Learn on PengiPengi Math (Grade 6)Chapter 7: Statistics and Probability

Lesson 3: Outliers and Their Impact on Data

In this Grade 6 lesson from Pengi Math Chapter 7, students learn to identify outliers as extreme data values and analyze how they affect the mean of a data set. Students compare the mean and median when outliers are present, discovering why the median is resistant to extreme values. Real-world situations are used to help students interpret and apply these concepts in context.

Section 1

Identifying Outliers

Property

Outliers are values that are significantly different from the rest of the data.
These are data points that stand far apart from the main group of values.
We can identify potential outliers by looking for values that seem unusually high or low compared to the other data points in the set.

Examples

Section 2

Analyzing the Effect of Outliers on the Mean

Property

An outlier is an extreme value that is much higher or lower than the other values in a data set.
Outliers have a strong effect on the mean because the mean uses all values in its calculation.
When an outlier is present, it pulls the mean toward the extreme value, making the mean less representative of the typical values in the data set.

To calculate the mean: mean=sum of all valuesnumber of values\text{mean} = \frac{\text{sum of all values}}{\text{number of values}}

Book overview

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Chapter 7: Statistics and Probability

  1. Lesson 1

    Lesson 1: What Is a Statistical Question?

  2. Lesson 2

    Lesson 2: Understanding Measures of Center

  3. Lesson 3Current

    Lesson 3: Outliers and Their Impact on Data

  4. Lesson 4

    Lesson 4: Understanding Variability in Data

  5. Lesson 5

    Lesson 5: Box Plots and the Five-Number Summary

  6. Lesson 6

    Lesson 6: Visualizing Data with Dot Plots and Histograms

  7. Lesson 7

    Lesson 7: Analyzing Data Distributions with Dot Plots and Histograms

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identifying Outliers

Property

Outliers are values that are significantly different from the rest of the data.
These are data points that stand far apart from the main group of values.
We can identify potential outliers by looking for values that seem unusually high or low compared to the other data points in the set.

Examples

Section 2

Analyzing the Effect of Outliers on the Mean

Property

An outlier is an extreme value that is much higher or lower than the other values in a data set.
Outliers have a strong effect on the mean because the mean uses all values in its calculation.
When an outlier is present, it pulls the mean toward the extreme value, making the mean less representative of the typical values in the data set.

To calculate the mean: mean=sum of all valuesnumber of values\text{mean} = \frac{\text{sum of all values}}{\text{number of values}}

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 7: Statistics and Probability

  1. Lesson 1

    Lesson 1: What Is a Statistical Question?

  2. Lesson 2

    Lesson 2: Understanding Measures of Center

  3. Lesson 3Current

    Lesson 3: Outliers and Their Impact on Data

  4. Lesson 4

    Lesson 4: Understanding Variability in Data

  5. Lesson 5

    Lesson 5: Box Plots and the Five-Number Summary

  6. Lesson 6

    Lesson 6: Visualizing Data with Dot Plots and Histograms

  7. Lesson 7

    Lesson 7: Analyzing Data Distributions with Dot Plots and Histograms