Box Plots

Learn interquartile range, median.

Lesson 2 of 32 parts Practice Flashcards

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Interquartile Range

Objective: Explain interquartile range, apply the stated method, and check its conditions.

The IQR is Q3−Q1 and measures the spread of the middle half of the data. Quartile computation conventions can vary for small samples, so supplied quartiles should be used as stated. IQR is more resistant to extremes than the full range. State a quartile convention when computing small-sample quartiles from raw data.

Formulas

$IQR=Q3−Q1$

Worked examples

Try itA synthetic box plot has Q1=7, median=13, and Q3=19. Find the IQR.Show answer

Step 1: IQR measures the middle half’s span. Step 2: Compute Q3−Q1=(19)−7. Step 3: IQR=12.

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Interquartile Range

Objective: Explain interquartile range, apply the stated method, and check its conditions.

Formulas

$IQR=Q3−Q1$

Worked examples

Try itA synthetic box plot has Q1=7, median=13, and Q3=19. Find the IQR.Show answer

Step 1: IQR measures the middle half’s span. Step 2: Compute Q3−Q1=(19)−7. Step 3: IQR=12.

Median

Objective: Explain median, apply the stated method, and check its conditions.

The median is the central value after sorting; for an even count, the usual numerical convention averages the two middle values. It is a measure of location resistant to extreme magnitudes. The unsorted middle entry is not necessarily the median. Sort before selecting the middle position.

Formulas

Median = middle of the sorted data

Worked examples

Try itA sorted dataset is 1, 7, 14. Find its median.Show answer

Step 1: With three ordered observations, the middle one is the median. Step 2: The middle position is 2. Step 3: The median is 7.

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