Unit Abstract

Students will develop tools and strategies that will help them make sense of data and communicate their conclusions. The focus will be on displaying data (to observe shape, location, outliers, clusters, and gaps) and then computing and interpreting summary statistics, such as measures of center (mean, median, and mode) and measures of variability (range, interquartile range, and standard deviation).  

Common Core Essential State Standards

Conceptual Category: Statistics and Probability; Number and Quantity

Domain: 1) Interpreting Categorical & Quantitative Data (S-ID)

               2) Quantities (N-Q)

Clusters: 

1)     Summarize, represent, and interpret data on a single count or measurement    

variable.  (S-ID)

Summarize, represent, and interpret data on two categorical and quantitative

variables. (S-ID)

2)     Reason quantitatively and use units to solve problems. (N-Q)

Standards:

N-Q.1 USE units as a way to understand problems and to guide the solution of multi-step problems; CHOOSE and INTERPRET units consistently in formulas; CHOOSE and INTERPRET the scale and the origin in graphs and data displays.

N-Q.2 DEFINE appropriate quantities for the purpose of descriptive modeling.

N-Q.3 CHOOSE a level of accuracy appropriate to limitations on measurement when reporting quantities.

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   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.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.

Standards for Mathematical Practice

“Unpacked” Concepts

(students need to know)

“Unwrapped” Skills

(students need to be able to do)

COGNITION

DOK

Numbers can be interpreted as quantities with appropriate units, scales, and levels of accuracy to effectively model and make sense of real world problems.

N-Q.1

I can label units through multiple steps of a problem.

I can choose appropriate units for real world problems involving formulas.

I can use and interpret units when solving formulas.

I can choose an appropriate scale and origin for graphs and data displays.

I can interpret the scale and origin for graphs and data displays.

N-Q.2

I can identify the variables or quantities of significance from the data provided.

I can identify or choose the appropriate unit of measure for each variable or quantity.

N-Q.3

I can report measured quantities in a way that is reasonable for the tool used to make the measurement.

I can report calculated quantities using the same level of accuracy as used in the problem statement.

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Various graphical displays of data reveal important patterns that can be interpreted within the context of the data.

Relate the shape of a distribution to the location of its mean and median.

Compare data sets using measures of center, measures of variability, and data displays that group data.

Recognize the importance of having the same scales on graphs that are used to compare data distributions.

Understand how measures of center respond to changes in the number and magnitude of data values (including outliers).

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.1

I can choose the best representation (dot plot, histogram, box plot) for a set of data.

I can decide if a representation preserves all the data values or presents only the general characteristics of a data set.

Dot plot:

I can choose the appropriate scale to represent data on a number line.

I can construct a dot plot for a set of data.

Histogram:

I can construct a histogram for a set of data.

Box plot:

I can calculate the five-number summary for a set of data.

I can construct a box plot based on the five-number summary.

S-ID.2

I can describe the center of the data distribution (mean or median).

I can choose the histogram with the largest mean when shown several histograms.

I can describe the spread of the data distribution (interquartile range or standard deviation).

I can choose the histogram with the greatest standard deviation when shown several histograms.

I can choose the box-and-whisker plot with the greatest interquartile range when shown several box-and-whiskers plots.

I can compare the distributions of two or more data sets by examining their shapes, centers, and spreads when drawn on the same scale.

S-ID.3

I can interpret the differences in the shape, center, and spread of a data set in the context of a problem.

I can identify outliers for the data set.

I can predict the effect an outlier will have on the shape, center, and spread of a data set.

I can decide whether to include the outliers as part of the data set or to remove them.

S-ID.5

I can read and interpret the data displayed in a two-way frequency table.

I can write clear summaries of data displayed in a two-way frequency table.

I can calculate percentages using the ratios in a two-way frequency table to yield relative frequencies.

I can calculate join, marginal, and conditional relative frequencies.

I can interpret and explain the meaning of relative frequencies in the context of a problem.

I can make appropriate displays of joint, marginal, and conditional distributions.

I can describe patterns observed in the data.

I can recognize the association between two variables by comparing conditional and marginal percentages.

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Essential Questions

Corresponding Big Ideas

In what ways can the choice of units, quantities, and levels of accuracy impact a solution?

Interpret numbers as quantities with appropriate units, scales, and levels of accuracy to effectively model and make sense of real world problems.

What types of patterns do different graphical displays reveal about data sets?  How do we interpret those patterns within the context of the data?

Use various graphical displays of data to reveal important patterns of data in a set and interpret those patterns in the context of the data.

How do you decide which measure of center to use when summarizing a set of data?

Compute measures of center and variability for sets of data and interpret the meaning of those statistics.

What effect do transformations have on the shape, center, and spread of distributions?

Transform distributions by adding a constant or my multiplying by a positive constant and recognize how those transformations affect shape, center, and spread of distributions.

Vocabulary

Dot plot, histogram, box plot, 5-number summary, median, lower quartile, upper quartile, minimum value, maximum value, frequency, interval, scale, distribution, shape, center, spread, mean, interquartile range, standard deviation, data distribution, outlier, scatter plot, linear, two-way frequency table, relative frequency,  joint relative frequency, marginal relative frequency, conditional relative frequency

Information and Technology Standards

HS.TT.1.1 Use appropriate technology tools and other resources to access information.

HS.TT.1.2 Use appropriate technology tools and other resources to organize information