Download CCSS Domain: Probability and Statistics (Grades 6-8)

CCSS Domain: Probability and Statistics (Grades 6‐8) Concepts to Emphasize Grade 6  Statistical investigations begin with a question in which data is collected that varies to answer the question. 
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Data about the questions can be plotted as dot plots, box‐n‐whiskers plots, and histograms to examine and identify clusters, peaks, gaps, and common shapes. Data distributions can be characterized by measures of center (mean and median) and measures of spread (variability, range, mean absolute deviation (MAD)) Grade 7  Understand that the proportion of “success” in a chance process is the probability of the event occurring. This is learned through repeated observations of random outcomes (coin toss, dice, cards, spinners, etc.)  Relative frequency and probability are connected. Known structures (cube, coin, etc) can have predicted or anticipated outcome and lead to probability. Unknown structures use relative frequencies and lead to statistics. .  Probability models such as organized lists, tables, or tree diagrams should be used to determine all possible outcomes. Explanation of Concept 
Instructional Examples/Ideas A statistical question is one that produces various answers – at this grade numerical answers. 
Identify statistical questions versus non statistical questions 
How many text messages does a middle school student send on average each day?
Graph given or collected data as well as look at graphs of data to describe the clusters, peaks, gaps, and/or shape. Use data collected to calculate the various data points Be able to determine which data point is needed to answer specific questions about the data 
Vocab: Skewed data, outlier, minimum, maximum, normal distribution 
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Mean = average Median = data that is in the middle (50% above, 50% below) Range = max value – min value MAD = average of the absolute value of the difference between the mean and the each data point. 
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Probability is a value between 0 and 1 that describes the “success” of an event occurring. EX: The probability of it raining tomorrow is 0.50. Relatively frequencies are used to make predictions of evens 
Calculate probabilities for various events 
Create tables to record relative frequencies of events occurring to determine the changes of the event Show all the possible outcomes using a list or a table. HH, HT, TH, TT are the possible outcomes when flipping two coins 
Have students create the tables and also collect data from experiments to find outcomes. CCSS Domain: Probability and Statistics (Grades 6‐8) 
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Understand the process of using a random sample and the purpose and value of using a random sample. Understand that the statistics collected from a random sample can be used to estimate or generalize the same characteristic to the population. Draw inferences to compare populations by using statistics about a sample population 
Understand what makes a sample random versus bias. 
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Use several samples from the same population to example the variability of data points. 
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Compare and contrast similar data from two populations. Make inferences from graphs of data samples 
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Grade 8  Plot bivariate data on a plane to create a scatterplot, describe patterns of clusters, gaps, unusual data points, and trends (positive association, negative association, no association). 
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For data that has associations, identify if it is linear as well as find the line of best fit by connecting the rate of change (slope) to the context of the problem. 
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Use associations to make inferences about data 
Identify if a sample is being representative of the population Discuss or identify ways to obtain a random sample of a population Design a method for gathering a random sample of the 7th grade to determine __________. Ask a sample of 10 people from the population a question. Ask another sample of 10 people to compare measures of center. Measure the boys and the girls and calculate measures of center and measures of variability. Make inferences Students should graph related data of two variables on a coordinate graph. Students should describe the data in terms of clustering outliers and association (positive, negative, or no) Students will need to have exposure to relationships that are linear and nonlinear. For linear relationships, draw and identify the line of best bit. Students are expected to associate the rate of change for linear associations to the meaning of the problem. 
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Compare test scores to hours of playing videos for the week. Compare girls versus boys 
Use technology to plot points and use real data. 
If the height of a tree is plotted to the number of years old it is, the rate of change or slope is its growth rate. CCSS Domain: Probability and Statistics (Grades 6‐8) Statistical Calculations: How many pets do you have in your family? Descriptive Definition Statistics Mean This is the average and is computed by adding all the numbers in the set and dividing the sum by the number of elements added. Outliers can really change the value of the mean. Median This is the value in the middle when data is ordered. Half of the value lie at or above the median and half below. The median is not effected by outliers. Mode The value that occurs most frequently in the data set.The mode is least useful as a descriptor of the whole set Range The range shows the spread of the data. You find it by subtracting the minimum value from the maximum value. Mean The deviation is how far each data value is from the mean. The Absolute mean absolute deviate is calculated by finding the average or mean Deviation of the absolute value of the difference of each data point from the mean Data Set: 1, 1, 3, 4, 5, 5, 7, 9, 9, 10 1 + 1 + 3 + 4 + 5 + 5 + 7 + 9 + 9 + 10 = 54 and 54/10 since there are 10 values = 5.4 The mean is 5.4 The data is in order already and the middle value is 5. Median = 5 The data set has three modes: 1, 5, and 9 10 – 1 = 9. This set of data has a range of 9 The data really varies. 10 – 5.4 = 4.6
9 – 5.4 = 3.6 9 – 5.4 = 3.6 7 – 5.4 = 1.6 5 – 5.4 = ‐0.4 5 – 5.4 = ‐0.4 4 – 5.4 = ‐1.4 3 – 5.4 = ‐2.4 1 – 5.4 = ‐3.4 1 – 5.4 = ‐3.4 Absolute Value = 4.6
Absolute Value =3.6 Absolute Value =3.6 Absolute Value =1.6 Absolute Value =0.4 Absolute Value =0.4 Absolute Value =1.4 Absolute Value =2.4 Absolute Value =3.4 Absolute Value =3.4 Sum of these = 24.8 Average = 24.8/10 = 2.48 Which measure of center would you use? Why? 
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Size of a shoe sold in a shoe store Salaries in a large company Salaries in a small company Cost of houses in your local area Test scores for a student 
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Size of cereal boxes in a grocery store Cost of hotel rooms at a particular hotel Number of text messages sent by a teenager CCSS Domain: Probability and Statistics (Grades 6‐8) Graphical Representations: Would one of these representations tell a different story? Stem and Leaf It is a combination of a table and a graph. It is a form of a bar graph in which numerical data are plotted by using the actual numerals in the data to form the graph. The stem is typically the high place value of the set of data and the leaf is the remaining digits. Line Plots Used with data that is along a numerical scale and shows the count. Every piece of data is represented on the line plot. This is an easy plot for students to create. Categorical Data Data that is represented by categories (types of ice cream flavors) is usually illustrated by bar graphs and picture graphs since there isn’t any numerical ordering. Histogram This is a form of a bar graph in which categories are consecutive equal interval along a numeric scale. The height of each bar is determined by the number of data elements falling into that particular interval. CCSS Domain: Probability and Statistics (Grades 6‐8) Line Graph The line graph is used where there is a numerical value associated with equally spaced points along a continuous number scale. Box‐N‐Whiskers This displays not only the median of the data set but the range and distribution of data. The box contains in the interquartile or middle 50% of the data. The lower whisker represents the values in the lowest quartile while the upper whisker represents the upper 25% of the data. Watch Prices for Store X Scatterplots Circle A circle graph is used data has been partitioned parts and interest in in ratios of each part to the when into the whole. A scatterplot shows a relationships of two variables on a coordinate grid. The point on the grid represents the value for two variables such as a boy’s weight and a boy’s height. Lines of best fit can be determined to predict data that hasn’t been gathered. CCSS Domain: Probability and Statistics (Grades 6‐8) Good Statistical Questions What is the age of the students in my school?” is a statistical question because one anticipates variability in students’ ages. 1. Your math teacher, Michael Phelps, has just graded your end‐of‐year exams. Michael Phelps says that he is not ready to post individual scores, but he will answer statistical questions. (a) Which of the following are statistical questions that you could ask? i. What was the highest score? ii. How did my class compare to the other classes? iii. How many students earned an A? iv. How were the scores on the multiple choice? v. How many students showed their work? Identify each of the following questions as statistical or non‐statistical. (a) How many pets are owned by each student in my grade? (b) How tall are professional basketball players? (c) How many books did Lebron James read this year? (d) How many cupcakes of each type were made in the bakery last week? (e) How many letters are in my name? (f) How old is Lil Wayne? (g) How many letters are in the names of each person in my class? (h) How many pets does Flo Rida own? (i) How much time does Miley Cyrus spend on homework? (j) How many cupcakes of each type are made in the bakery each week? (k) How much time do students at my school spend on homework? (l) How tall is Adrian Peterson? (m) How old are the students in my school? (n) How many chairs are in this classroom? (o) How many books did the students at your school read this summer? CCSS Domain: Probability and Statistics (Grades 6‐8) What makes a sample population random? Breaking News: The school newspaper surveyed 25 people and used the results to predict that Alexis would win the SGA Presidential Election by a landslide. The survey results are displayed in the table below. Is this a valid prediction? Candidate Number of Votes Alexis 20 Dan 5  Scenario 1: 25 student ID numbers were selected randomly from the entire student body.  Scenario 2: A 6th grade science class containing 25 students were selected to vote.  Scenario 3: 25 members of the school staff were surveyed during a faculty meeting.  Scenario 4: Students were invited to participate in an online survey. The first 25 students that responded.  A radio station wishes to examine the proportion of its listeners who voted in the last presidential election. They conduct a poll by asking listeners to call the station. Would this sample be representative of the population? Why or why not?  A television station will conduct a survey to determine the most popular television show in its viewing area. They survey 50 randomly selected people who enter the television station. Would this sample be representative of the population? Why or why not?  Inés wants to conduct a survey to determine how many customers see the advertisement for her store. She will survey customers who live near her store. Would this sample be representative of the population? Why or why not?  Inés wants to conduct a survey to determine how many customers see the advertisement for her store. She will survey customers who shop at her store on weekends. Would this sample be representative of the population? Why or why not?