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Data Foundations Checkpoint

A free Statistics and Data Analysis lesson from the “Data Foundations” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint reviews data types, displays, center, spread, outliers, and distribution comparisons before moving into two-variable data.

What you'll learn

Why it matters: Statistics assessments mix computation with interpretation, just like real reports: the numbers matter, but the conclusion has to match the context and the study design.

Worked example

Problem. A bar chart has 10 votes for A out of 27 total votes. About what percent chose A? Enter the nearest whole percent.

  1. Worked Example: First identify exactly what the question is asking: A bar chart has 10 votes for A out of 27 total votes. About what percent chose A? Enter the nearest whole percent.
  2. For percents, convert the percent to a decimal or fraction and connect it to the base amount in the problem.
  3. Relative frequency is count divided by total.
  4. 10 / 27 is about 37%.

Answer: 37

Practice problems

1. Review case A: A bar chart has 10 votes for A out of 27 total votes. About what percent chose A? Enter the nearest whole percent.

Show solution
  1. Checkpoint Review: First identify exactly what the question is asking: A bar chart has 10 votes for A out of 27 total votes. About what percent chose A? Enter the nearest whole percent.
  2. For percents, convert the percent to a decimal or fraction and connect it to the base amount in the problem.
  3. Relative frequency is count divided by total.
  4. 10 / 27 is about 37%.
  5. Check the result by substituting or estimating: the response should match 37 and make sense in the original problem.

Answer: 37

2. Review case B: Which display is best for comparing counts across categories?

Choices: Residual plot · Bar chart · Histogram · Box plot

Show solution
  1. Checkpoint Review: First identify exactly what the question is asking: Which display is best for comparing counts across categories?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A bar chart compares category counts.
  4. Histograms and box plots are for quantitative distributions.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Bar chart

3. Review case C: A histogram is used mainly to show:

Choices: the shape of quantitative data · the exact value of a population parameter · the cause of an association · the treatment in an experiment

Show solution
  1. Checkpoint Review: First identify exactly what the question is asking: A histogram is used mainly to show:
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Histograms group quantitative values into intervals.
  4. That reveals distribution shape.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: the shape of quantitative data

4. Review case D: A box plot has Q1 = 12, median = 14, and Q3 = 16. Find the IQR.

Show solution
  1. Checkpoint Review: First identify exactly what the question is asking: A box plot has Q1 = 12, median = 14, and Q3 = 16. Find the IQR.
  2. For data questions, identify what each statistic measures before calculating so the result matches the question.
  3. IQR measures the spread of the middle half.
  4. 16 - 12 = 4.
  5. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

5. Review case E: Find the median of 13, 4, 16, 7, 10.

Show solution
  1. Checkpoint Review: First identify exactly what the question is asking: Find the median of 13, 4, 16, 7, 10.
  2. For data questions, identify what each statistic measures before calculating so the result matches the question.
  3. Order the data from least to greatest.
  4. The middle value is 10.
  5. Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.

Answer: 10

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