Thinking Mathematically

Statistics:12.1 Sampling, Frequency Distributions, and Graphs

Statistics

Statistics is the science of data. This involves collecting, organizing, analyzing, and interpreting numerical information, as well as drawing conclusions based on the data.

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.

Populations and Samples• A population is the set containing all the objects

whose properties are to be analyzed• A sample is a subset of the population.• 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.Exercise Set 12.1 #1 (from text)

Frequency Distribution

• Collected data presented in a two column table. The first column list the data values, the second column the number of times each value occurs.Exercise Set 12.1 #7

A random sample of 30 college students is selected. Each student is asked how much time s/he spent on homework during the previous week. The following times are obtained:16, 24, 18, 21, 18, 16, 18, 17, 15, 21, 19, 17, 17, 16, 19, 18, 15, 15, 20, 17, 15, 17, 24, 19, 16, 20, 16, 19, 18, 17.

Construct a frequency distribution for the data.

Grouped Frequency Distribution

• Data is organized in to groups or classes.• The minimum value for a class if the lower class

limit, the maximum is the upper class limit.• The difference between the lower class limit and

the upper class limit is the class width and is the same for all classes.

• The grouped frequency distribution lists the number of data points in each class.Exercise Set 12.1 #17

Construct a grouped frequency distribution for the age at which U.S. presidents were inaugurated (see text)

Histograms and Frequency Polygon

• In a histogram the vertical axis gives the frequency (or proportion) for each class of data (the horizontal axis).

• Like the histogram, the axis of a frequency polygon represent data class (horizontal) and frequency for that class (vertical). In the frequency polygon this data points are connected by line segments.Construct a histogram and a frequency polygon for the

data in exercise 17.

Stem-and-Leaf Display

• Data is ordered and grouped– Grouping is often by highest digit

• Left column is the ‘group number’• Individual of the group are listed in right columnConstruct a stem and leaf plot for the data in

exercise 17.

Thinking Mathematically

Statistics:12.1 Sampling, Frequency Distributions, and Graphs