Categorical data are data where the values are divided into groups, or categories. 

For example, the breeds of 10 different dogs are categorical data. Another example is the colors of 100 different flowers.

The distribution of a data set tells how many times each value occurs.

The five-number summary is one way to describe the distribution of a data set. The five numbers are the minimum, the three quartiles, and the maximum. 

This box plot represents a data set with the following five-number summary: The minimum is 2, the three quartiles are 4, 4.5, and 6.5, and the maximum is 9.

A non-statistical question is a question that can be answered by a specific measurement or procedure where no variability is expected. 

For example:

• How high is that building?
• If I run at 2 meters per second, how long will it take me to run 100 meters?
• Who was the first woman appointed to the Supreme Court?

Numerical data are data where the values are numbers, measurements, or quantities. Numerical data is also called measurement data or quantitative data.

For example, the weights of 10 different dogs are numerical data.

An outlier is a data value that is far from the other values in the data set. A value is considered an outlier if it is:

• More than 1.5 times the interquartile range greater than Q3. 
• More than 1.5 times the interquartile range less than Q1.

In this box plot, the minimum, 0, and the maximum, 44, are both outliers.

In a skewed distribution, one side has more values farther from the bulk of the data than the other side. The mean is usually not equal to the median. The dot plot or histogram for the data shows only one peak leaning to one side.

This dot plot shows a skewed distribution. The data values on the left, such as 1, 2, and 3, are farther from the bulk of the data than the data values on the right.

The standard deviation is a measure of the variability, or spread, of a distribution. It is calculated by a method similar to the method for calculating the MAD (mean absolute deviation). The exact method is studied in more advanced courses.

A statistic is a quantity that is calculated from sample data, such as mean, median, or MAD (mean absolute deviation).

A statistical question is a question that can only be answered by using data in which variability is expected.

For example:

• Who is the most popular musical artist at our school?
• When do students in our class typically eat dinner?
• Which classroom in our school has the most books?

In a symmetric distribution, the data values on each side of the center mirror each other. The dot plot or histogram for the data has a vertical line of symmetry in the center, where the mean is equal to the median.

This dot plot shows a distribution that is symmetric about the data value 5.

In a uniform distribution, the data values are evenly spread out across the range of the data. The dot plot or histogram for the data shows no peaks.

This dot plot shows a uniform distribution.