--- title: "Box plot; third quartile of suspended solids" subject: "Probability and Statistics" chapter: 1 key: "semester_5/probability_and_statistics:box-plot-third-quartile-solids" source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/box-plot-third-quartile-solids site: BCT Engineering --- # Box plot; third quartile of suspended solids Probability and Statistics · Chapter 1: Descriptive Statistics and Basic Probability - Asked in: 2074 Asoj, 3+3 marks - Video: [Box and Whisker Plots Explained | Understanding Box and Whisker Plots (Box Plots) | Math with Mr. J](https://www.youtube.com/watch?v=nV8jR8M8C74) — Math with Mr. J - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/box-plot-third-quartile-solids - Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1 ## Question What is Box plot and what does it measure? Explain the meaning of its different parts with diagram. A civil engineer monitors water quality by measuring the amount of suspended solids in a sample of river water. Over 11 weekdays, he observed 14, 12, 21, 28, 30, 63, 29, 65, 55, 19, 20 suspended solids (parts per million). Find the third quartile and interpret its meaning. ## Short answer A box plot displays the five-number summary and reveals centre, spread, and skewness. For the 11 ordered suspended solids values, the third quartile is the 9th value: Q3 = 55 ppm, meaning 75% of days had 55 ppm or less. ## Answer #### Box plot A **box plot** (box-and-whisker plot) is a graph of the five number summary: minimum, Q₁, median, Q₃ and maximum. It measures the **centre** (median), **spread** (IQR and range), **skewness** and **outliers** of a data set, and is useful for comparing several groups. #### Parts of a box plot ```text o (outlier) |-----[====|=====]-------| min Q1 median Q3 max |<-- IQR -->| ``` - **Box:** from Q₁ to Q₃. It holds the middle 50% of data. Its length is the interquartile range IQR = Q₃ − Q₁. - **Line inside the box:** the median. If it is off-centre, the data are skewed. - **Whiskers:** lines from the box to the smallest and largest values that are not outliers (within 1.5 × IQR of the box). - **Outliers:** points beyond Q₁ − 1.5 IQR or Q₃ + 1.5 IQR, drawn as separate dots. #### Third quartile of suspended solids Order the 11 values: ```text 12, 14, 19, 20, 21, 28, 29, 30, 55, 63, 65 ``` Q₃ is at position 3(n + 1)/4 = 3 × 12/4 = 9, which is the 9th value. (The median of the upper half 29, 30, 55, 63, 65 gives the same result.) ```text Q3 = 55 ppm ``` **Interpretation:** 75% of the days had suspended solids of 55 ppm or less, and only 25% of days were above 55 ppm. The high values (55, 63, 65) show a right-skewed pattern in the river's pollution. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does a box plot show? A. Only the mean B. Five-number summary: centre, spread, skew, outliers C. Only frequencies D. Only the mode Answer: B. It graphs min, Q1, median, Q3, max. (Key point: Box plot meaning) 2. What does the box represent? A. Min to max B. Mean +/- SD C. Middle 50% of data, Q1 to Q3 D. Outliers Answer: C. Length is the IQR. (Key point: Box) 3. What is Q3 for the 11 values? A. 30 ppm B. 63 ppm C. 29 ppm D. 55 ppm, the 9th value Answer: D. 3(11+1)/4 = 9th ordered value. (Key point: Third quartile) 4. What does Q3 = 55 mean? A. 75% of days had 55 ppm or less B. 75% above 55 C. Mean is 55 D. 25% below 55 Answer: A. Q3 is the 75th percentile. 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