Statistics Portfolio
Welcome to my introduction of statistics. I promise it will be short, sweet, and easy to understand. These are based off my VARK learning style, which was multi-modal. In other words, I like to learn in a variety of ways, using pictures, text, and examples.
|
Introduction to Concepts in Statistics
Types of Samples
Levels of Measurement
Measures of Central Tendency
Statistical Distributions
Blank standard distribution curve used from this site.
Skewed distribution curve used from this website. It has been modified from original image to explain the relationship to measures of central tendency.
Bimodal distribution curve used from this site.
Skewed distribution curve used from this website. It has been modified from original image to explain the relationship to measures of central tendency.
Bimodal distribution curve used from this site.
Variation
Standard Deviation is a is a measure of the average differences within a sample.
Confidence Intervals are ranges based off of the standard deviation that can be used to predict two things.
- The larger the standard deviation, the more variable a sample.
- The smaller the standard deviation, the less variable a sample.
- As range increases, this increases the standard deviation.
- Mathisfun provides an excellent and clear example of how to calculate the standard deviation.
Confidence Intervals are ranges based off of the standard deviation that can be used to predict two things.
- A confidence interval calculated using the standard deviation and the mean predict where the data from a sample lies within:
- A confidence interval calculated using the standard error and the mean predict where the mean for the population lies within a 68%, 95%, or a 99% certainty range.
- The most commonly calculated confidence interval is the 95% confidence interval. This can only be used with data that has a normal distribution.
Standard Error is a measure of how accurately a sample reflects the population.
- As the number of of measurements in a sample increase, the standard error decreases, as long as the sample is not biased.
- Data which is skewed positively or negatively is biased data. In other words, if the sample does not resemble a normal curve, it is biased.
- Explorable.com provides a wonderful explanation of how the standard error is calcluated.
Independent Variable is the variable that you control in an experiment.
Dependent Variable is the variable that changes when the independent variable changes. In other words, you never actually make direct changes to this variable.
When I took the VARK assessment to determine what my learning style was, I discovered that I had a multimodal learning style. This explained quite a bit to myself, as I always wanted more sources, more examples, and more ways to learn new material. For example, I only provided explanations for the pink sample set used above. Someone who learns as I do would benefit from calculating the mean, median, and mode for the purple data set and checking the answers provided here. For the purple sample from 100 squares, the mean is 2.48, the median is 2.5, and the mode is 3. Because statistics is based off calculations and numbers, I chose to supplement them with pictures and links to explanations so a person new to the material could visually grasp the patterns that statistics tries to describe. Aside from the three linked images, all other images and examples were created using powerpoint and excel.