphically Numerically

Describing Data Graphically Dotplot Histogram Boxplot

Describing Data Numerically Measures of Center – mean, median Measures of Spread – range, interquartile range, standard deviation

What is the typical value? Measures of Center What is the typical value? Note: Students do NOT need to copy down these definitions at this point – more with these will come later in the unit.

Measures of Spread How much do values typically vary from the center? Range Interquartile Range (IQR) Standard Deviation

Common Core Math I Unit 2 Days 17 and 18 Frequency Tables and Histograms

Link Up Frequency Distribution Table Histogram (by hand) How many links can you put together in one minute? One student will time another student for 60 seconds. The student being timed will link together as many paper clips as he or she can in 60 seconds, and record this number on his or her paper. The students should then switch roles so the other student can link paper clips. Collect data and have students record on the board in a frequency distribution table. You may want to ask for the minimum and maximum values so that you can determine intervals. Show how to make a histogram from this by hand. Make sure that you are not just making a bar graph. The bars should be touching (like the next slide) to show the continuity of the data. Usually the lower value for each interval is marked on the x-axis on the left side of the corresponding “bar”, although you can also use the midpoint of the interval as well. Discuss with students – what is the difference between a bar graph and a histogram? (bars touching; bar graphs used with categorical data & histograms used with quantitative data divided into intervals)

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.

Shape Mound shaped & symmetrical Skewed left (extreme low values) Skewed right (extreme high values) Uniform Go over 4 types of shapes. What shape does our links distribution have?

Center When describing a distribution at first, the center can be “eyeballed.” 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?

Spread BE SURE TO STATE EVERYTHING IN CONTEXT!! Range 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? 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! For example: The distribution of the number of links a student can put together in one minute is skewed to the right. Students can typically hook up about 35 links in one minute, with a few really dexterous students able to link together 60 or more. The number of links put together varied from 16 to 68.

NFL Rushing Statistics Group activity: Make a frequency distribution table for your assigned column of data. Draw the corresponding histogram on graph paper. Write a paragraph about your data that addresses shape, center, spread, and outliers. Guided practice: Divide students into groups and assign each group a column from the 2011 NFL Rushing Statistics for Top 50 Rushers: Rushing Attempts, Total Yards for the Season, Average Yards per Attempt, Average Yards per Game, Number of Rushing Touchdowns, Longest Run of the Season (if you have more than 6 groups, have 2 groups use the same category). Have each group present their graph and description to the class. If time is limited, ask students to work on the same column of data.