### Statistics: Summarizing Measured Data

#### What Is Statistics?

• You wish to learn about a universal population.

• You observe a sample of the universal population.

• Statistics is a collection of techniques to make inferences about the universal population from the sample.

#### Example:

Question: What is the mean time required to complete HW1 in CS5014 this semester?

Answer: Pick 10 students (the sample). Record their completion times. Compute the sample mean, which is an estimate of the mean for the entire population (all CS5014 students).

#### A Statistic

A statistic is a number that summarizes data. Jain asks [p. 177] ...

• How can the data be reduced to a single number?
• How should you report variability of the data?
• Should you be confident in the data if variability is high?
• How many data points (measurements) are needed for a desired level of statistical significance?
• How should you summarize the results of an experiment?
• How should you compare two systems using experimental data?
• What model best describes the relationships among components of a system?

#### What should I know?

• Sample vs. population and distribution
• Mean vs. sample mean
• Variance vs. sample variance
• Two famous distributions: uniform, normal
• Mean vs. median vs. mode.
• Quantile, percentile.
• Coefficient of variation.

#### Can you explain ...

• quote on top of pg. 182, "An alpha-quantile of a unit normal ... has a N(0,1) distribution."
• Example 12.4

CS 5014, C. J. Ribbens, 09/17/2001