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# 2022 PA-D-1-2

last edited by 1 month, 1 week ago

PA.D.1.2

PA.D.1.2 Explain how outliers affect measures of center and spread.

## In a Nutshell

Students will work to develop the definition of an outlier, a value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. Students should be able to recognize how data analysis changes if true outlier values are disregarded.

## Teacher Actions

• Develop Mathematical Reasoning by developing mathematical arguments for how an outlier value affects the mean, median, mode, and range of a data set.

• Develop the Ability to Communicate Mathematically when using appropriate mathematical language to describe properties of outlier values and explain the reasoning for predictions of an outlier's affection on measures of central tendency and spread with verbal, written, and/or visual representations.

• Develop the Ability to Make Conjectures, Model, and Generalize when examining properties of outlier values in both upper and lower boundaries of a data set and developing a general conclusion for how an outlier value impacts the measure of center and spread for any data set.
• Use and connect mathematical representations by presenting data for students to analyze in various forms (scatter plots, lists, tables, box-and-whisker plots, stem and leaf plots, etcâ€¦)

• Implement tasks that promote reasoning and problem-solving that allow students to routinely predict how properties of outliers affect measures of center and spread for mathematical situations including a variety of data sets, including real-world applications, and compare predictions to actual calculations.

• Facilitate meaningful mathematical discourse by presenting several real-life cases where outliers exist and have students debate the pros and cons on keeping the outlier in the calculation to accurately describe the data set.

## Misconceptions

• An outlier is identified as a value that is much larger or smaller than a majority of the other values in a data set.

• Mean is the only central tendency measure that is always affected by an outlier value. An outlier value will skew the mean of a data set.

• Median is a more accurate description of a set of data containing an outlier.  Outlier values have little to no effect on the median.

• The spread (range) of a data set increases when the data set includes an outlier value.

• Outlier values have no effect on the mode for a set of data.

• Students may believe that an outlier exists because there is a bigger gap between two data points than with the other data points, when in reality it is within the relative bounds.

• Students might believe that an outlier is always greater than the other data points.

• Students may believe that all measures of central tendency are affected by outliers and in the same manner.

• Students may forget to change the value of the divisor when comparing mean calculations with and without an outlier value.

## Prior Knowledge

• Interpret the mean, median, and mode for a set of data (6.D.1.1).

• Design simple experiments, collect data, and calculate measures of center and spread (7.D.1.1).

• Collect data and analyze scatter plots for patterns, linearity, and outliers (A1.D.1.2).

• Collect data and use scatter plots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables (A2.D.1.2).

## Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

OKMath Framework Introduction

Pre-Algebra Introduction