## Learning Math: Data Analysis, Statistics, and Probability

# Data Organization and Representation

## Explore different ways of representing, analyzing, and interpreting data, including line plots, frequency tables, cumulative and relative frequency tables, and bar graphs. Learn how to use intervals to describe variation in data. Learn how to determine and understand the median.

**In This Session**

**Part A: **Patterns in Variation

**Part B: **Line Plots

**Part C: **Frequency Tables

**Part D: **The Median

**Part E: ** Bar Graphs and Relative Frequencies

**Homework**

In the previous session, you explored measurement and variation. You learned that there is almost always variation in statistical data, and you looked at potential sources of the variation, including random error and bias. You may also recall that there are four components to statistical problem solving:

1. Ask a Question

2. Collect Data

3. Analyze Data

4. Interpret Results

**Learning Objectives**

In this session, we will focus on the last two steps of this process — analyzing data and interpreting results. A proper analysis of data can help you provide better answers to statistical questions. Note 1

In this session, you will learn how to do the following:

- Organize data in a line plot and a frequency table
- Organize data in a cumulative frequency table
- Use intervals to answer a statistical question
- Determine the median of a set of data
- Determine relative frequencies and create bar graphs of your data

### Key Terms

**Previously Introduced:**

data

quantitative data

variation

**New in This Session:**

cumulative frequency

cumulative frequency table

discrete data

distribution

frequency

frequency bar graph

frequency table

interval

line plot

median

mode

relative frequency

relative frequency bar graph

### Notes

**Note 1**

The following materials are needed for those choosing to do hands-on activities:

**Materials Needed:**

- Large poster board
- Collection of nickels (about 100)
- Magnifying glasses (if needed to see the mint marks on the coins)
- String
- Sets of 17 half-ounce boxes of raisins (one set per group or for each individual working alone). All 17 should be from the same brand, but each set should be different; e.g. 17 boxes of Brand X, 17 boxes of Brand Y, etc.