I figured a great start would be to explain what statistics by defining the basic terms with non-mathematical language.
Statistics
What: Statistics is the study of data.
Why: To understand the world around us and try to make better decisions.
Outlier
What: An outlier is a data point that is far away from the rest of the data
Why: Outliers affect the mean and standard deviation.
Population
What: The population is the entire group of people or objects you are studying.
Why: It is important to understand your population so that you are collecting the right data.
Sample
What: The sample is a group of individuals taken from the population.
Why: It would be almost impossible to collect data on the entire population in most cases. So statisticians use samples to help make decisions.
Measures of Central Tendency
What: Measures of central tendency are ways to find the middle of the data set.
Why: Statistics is about finding the most likely event and a way to do that is to find the middle.
Mean
What: The mean is the average of a set of data. It the total of the data divided by the number of data points. It is a measure of central tendency.
Why: The mean is a way to find the middle, but it can be skewed by outliers. However, the mean is still a great way to find the middle in most situations
Median
What: The median is the data point that is in the middle of the data.
Why: The median is not affected by outliers, which makes it useful in cases with outliers like income (there are people who make hundreds of times the median income).
Measures of Variability
What: Measures of variability are ways to determine how spread the data is.
Why: Measures of variability help to compare the data and make decisions.
Range
What: The range is the difference in the smallest and largest value.
Why: The range is used to understand how spread the data is. It is affected by outliers.
Standard Deviation
What: The standard deviation is the way of measuring the differences in the data. It is defined by the following formula where Σ is the sum, x is the data point, and n is the number of data points.
Why: Standard deviation helps define the statistical distributions.
Inter-Quartile Range (IQR)
What: The Inter-quartile range is the difference in the 25th and 75th percentile.
Why: It helps find the spread in the center of the data, and isn’t affected by outliers.
Normal Distribution
What: The most commonly used distribution in statistics.
Why: If there are enough data points all things follow the normal distributions.
Margin of Error
What: The margin of error is a way of explaining error in a sample. Samples don’t have all the information so they have error.
Why: Since samples are incomplete they don’t have all the information on the entire population. Margin of error helps us acknowledge that the observed mean is different from the actual mean.
This is not the end of statistics, but these are the basic terms I will frequently use.