# Shape of Data Distribution Worksheets

When we graph data, of any kind, we are often looking to find a relationship or trend that exists within the data. We often can explore the nature of these graphs to explore the spread of the data. A spread indicates how scatter the data is from what can be considered the norm. This indicate the variability that is present within the data set. If the data is stretched a great deal of variability is present and the relationship that can be established is less compelling than if the data set exhibits more of a squeezed presence. These worksheets and lessons help students learn how to graph of a probability distribution and also make sense of the visual display to others.

### Aligned Standard: HSS-MD.A.1

- Working the Data Step-by-step Lesson- You are given pretty random data and you need to graph the distribution and comment on it.
- Guided Lesson - On the third problem we give you the characteristics of a normal curve and ask you to add it to the second graph.
- Guided Lesson Explanation - I just generated one graph for number three, it is all there though.
- Practice Worksheet - Three full out problems for you to work twice over.
- Matching Worksheet - This is just a quick introduction. It is very helpful because most national tests will just hit you with multiple choice questions similar to this.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

It's all about drawing relative frequency histograms of the data.

- Homework 1 - We create a histogram using the values dictated by the table to the right. The relative frequency histogram is symmetric.
- Homework 2 - Focus on the symmetry of the histogram to make sense of it.
- Homework 3 - Compare the area of the rectangle for heights between 30 and 30.9 inches to the area under the normal curve for heights between 30 and 30.9 inches.

### Practice Worksheets

Make sure to explain the shape of the data distribution.

- Practice 1 - Draw a relative frequency histogram of the data. Comment on the shape of the distribution.
- Practice 2 - A symmetric relative frequency histogram favors the middle value, just like a bell curve.
- Practice 3 - See if the normal curve is slightly above the point in question.

### Math Skill Quizzes

Some of the work on quiz 3 is pretty difficult.

- Quiz 1 - These values were taken from short quiz grades.
- Quiz 2 - More quiz grades for you to interpret.
- Quiz 3 - For extra credit, see if there are any outliers.

### Characterizing Shapes of Distributions

The nature of any distribution is based on several factors. They mostly rely on the number of peaks that exist, if symmetry is present, any sense of uniformity whatsoever, and the presence of a skew in one direction or another. The peaks are the portions of the graph that visibly stick out from the norm. We traditional see data collected on a population possess a single peak in the direct center. This resembles a bell shape which is why this is referred to as a bell curve. Bell curves are the picture of symmetry when the left half and right half of the curves are mirror images of one another. When you see distributions such as this they are referred to as normal. This makes them easier to work with and make sense of. There are many times you work with distributions that are skewed to the right or left. If they are skewed to the right, fewer data points will be found on the right of the graph. This indicates that the mean is being pulled towards the tail and is larger than the median. If it is skewed to the left, the opposite is true. There are also times that you will come across distributions that complete lack any form of peak at all. These are called uniform.

### Tips For Graphing Probability Distributions

A function that can be used to obtain possible values for a random variable is termed as probability distribution. The value of variables depends on probability distribution. The function helps in describing probabilities.

The sum of all probabilities is equal to one. The probability of a single event must always lie between the 0 and 1. There are different types of probability distributions including binomial, Chi-square, F-distribution, Normal, and student's t distribution. Probability distributions can be graphed, and the visual representation of the distribution helps in showing the features that were not visible in the data on paper. You must always place the random variable on the x-axis and plot its probability on the y-axis.

Discrete random variables always use histograms while continuous random variable uses a smooth curve. The area of the curve helps in calculating the probability. A probability distribution graph will never include negative values on the y-axis.