Statistical Reports

Grade 11 · statistics · 100 practice problems · read aloud

🔊 Listen to this explanation

Statistical Reports: Making Sense of Data 📊

What is a Statistical Report?

A statistical report is a summary of data analysis that presents findings in an organized, interpretable way. It's useful because it helps you communicate patterns, trends, and conclusions from raw data to support decision-making in fields like science, business, and social studies.

How to Create a Statistical Report

  1. Define the Problem: What question are you trying to answer?
  2. Collect & Organize Data: Gather relevant data and sort it.
  3. Calculate Descriptive Statistics: Find mean, median, mode, range, and standard deviation.
  4. Create Visualizations: Use appropriate graphs (histograms, box plots, scatter plots).
  5. Write the Analysis: Interpret your statistics and graphs in context.
  6. State Conclusions: Summarize what you learned and its significance.

Worked Examples

Example 1: Test Score Analysis

Data: 78, 85, 92, 85, 67, 91, 78

Steps:

  1. Mean = (78+85+92+85+67+91+78)/7 = 576/7 ≈ 82.29
  2. Median = 85 (middle value when sorted)
  3. Mode = 78 & 85 (both appear twice)
  4. Range = 92 - 67 = 25
  5. Standard Deviation ≈ 8.27

Conclusion: Scores are moderately spread out around the mean of 82.3.

Example 2: Correlation Study

Question: Is there a relationship between study hours and test scores?

Approach: Create a scatter plot, calculate correlation coefficient (r ≈ 0.89).

Conclusion: Strong positive correlation - more study time generally leads to higher scores.

Common Mistakes to Avoid

  • Confusing mean and median: Mean is affected by outliers; median shows the true center for skewed data.
  • Correlation vs. causation: Just because two things are correlated doesn't mean one causes the other.
  • Misleading graphs: Always check the scale on axes - truncated axes can exaggerate differences.
  • Forgetting context: Always interpret statistics within the real-world situation.

Tips & Tricks

  • Use the acronym COSMOS: Collect, Organize, Summarize, Model, Output, Synthesize
  • For standard deviation, remember: ≈68% of data falls within 1 SD of the mean, ≈95% within 2 SD
  • Always label your graphs clearly with titles and axis labels
  • Use technology! Calculators and spreadsheet software can handle complex calculations

Practice Suggestions

  • Analyze real data from your life: screen time, exercise habits, or grades
  • Practice interpreting different graph types (histograms, box plots, scatter plots)
  • Write mini-reports (1-2 paragraphs) explaining statistical findings
  • Work with classmates to peer-review each other's reports for clarity

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 log₃(27) + cos(π) = ?

Hint: Consider what power you need to raise the base to get the argument, and recall the cosine value at π radians.

Show the answer

Answer: 2

  1. Evaluate log₃(27). We need to find x such that 3^x = 27.
  2. Since 3^3 = 27, log₃(27) = 3.
  3. Evaluate cos(π). At π radians, the cosine value is -1.
  4. Add the results: 3 + (-1) = 2.

The answer is 2.

2 log₂(16) + cos(π) = ?

Hint: Consider what power you need to raise 2 to in order to get the first number, and recall the value of cosine at specific angles on the unit circle.

Show the answer

Answer: 3

  1. Evaluate log₂(16). This asks: 2 to what power equals 16? Since 2^4 = 16, log₂(16) = 4.
  2. Evaluate cos(π). On the unit circle, at angle π radians (180°), the x-coordinate is -1. So cos(π) = -1.
  3. Add the results: 4 + (-1) = 3.

The answer is 3.

3 log₂(8) + sin(π/2) = ?

Hint: Consider the definitions of logarithmic and trigonometric functions. For example, log base 10 of 100 equals 2 because 10 squared is 100, and the sine of 90 degrees is 1.

Show the answer

Answer: 4

  1. Evaluate log₂(8) We ask: "2 raised to what power equals 8?" Since 2³ = 8, log₂(8) = 3.
  2. Evaluate sin(π/2) π/2 radians is 90 degrees. sin(90°) = 1. So sin(π/2) = 1.
  3. Add the results log₂(8) + sin(π/2) = 3 + 1 = 4. Final answer: 4

Let's solve step by step.

4 log₂(16) + 3cos(0) = ?

Hint: Consider what power you need to raise 2 to in order to get the first number, and recall the value of cosine at 0 radians.

Show the answer

Answer: 7

  1. Evaluate log₂(16). Since 2^4 = 16, log₂(16) = 4.
  2. Evaluate 3cos(0). cos(0) = 1, so 3 × 1 = 3.
  3. Add the results: 4 + 3 = 7.

The answer is 7.

5 log₂(8) + sin(π/6) = ?

Hint: Remember that logarithms and trigonometric functions have specific values at common angles and bases. For example, log base 4 of 16 equals 2, and the sine of 45 degrees is √2/2.

Show the answer

Answer: 3.5

  1. Evaluate log₂(8). Since 2 raised to the power of 3 equals 8, log₂(8) = 3.
  2. Evaluate sin(π/6). The sine of π/6 radians (which is 30 degrees) is 1/2.
  3. Add the results: 3 + 1/2 = 3.5.

The answer is 3.5.

6 log₂(32) + sin(π/2) = ?

Hint: Consider the definition of logarithms and the unit circle values for trigonometric functions. For example, log base 10 of 100 equals 2, and cosine of 0 equals 1.

Show the answer

Answer: 6

  1. Evaluate log₂(32) We need to find the exponent such that 2 raised to that power equals 32. 32 = 2 × 2 × 2 × 2 × 2 = 2⁵ So log₂(32) = 5.
  2. Evaluate sin(π/2) π/2 radians is 90 degrees. sin(90°) = 1.
  3. Add the two results log₂(32) + sin(π/2) = 5 + 1 = 6. Final answer: 6

Let's solve step by step.

Practise this topic — 10 free problems, no signup →