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Common Core Learning Standards for MathematicsHigh School Algebra 1Descriptive Statistics

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Summarize, represent, and interpret data on a single count or measurement variable.In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.

Representing Data

S.ID.1Organize data using a chart or a listPlot points of data on a number lineRepresent single variable data as a box-and-whisker plotRepresent single variable data as a histogram

DataNumber lineDot plotHistogramBox plotMinimumMaximum Quartiles

S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S.ID.2Compare the mean and median (measures of center) of two or more data setsDetermine the standard deviation of a given set of dataDetermine the shape, center and spread of a set of dataCompare mean and standard deviation of one data set to the mean and standard deviate of a second data satCompare the median and IQR of one data set to the median and IQR of the second data set

MedianMeanShapeCenterSpreadInterquartile rangeStandard deviation

S.ID.3Identify outliers in a set of dataDetermine the shape, center and spread of a set of data, accounting for outliers

Outlier

SAMPLE TASKSCopyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

SAMPLE TASKS continued:I. A teacher asked his class of 20 students, “What is your age?” Their responses are shown on the line plot below.

Find the mean, median, and mode of the data.

II. Alex earned scores of 60, 74, 82, 87, 87, and 94 on his first six algebra tests. What is the relationship between the measures of central tendency of these scores?

1) median < mode < mean

2) mean < mode < median

3) mode < median < mean

4) mean < median < mode

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

III. The values of 11 houses on Washington St. are shown in the table below.

Find the mean value of these houses in dollars. Find the median value of these houses in dollars. State which measure of central tendency, the mean or the median, best represents the values of these 11 houses. Justify your answer.


IV. This frequency table shows some data from accident reports at a traffic police station.

Find the median of the skid mark lengths.

Use that number for d in the formulas=√15d in order to find the corresponding car speed to the nearest meter per second.


V. In the time trials for the 400-meter run at the state sectionals, the 15 runners recorded the times shown in the table below.

a Using the data from the frequency column, draw a frequency histogram on the grid provided below.

b What percent of runners completed the time trial between 52.0 and 53.9 seconds?


VI. The test scores from Mrs. Gray’s math class are shown below.

72, 73, 66, 71, 82 ,85 ,95 ,85 ,86 ,89 ,91 ,92 Construct a box-and-whisker plot to display these data.

State the minimum, maximum, 1st quartile, median, 3rd quartile and interquartile range.

VII. The box-and-whisker plot below represents the math test scores of 20 students.

What percentage of the test scores are less than 72?


http://www.google.com/imgres?q=blank+number+line&um=1&hl=en&safe=active&sa=N&biw=1366&bih=587&tbm=isch&tbnid=7ZRWs1KkPnDW8M:&imgrefurl=http://exchange.smarttech.com/details.html?id=37365990-f74d-4533-b8e8-92754258e7ed&docid=ZfSBBFXH4C1QGM&imgurl=http://exchangedownloads.smarttech.com/public/content/37/37365990-f74d-4533-b8e8-92754258e7ed/previews/medium/0001.png&w=420&h=39&ei=a37CTsTDAqrr0gG2qfX7Dg&zoom=1

VIII. The heights of the players on a basketball team are 74 inches, 79 inches, 71.5 inches, 81 inches, 73 inches, 76 inches, 78 inches, 71 inches, 72 inches, and 73.5 inches. a. Create a box-and-whisker plot to display the above data.

b. What percentage of players are less than or equal to 73.5 inches tall.

c. If the 76 inch player is replaced with a 72 inch player, how does this affect the percentile rank of the 73.5 inch tall player?


IX. A movie theater recorded the number of tickets sold daily for a popular movie during the month of June. The box-and-whisker plot shown below represents the data for the number of tickets sold, in hundreds.

Which conclusion can be made using this plot?1) The second quartile is 600.

2) The mean of the attendance is 400.

3) The range of the attendance is 300 to 600.

4) Twenty-five percent of the attendance is between 300 and 400.


X. Below are histograms showing data collected from a city in Tennessee and a city in New York.

Compare the center and the spread of the distributions of the snowfall in each city.


XI. An automobile brake and muffler shop reported the repair bills for their customers last week (in dollars). 88, 283, 312, 290, 172, 154, 400, 381, 346, 181, 203, 118, 143, 252, 227, 56, 192, 292, 213, 422

Find the mean and standard deviation of the repair costs. Is it appropriate to use the mean and standard deviation to summarize these data? Explain.

XII. Use the box plots of test scores below to compare Mrs. Rothwell’s two classes. Compare the range, median, interquartile range of the two classes.

TEST SCORES

a. Compare the range, median, interquartile range of the two classes.

b. Which class do you feel performed better? Why?


Mrs. Rothwell’s 1st Period Class

Mrs. Rothwell’s 8th Period Class

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Summarize, represent, and interpret data on two categorical and quantitative variables.Students take a more sophisticated look at using a linear function to model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals.S.ID.6b should be focused on linear models, but may be used to preview quadratic functions in Unit 5 of this course.

Categorical and

Quantitative Data

S.ID.5Construct a two-way frequency tableDraw conclusions about the data represented in a two-way frequency tableRecognize possible associations in the dataRecognize trends in the data

Two-way frequency tableRelative frequencyMarginal frequencyConditional frequencyAssociationTrend

S.ID.6aCreate a scatter plot, using multi-variable plotCompute a linear regression from a set of multi-variable dataCreate a linear regression modelDetermine a linear or exponential model for a given data setUse linear regression equation to solve problems in the context of the data

Explanatory variableResponse variableRegressionLinear modelExponential model

S.ID.6bInvestigate the residual of the data to assess the fit of the function

ResidualResidual plot

S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.a) Fit a function to the data; use functions fitted

to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and

S.ID.6cCreate a linear regression model


exponential models.b) Informally assess the fit of a function by

plotting and analyzing residuals.c) Fit a linear function for a scatter plot that

suggests a linear association.

SAMPLE TASKSI. For her survey, Jenna recorded the gender of each student. The results are shown in the two-way frequency table below. Each entry is the

frequency of students who prefer a certain pet and are a certain gender. For instance 8 girls prefer dogs as pets.

Dog Cat Other TotalGirl 8 7 1

Boy 10 5 9Total

a. Complete the table.b. If you know that a student prefers cats as pets, what prediction can you make about the student’s gender given the conditional relative

frequencies given the above table?c. If you know that a student is a boy, what prediction can you make about the student’s preferred pet?

II. Below is a two-way relative frequency table representing favorite ice cream flavors by gender.


Preferred Pet

Gender

If there are 200 people surveyed, how many boys preferred vanilla ice cream?

III. The table below shows the number of calories and the number of grams of carbohydrates in a half-cup serving of ten different canned or Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

Ice Cream Flavor

Gender

Vanilla Chocolate Other TotalBoy 0.05 0.3 0.2 0.55Girl 0.15 0.2 0.1 0.45Total 0.2 0.5 0.3 1.0

frozen vegetablesCarbohydrates 9 23 4 5 19 8 12 7 13 17

Calories 45 100 20 25 110 35 50 30 70 80

a) Draw a scatter plot on graph paper. Let the horizontal axis represent grams of carbohydrates and the vertical axis represent the number of calories

b) Find the mean number of grams of carbohydrates in a serving of vegetables and the mean number of calories in a serving of vegetables

c) Determine the line of best fit and sketch the line on the graph. Round to the nearest hundredth.

d) Use your linear regression equation to find the expected number of calories in a serving of vegetables with 20 grams of carbohydrates.

IV. The graphs below represent two data sets that have the same equation for line of best fit


Compare the fit of the function on each graph. Discuss how the points are related to the linear model.

V. Below are three residual plots. Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

How does each of these three residual data plots assess the fit of the function?

VI. The mid-September statewide average gas prices, in dollars per gallon, (y), for the years since 2000, (x), are given in the table below.Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics— Permission to use (not alter) and reproduce for educational purposes only.

Write a linear regression equation for this set of data. Using this equation, determine how much more the actual 2005 gas price was than the predicted gas price if the actual mid-September gas price for the year 2005 was $2.956. Round to the nearest thousandth.


Common Core Learning Standards Concepts Embedded Skills VocabularyInterpret linear models.Build on students’ work with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. The important distinction between a statistical relationship and a cause-and-effect relationship arises in S.ID.9.

Interpreting Linear Models

S.ID.7Interpret the slope of a linear model in the context of the dataInterpret the intercept of a linear model in the context of the data

SlopeIntercept

S.ID.8Define correlation coefficientFind the correlation coefficient of a linear model using technologyInterpret the correlation coefficient

Correlation coefficient

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.S.ID.9 Distinguish between correlation and causation.

S.ID.9Distinguish between correlation and causationDetermine the different types of statistical relationships, specifically cause-and-effect relationships

CorrelationCausation

SAMPLE TASKSI. The relationship of a woman’s shoe size and length of a woman’s foot, in inches, is given in the accompanying table.

a) What is the linear correlation coefficient for this relationship?

b) What does the correlation coefficient say about the relationship of the data?


II. The availability of leaded gasoline in New York State is decreasing, as shown in the accompanying table.

Determine a linear relationship for x (years) versus y (gallons available), based on the data given. The data should be entered using the year and gallons available (in thousands), such as (1984, 150).

a. Interpret the slope.

b. If this relationship continues, determine the number of gallons of leaded gasoline available in New York State in the year 2005. If this relationship continues, during what year will leaded gasoline first become unavailable in New York State?


III. For the following question, use the graph below.

a. Determine an equation that represents the line of best fit of the data above. Sketch the linear model on the graph.

b. Determine the correlation coefficient of the linear model created.

c. Interpret the slope.

d. Interpret the y-intercept.


IV. The chart below shows the prices of gasoline and milk at a local convenience store, over a 3-week period.

What type of association, if any, during this three week period existed between the price of gasoline and the price of milk? Could either of these events cause the other? Explain your answer.

V. The chart below shows the height a child along with the month they were measured.

Age (months) 2 4 6 8 10 12Height (cm) 55 63 68 70 75 79

a. Create a linear model.

b. Interpret the y-intercept.


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