Data Interpretation and Statistics

Quick Answer: Data interpretation and statistics account for about 18 questions (~32%) on the Math subtest. You'll need to read various graph types, calculate mean/median/mode, and understand basic statistical concepts. Practice extracting specific values from graphs and tables—these skills are directly testable.

Reading Graphs and Charts

Types of Graphs You'll Encounter

Reading Bar Graphs

Key Steps:

1. Read the title to understand what's measured
2. Check axis labels and units
3. Note the scale (does it start at 0?)
4. Compare bar heights carefully

Worked Example: Bar Graph Interpretation

Problem: A bar graph shows test scores for 5 students: Amy (85), Ben (72), Cara (91), Dan (78), Eva (85). What is the range of scores?

Solution:

1. Find highest score: 91 (Cara)
2. Find lowest score: 72 (Ben)
3. Calculate range: 91 - 72 = 19 points

Test Tip: When a question asks about a graph, always verify you're reading the correct data point. Misreading an axis is a common error.

Reading Pie Charts

Pie charts show parts of a whole (100%). To find a value:

$\text{Actual Value} = \text{Total} \times \frac{\text{Percentage}}{100}$

Worked Example: Pie Chart

Problem: A pie chart shows a school budget of $500,000 with 45% for salaries, 30% for facilities, 15% for supplies, and 10% for other. How much is allocated to supplies?

Solution: $500,000 × 0.15 = $75,000

Data Tables

Extracting Information

When working with tables:

1. Read row and column headers carefully
2. Note units (thousands, millions, percentages)
3. Identify the specific cell needed
4. Watch for totals vs. individual values

Worked Example: Two-Way Table

Problem:

What percentage of students who studied passed the test?

Solution:

• Students who studied: 50
• Of those who passed: 45
• Percentage: 45/50 × 100% = 90%

Measures of Central Tendency

Mean (Average)

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$

Example: Scores: 78, 82, 85, 91, 94

• Sum = 78 + 82 + 85 + 91 + 94 = 430
• Mean = 430 ÷ 5 = 86

Calculator Tip: Add all values first, then divide by the count. For the example above: 78 + 82 + 85 + 91 + 94 = (note the total), then ÷ 5 =.

Median (Middle Value)

The median is the middle value when data is ordered.

Steps:

1. Order values from least to greatest
2. If odd count: median is the middle number
3. If even count: median is average of two middle numbers

Example (odd count): 12, 15, 18, 22, 30

• Middle value (3rd of 5): 18

Example (even count): 12, 15, 18, 22

• Middle values: 15 and 18
• Median = (15 + 18) ÷ 2 = 16.5

Mode (Most Frequent)

The mode is the value that appears most often.

Example: 5, 7, 7, 8, 9, 7, 10

• Mode = 7 (appears 3 times)

Notes:

• A data set can have no mode (all values unique)
• A data set can have multiple modes (bimodal, multimodal)

Choosing the Right Measure

Worked Example: Comparing Measures

Problem: House prices on a street (in thousands): $200, $220, $215, $230, $800. Which measure best represents a "typical" house price?

Solution:

• Mean = (200 + 220 + 215 + 230 + 800) ÷ 5 = 1665 ÷ 5 = $333,000
• Median = $220,000 (middle value when ordered)

Answer: The median ($220,000) is better because the $800,000 outlier skews the mean upward.

Range and Spread

Range

$\text{Range} = \text{Maximum} - \text{Minimum}$

The range shows how spread out the data is, but is sensitive to outliers.

Standard Deviation (Conceptual)

Standard deviation measures how far data points typically are from the mean.

Example:

• Set A: 48, 49, 50, 51, 52 (small SD, clustered)
• Set B: 10, 30, 50, 70, 90 (large SD, spread out)
• Both have mean = 50, but very different spreads

Note: You won't calculate standard deviation by hand on Praxis Core, but you should understand what it represents and be able to compare relative spreads.

Scatter Plots and Correlation

Types of Correlation

Strength of Correlation

Worked Example: Scatter Plot

Problem: A scatter plot shows study hours (x-axis) vs. test scores (y-axis). Points trend upward from left to right, staying close to an imaginary line. Describe the correlation.

Solution: Strong positive correlation—as study hours increase, test scores increase, and the points are clustered near a line.