Unit 9 — Statistics, Probability, and Data Analysis

Welcome back!

Every day we encounter information presented as numbers, tables, charts, and graphs.

Scientists analyze experimental results.

Businesses study sales.

Doctors examine health data.

Meteorologists predict the weather.

Understanding statistics helps us interpret information and make thoughtful decisions.

What Is Statistics?

Statistics is the study of collecting, organizing, analyzing, interpreting, and presenting data.

Data help answer questions and identify patterns.

Statistics allows us to make informed decisions based on evidence rather than guesswork.

Types of Data

Data may be collected in many forms.

Examples include:

• measurements
• counts
• survey responses
• observations
• scientific experiments
• test scores
• temperatures
• rainfall amounts

Good data begin with careful observation and accurate recording.

Organizing Data

Data are often organized using:

• tables
• frequency charts
• tally charts
• spreadsheets

Organized data make patterns easier to recognize.

Always label tables clearly.

Graphing Data

Graphs help people understand information quickly.

Common graphs include:

• bar graphs
• line graphs
• circle graphs (pie charts)
• histograms
• dot plots

Choose the graph that best represents the data.

Always include:

• a title
• labeled axes (when appropriate)
• units of measurement
• a consistent scale

Measures of Center

Statistics often summarize data using measures of center.

Mean

The average.

Add all values and divide by the number of values.

Median

The middle value after arranging the data in order.

Mode

The value that appears most often.

Different measures are useful in different situations.

Range

The range measures how spread out the data are.

Range = largest value − smallest value

A larger range means the data are more spread out.

Probability

Probability describes how likely an event is to occur.

Probability ranges from:

0

(impossible)

to

1

(certain)

Examples:

Rolling a standard six-sided die:

Probability of rolling a 3:

1/6

Probability helps people evaluate uncertainty.

Experimental and Theoretical Probability

Theoretical probability

Based on reasoning before an event occurs.

Experimental probability

Based on actual observations after performing an experiment.

Comparing both helps us understand chance events.

Interpreting Data

When studying graphs and tables, ask:

• What patterns appear?
• Are there unusual values?
• What conclusions are supported?
• Are additional data needed?
• Could there be another explanation?

Good statisticians avoid drawing conclusions that are not supported by the evidence.

Activity

Complete the following:

• collect data from twenty classmates or family members
• organize the results in a table
• create two different graphs
• calculate the mean, median, mode, and range
• conduct a probability experiment using a coin or die
• compare experimental and theoretical probability

Write a short report describing your conclusions.

Practice

Answer these questions.

What is statistics?

What is the difference between data and information?

What are the mean, median, and mode?

What does the range measure?

How is probability expressed?

What is the difference between theoretical and experimental probability?

Review

Today you learned:

• statistics help organize and interpret data
• graphs reveal patterns and trends
• mean, median, mode, and range summarize data
• probability measures the likelihood of events
• theoretical and experimental probability may differ slightly
• careful interpretation leads to better conclusions

Statistics helps people understand evidence and make informed decisions in science, business, medicine, engineering, and everyday life.

Looking Ahead

Next we will begin Grade 6 Science by studying scientific inquiry, laboratory safety, measurement, experimental design, and the methods scientists use to investigate the natural world.