Key Takeaways
- Mean is the average; median is the middle; mode is most frequent
- Range measures spread (highest - lowest)
- Order data before finding median
- Always read graph titles and labels carefully
- Use real data to make statistics meaningful for students
Data Analysis and Statistics
The ParaPro tests your ability to interpret data from graphs and tables and calculate basic statistics.
Reading Graphs and Charts
Bar Graphs: Compare categories with rectangular bars
- Height/length shows quantity
- Can be vertical or horizontal
Line Graphs: Show change over time
- Points connected by lines
- x-axis usually shows time
Pie/Circle Graphs: Show parts of a whole
- Each "slice" is a percentage
- All slices total 100%
Tables: Organize data in rows and columns
- Headers label each row/column
- Easy to compare specific values
Measures of Central Tendency
| Measure | Definition | How to Find |
|---|---|---|
| Mean | Average | Add all values, divide by count |
| Median | Middle value | Order values, find the middle |
| Mode | Most frequent | Value that appears most often |
| Range | Spread | Largest value - smallest value |
Calculating Mean (Average)
Formula: Mean = Sum of all values ÷ Number of values
Example: Find the mean of 5, 8, 12, 10, 5
- Sum: 5 + 8 + 12 + 10 + 5 = 40
- Count: 5 values
- Mean: 40 ÷ 5 = 8
Finding the Median
Steps:
- Order values from least to greatest
- Find the middle value
- If even number of values, average the two middle values
Example: Find the median of 5, 8, 12, 10, 5
- Ordered: 5, 5, 8, 10, 12
- Middle value: 8
Example with even count: Find the median of 4, 7, 9, 12
- Ordered: 4, 7, 9, 12
- Two middle values: 7 and 9
- Median: (7 + 9) ÷ 2 = 8
Finding the Mode
The mode is the value that appears most frequently.
Example: Find the mode of 5, 8, 12, 10, 5
- 5 appears twice; others appear once
- Mode: 5
Note: A data set can have no mode, one mode, or multiple modes.
Calculating Range
Formula: Range = Maximum value - Minimum value
Example: Find the range of 5, 8, 12, 10, 5
- Maximum: 12
- Minimum: 5
- Range: 12 - 5 = 7
Interpreting Data
When answering data questions:
- Read the title and labels carefully
- Identify what is being asked
- Locate the relevant data
- Perform any necessary calculations
- Check that your answer makes sense
Classroom Application
Help students with data analysis by:
- Creating class surveys and graphing results
- Using real data from sports, weather, or classroom activities
- Teaching the difference between mean, median, and mode
- Practicing graph reading with age-appropriate materials
- Having students create their own graphs
What is the median of the following data set: 3, 7, 9, 15, 21?
A class had test scores of 70, 85, 90, 85, and 95. What is the mode?