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Worksheet Grade 11 Science

Otterburn Plant Chlorine Residual: Comparing Shift Statistics

A grade 11 statistics worksheet comparing the center and spread of two shifts of chlorine-residual data at a fictional plant, with an outlier from a pump error.

Objectives

  1. Students will calculate the mean, median, and range of two data sets and compare their spread.
  2. Students will interpret how an outlier changes the mean and median differently in monitoring data.

Vocabulary

Key words: mean, median, range, standard deviation, outlier

Teacher overview

Operators at the fictional Otterburn Water Treatment Plant record the free chlorine residual leaving the plant several times each shift, because a residual that swings too much is a warning sign even when the average looks fine. This worksheet gives students two small data sets, one from the day shift and one from the night shift, and asks them to compare center and spread the way a regulator would. A common misconception this worksheet corrects is that two data sets with nearly the same average are equally well controlled; here the averages match while the spread does not.

Otterburn Plant Chlorine Residual: Comparing Shift Statistics — Grade 11 Science
Name: ____________________________ Date: ______________

Student Worksheet

All readings are free chlorine residual in mg/L at the fictional Otterburn plant, measured at the entry to the distribution system. The maximum residual disinfectant level is 4.0 mg/L, and systems usually hold 0.2 to 2.0 mg/L in distribution. A calculator's standard-deviation function is allowed.

  • Day shift readings: 1.0, 1.1, 0.9, 1.0, 1.2, 1.1, 0.9, 1.0
  • Night shift readings: 0.6, 1.4, 0.8, 1.5, 0.5, 1.3, 0.7, 1.6
  1. Calculate the mean of the day-shift readings. Round to the nearest hundredth.
  2. Find the median of the day-shift readings.
  3. Find the range of the day-shift readings.
  4. Calculate the mean of the night-shift readings. Round to the nearest hundredth.
  5. Find the median of the night-shift readings.
  6. Find the range of the night-shift readings.
  7. The sample standard deviation is about 0.10 mg/L for the day shift and about 0.44 mg/L for the night shift. State which shift held a more consistent residual and explain how the two standard deviations support your answer.
  8. Both shifts stayed well below the 4.0 mg/L maximum. Explain in two or three sentences why the spread of the readings, not just the average, matters for keeping disinfection both effective and safe.
  9. A ninth day-shift reading of 3.2 mg/L was logged after a chemical-feed pump error. Recompute the day-shift mean and median with this value included, and state which one changed more.
  10. Using center and spread from your results, write one sentence of advice for the night-shift operators.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 1.03 mg/L.
    Sum of the eight readings = 8.2 mg/L; 8.2 / 8 = 1.025, which rounds to 1.03 mg/L.
  2. Answer: 1.0 mg/L.
    Sorted, the middle two values are 1.0 and 1.0, so the median is 1.0 mg/L.
  3. Answer: 0.3 mg/L.
    Range = 1.2 - 0.9 = 0.3 mg/L.
  4. Answer: 1.05 mg/L.
    Sum of the eight readings = 8.4 mg/L; 8.4 / 8 = 1.05 mg/L.
  5. Answer: 1.05 mg/L.
    Sorted: 0.5, 0.6, 0.7, 0.8, 1.3, 1.4, 1.5, 1.6; the middle two values are 0.8 and 1.3, and their average is 1.05 mg/L.
  6. Answer: 1.1 mg/L.
    Range = 1.6 - 0.5 = 1.1 mg/L.
  7. Answer: the day shift.
    The day shift held a more consistent residual because its standard deviation of about 0.10 mg/L is much smaller than the night shift's 0.44 mg/L. A smaller standard deviation means the readings sit closer to the mean, so the residual varied less across the shift.
  8. Answer: spread controls the low and high extremes.
    Even with a safe average, wide spread means some individual readings can dip toward levels that risk losing disinfection or climb toward levels that create taste and byproduct problems. A tightly controlled residual keeps every reading, not just the average, inside a safe band. Accept any answer that connects spread to the risk at the extremes.
  9. Answer: 1.27 mg/L mean, 1.0 mg/L median.
    New mean = (8.2 + 3.2) / 9 = 11.4 / 9 = 1.267, about 1.27 mg/L. New median: sorted nine values are 0.9, 0.9, 1.0, 1.0, 1.0, 1.1, 1.1, 1.2, 3.2, so the median is the fifth value, 1.0 mg/L. The mean changed much more than the median, which stayed at 1.0, showing that the median resists a single outlier.
  10. Answer: reduce the night-shift swing.
    Accept any one-sentence answer that uses both center and spread, for example: the night shift's average is fine, but its much larger spread means the dosing needs steadier control so individual readings stop swinging between 0.5 and 1.6 mg/L.

Differentiation

Support

Provide the day-shift and night-shift readings already sorted from least to greatest so students can find the median and range without re-sorting. Give a worked mean for a third short list before item 1.

Extension

Have students build a simple back-to-back number-line plot of the two shifts and mark each mean, then explain in writing how the plot shows equal centers with unequal spread more clearly than the summary numbers alone.

ELL supports

Pre-teach mean, median, range, and spread with a labeled example on five simple numbers. Allow items 8 and 10 to be completed with a provided sentence frame: "The night shift's readings are more spread out, which means ___."