U6T1 SLT 1 Data Distributions & Normal Distribution

PART I: Data Distribution Let’s construct class HISTOGRAMS With Post-Its

4 Main Histogram Shapes

What are examples of data that might be...

a. Skewed Left? B. Skewed Right C. Symmetric?

Data Shape: Range: (diff between largest and smallest values)

Class Height

Birth Weight

Number of Siblings

Objectives: 1. Being able to identify different histogram shapes and vocabulary associated with the shape. 2. Being able to calculate mean, median, and mode and identify potential pitfalls associated with them.

Uniform Symmetric Skewed right or positively skewed

Skewed left or negatively skewed

Other Histogram Shapes: Sometimes a histogram has a single, central, or several different peaks. These peaks are

called: _____________________________________

Mode is: ____________________________________________________________________________

A histogram with: Example:

1 peak: _____________________

2 peaks: ______________________

3+ Peaks: _______________________

no mode: ________________________

When might we see a bimodal distribution?

Part II: Central Tendency

Excerpt taken from Naked Statistics, by Charles Wheelan, regarding the economic health of the middle class:

From baseball to income, the most basic task when working with data is to summarize a great deal of information. There are some 330 million residents in the United States. A spreadsheet with the name and income history of every American would contain all the information we could ever want about the economic health of the country-yet it would also be so unwieldy as to tell us nothing at all. The irony is that more data can often present less clarity. So we simplify. We perform calculations that reduce a complex array of data into a handful of numbers that describe those data, just as we might encapsulate a complex, multifaceted Olympic gymnastics performance with one number: 9.8

Measures of central tendency are one way that we can simplify the data.

Example: You are currently taking 7 classes at Richard Montgomery and the following is a data set representing the number of tests that you take per class in the 4th quarter: {0, 1, 1, 2, 2, 2, 4}

What are the three measures of central tendency? How do you calculate each of them using the example above? 1. 2. 3.

Hint

Part III: Normal Distribution This is a frequency distribution.

This is an example of a distribution curve.

The image below shows both a frequency distribution and a distribution curve.

1) What is the difference between a frequency distribution and a distribution curve? One important type of data distribution is called a “normal distribution.” In this task you will be given pairs on the powerpoint of data distributions represented with histograms and distribution curves. In each pair, one distribution is normal and one is not. 2. What differences do you see between these distributions? 3. Based upon the examples you have seen in the powerpoint, what are the features of a normal distribution?