# Ch 1: Common Core HS Statistics & Probability: Quantitative Data

### About This Chapter

**Standard:** Represent data with plots on the real number line (dot plots, histograms, and box plots). (CCSS.Math.Content.HSS-ID.A.1)

**Standard:** 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. (CCSS.Math.Content.HSS-ID.A.2)

**Standard:** Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (CCSS.Math.Content.HSS-ID.A.3)

**Standard:** Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (CCSS.Math.Content.HSS-ID.A.4)

## About This Chapter

A clear understanding of using quantitative data allows students to create dot plots, histograms and box plots. Students who are able to perform the calculations for mean, median, mode and range will be prepared to comprehend and discuss the difference between mean and median.

The lessons for these standards encompass the following topics:

- Histograms
- Dot and box plots
- Mean, median, mode and range
- Shape, symmetry and skewness
- Maximums, minimums and outliers
- Quartiles and interquartile range
- Shifts in the mean and standard deviation
- Normal distribution
- Z-scores

Your students will show they understand the concepts of these standards when they are able to create and interpret quantitative data on histograms, dot plots and box plots. They should also feel comfortable with the concepts of standard deviation and shifts in the mean while using normal distribution and normal curve for estimation purposes. These standards and lessons can prepare students for college courses requiring an ability to understand research results in all areas of study.

**How to Use These Lessons in Your Classroom**

Here are some tips for using these lessons in your curriculum to meet the common core standards:

#### Pre-Lesson and Post-Lesson Quizzes

Before viewing the videos for *How to Calculate Mean, Median, Mode & Range* and *Standard Deviation and Shifts in the Mean* lessons with your students, ask them to complete the quizzes that accompany each. This will focus attention on what they already know and what they still need to learn. After sharing the video lessons, students will take the quizzes again to demonstrate understanding.

#### Histograms and Box Plots Lessons

View the video lessons that outline how to create and interpret histograms and box plots. Supply your students with data indicating the season batting averages for a group of baseball players, along with the batting averages from the World Series of that same year. As a group, create histograms and box plots and then analyze the results.

#### Box Plots, Standard Deviation, Center, Spread and Outliers Lessons

Share the video lessons pertaining to the topics listed above. Provide pennies or another type of stackable manipulative. Students will stack, count and note how many coins each could pile with their dominant and then non-dominant hands. Have students construct box plots to compare results. Explore standard deviation, center, spread and outliers.

### 1. What is Quantitative Data? - Definition & Examples

Watch this video lesson to find out the difference between saying you have seven apples and saying that those apples are delicious. You will learn about quantitative data and why it is useful.

### 2. What is a Histogram in Math? - Definition & Examples

Watch this video lesson to see how useful a histogram can be when you need to show a bunch of data in an easy to read format. Also, learn how you can easily gather the information you need from looking at a histogram.

### 3. Creating & Interpreting Dot Plots: Process & Examples

Dot plots are a visual way to display the frequency distribution in a data set. In this lesson, you will learn how to construct a dot plot and understand its uses.

### 4. What is the Center in a Data Set? - Definition & Options

Finding the center in a data set can sometimes be a little confusing. This lesson will help you determine the correct method for finding the center in a data set, and when you are finished, test your knowledge with a short quiz!

### 5. How to Calculate Mean, Median, Mode & Range

Measures of central tendency can provide valuable information about a set of data. In this lesson, explore how to calculate the mean, median, mode and range of any given data set.

### 6. Calculating the Mean, Median, Mode & Range: Practice Problems

Calculating the mean, median, mode, and range of a data set is a fundamental part of learning statistics. Use this video to practice your skills and then test your knowledge with a short quiz.

### 7. Visual Representations of a Data Set: Shape, Symmetry & Skewness

Visual representations are a fantastic way of understanding and analyzing your data. Use this lesson to understand the characteristics of visual representations of data.

### 8. The Mean vs the Median: Differences & Uses

Most people can find the mean and the median of a data set, but do you know when to use the mean and when to use the median to describe the information?

### 9. Spread in Data Sets: Definition & Example

Identifying the spread in data sets is a very important part of statistics. You can do this several ways, but the most common methods are through range, interquartile range, and variance.

### 10. Maximums, Minimums & Outliers in a Data Set

When analyzing data sets, the first thing to identify is the maximums, minimums, and outliers. This lesson will help you learn how to identify these important items.

### 11. Quartiles & the Interquartile Range: Definition, Formulate & Examples

Quartiles and the interquartile range can be used to group and analyze data sets. In this lesson, learn the definition and steps for finding the quartiles and interquartile range for a given data set.

### 12. Creating & Interpreting Box Plots: Process & Examples

Box plots are an essential tool in statistical analysis. This lesson will help you create a box plot and understand its meaning. When you are finished, test your understanding with a short quiz!

### 13. Calculating the Standard Deviation

In this lesson, we will examine the meaning and process of calculating the standard deviation of a data set. Standard deviation can help to determine if the data set is a normal distribution.

### 14. Normal Distribution: Definition, Properties, Characteristics & Example

In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.

### 15. Finding Z-Scores: Definition & Examples

Talking about multiples of standard deviations can get exhausting and confusing. Luckily, z-scores allow us to talk about how far a point is removed from a mean in terms of how many standard deviations away it is.

### 16. Estimating Areas Under the Normal Curve Using Z-Scores

So now that we have a Z-score, what is it used for? Sure, it can make your life easier when describing standard deviations, but finding the area under the normal curve is where the Z-score shines.

### 17. Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples

If you've been working with z-scores for long, you probably get tired of checking those tables every time you need to check the area under the curve. Luckily, the empirical rule helps us memorize the most important values.

### 18. Using the Normal Distribution: Practice Problems

In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. Review the concepts with a short quiz at the end.

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### Other Chapters

Other chapters within the Common Core Math - Statistics & Probability: High School Standards course