advertisement

Thinking Mathematically Sampling, Frequency Distributions, and Graphs Statistics Statistics is the science of data. This involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information. Types of Statistics • Descriptive Statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set, and to present that information in a convenient form. • Inferential Statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data. 1 Random Samples A random sample is a sample obtained in such a way that every element in the population has an equal chance of being selected for the sample. If we want to select a random sample from a large city to determine how the city’s citizens feel about casino gambling we might randomly select neighborhoods of the city and then randomly survey people within the selected neighborhoods. If we only select specific neighborhoods or the first 200 people we find in the telephone directory, then not everyone has an equal chance of being selected. Describing Qualitative Data • A class is one of the categories into which qualitative data can be classified. • The class frequency is the number of observations in the data set falling in a particular class. Histogram A histogram is like a bar graph in that the vertical axis gives the proportion (or relative frequency) for each interval of data while the horizontal axis is divided into specified intervals of equal width known as measurement classes. However, in a histogram, each column shares a side or touches while in a bar graph each column is separated. 2 Frequency Polygon A line graph called a frequency polygon can also be used to visually convey information. The axes are labeled just like those in a histogram. Once a histogram has been constructed, put a dot at the top of each rectangle at its midpoint. Connect each of these midpoints with a straight line. Finally, draw each endpoint down to touch the horizontal axis. 3 Stem-and-Leaf Display Two columns are created, one for the stem and one for the leaf. The place value for the stem is determined for the left column and the following place value in each piece of data will be written next to the appropriate stem in the leaf column. As an example, if the data value is 32, the 3 may be designated as the stem in which case the 2 would be the leaf. If the data point is 5.8, the ones place may be the stem and the tenths place the leaf so that the 5 would be in the stem column with the 8 next to it in the leaf column. Thinking Mathematically Sampling, Frequency Distributions, and Graphs 4