Box plots and informal confidence intervals

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What this lesson covers

  • A box plot shows the median and the middle 50%.
  • The interval is median ± 1.5 × IQR ÷ √n.
  • Bigger samples give narrower intervals.
Key idea

The informal interval

  • Find the sample median and interquartile range, the IQR.
  • The interval is median ± 1.5 × IQR ÷ √n.
Worked example

Sample of 36

  • Median 52, IQR 18, n = 36.
  1. 1.5 × 18 ÷ √36 = 4.5
  2. 52 − 4.5 = 47.5
  3. 52 + 4.5 = 56.5
  4. interval: 47.5 to 56.5
Worked example

Why sample size matters

  • The same median and IQR with other sample sizes.
nMarginInterval
255.446.6 to 57.4
364.547.5 to 56.5
1002.749.3 to 54.7

Common mistakes

  • Saying the interval holds all the data.
    It estimates the population median, not individual values.
  • Dividing by n instead of √n.
    The formula uses the square root.

Your turn

  • 1. Median 30, IQR 10, n = 25. Find the interval.
  • 2. What is the margin if n grows to 100?
Show answer

1. 27 to 33 2. 1.5

Summary

What to take away

  • The interval is about the population median.
  • A larger sample gives a narrower interval.

More in AS 91264

Sampling and the enquiry cycleNotesBox plots and informal confidence intervalsNotesComparing two samplesNotesMaking and justifying an inferenceNotes

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