Statistics plays a large role in our society. For College Mathematics, an overview of Statistics is covered. Topics include Sampling Techniques, Graphical Displays, Measures of Center, Measures of Dispersion(spread), and the Normal Model.
In this section, we will look at different types of statistical graphs or displays. We will also look at how to create a frequency distribution given the first class width. Types of displays that will be included are histograms, frequency polygons, stem and leaf displays (stem plots), and circle graphs.
Measures of central tendency are typical values of the data set. They include the mean, median, mode, and midrange. The median is always in the middle regardless of outliers. The median is the middle value when the data set is arranged from smallest to largest. The mean is influenced by outliers, and isn't always in the center. The mode is the data value that occurs the most frequently. A data set can have one mode, no mode, or many modes. The midrange is the midpoint of the range. It is found by doing the maximum minus the minimum divided by two. The textbook I currently teach from also includes quartiles in this section, which typically go in the measures of position section, so I included them here as well.
Finding the Mean
Finding the Median
Finding the Mode
Quartiles
Find the Midrange
Find the Mean and Median of a Frequency Distribution
Measures of Dispersion
Measures of dispersion are also known as measures of variation or measures of spread. They include the range and the standard deviation. For this course, it is only necessary to cover the sample standard deviation since it is more typically used than the population standard deviation. The standard deviation measures on average how far each of the data points is from the sample mean. The smaller the standard deviation the less variability or spread in the data. The larger the standard deviation the more variability there is in the data set. The range is the maximum minus the minimum. The range only deals with the most extreme points, and is strongly influenced by outliers. The range is a single value. The larger the range, the more variability in the data.
The normal curve or the normal model is the most used distribution in statistics. This course only covers the basics of the normal curve. When dealing with the normal curve it is important to be able to find z-scores. A z-score is the number of standard deviations above or below the mean that a data value is. It is also important to be able to find the percent or the area under the normal curve for given data values or z-scores.