Chapter 21 Basic Statistics

Objectives Define and distinguish between population and sample statistics. Calculate and interpret measures of dispersion and central tendency. Construct and interpret diagrams and charts. Describe and distinguish between descriptive and inferential statistical studies, and evaluate their results to draw valid conclusions.

Basic Terms Population: refers to the entire set of items under discussion. It is typically not feasible to measure characteristics of the entire population. Therefore a statistical study will randomly select a sample from the population, and measure each item in the sample. The analysis of the sample data produces statistics.

Central Limit Theorem The central limit theorem (CLT) states that regardless of the shape of the population, the sampling distribution of the mean is approximately normal if the sample size is sufficiently large. The approximation improves as the sample size gets larger (30 or more) (figure 21.4, page 125). The CLT is used for calculating confidence intervals as well as for various hypothesis tests. Control charts depend on the CLT.

Descriptive Statistics Diagrams such as frequency distributions, dot plots, and histograms of data (figure 21.5, page 126) reveal information about the sample data that is not obvious from the data list such as: the spread of the sample, the shape of the sample, and the approximate center of the sample.

Descriptive Statistics The spread (measures of dispersion) of the sample is given by the sample range or the sample standard deviation. The sample range is defined as the highest value minus the lowest value. The sample standard deviation is given on page 127.

Descriptive Statistics The center of the sample may be quantified in 3 ways (measures of central tendency): 1. The mean is the arithmetic average of the data set. 2. The median is the middle value of an ordered data set. If the data set is composed of an even number of data points the median is the average of the two middle values of the ordered data set. 3. The mode is the most frequently found value in the data set. Note there may be more than one mode present.

Graphical methods 1. Tally: Provides a quick diagram to make a preliminary judgment on skewness. 2. Frequency distribution: Summarizes data from a tally. 3. Stem and leaf diagram: Provides information on the contents of a cell in a frequency distribution. Useful when the behavior of data within the cells is needed. 4. Box and whisker chart (fig 21.9, page 131): Illustrates range, median, and location of middle 50% of data. 5. Scatter Diagram (fig 21.12, page 134): Detects possible correlation between two variables. 6. Run Chart: Provides a visual set of data over time.

Valid Statistical Conclusions Statistical studies provide tools for squeezing information out of data. The two principle types of statistical studies are called descriptive studies and inferential studies. Descriptive studies use techniques such as finding the mean, median, mode, standard deviation, histogram or scatter plot. Inferential studies analyze data from the sample to infer properties of the population from which the sample was drawn.

Summary Population refers to the entire set of items under discussion. The analysis of the sample data (The approximation improves as the sample size gets larger - 30 or more) produces statistics. Diagrams such as frequency distributions, dot plots, and histograms of data reveal information about the sample data that is not obvious from the data list such as: the spread of the sample, the shape of the sample, and the approximate center of the sample. The sample range is defined as the highest value minus the lowest value. The mean is the arithmetic average of the data set. The median is the middle value of an ordered data set. The mode is the most frequently found value in the data set. Scatter Diagram: Detects possible correlation between two variables. Descriptive studies use techniques such as finding the mean, median, mode, standard deviation, histogram or scatter plot. Inferential studies analyze data from the sample to infer properties of the population from which the sample was drawn.

Home Work 1. Distinguish between population and statistics. 2. What is a minimum sample size? 3. What 3 attributes do diagrams reveal about sample data? 4. Define sample range. 5. Explain the 3 ways of quantifying the center of a sample. 6. Explain the two principle types of statistical studies.