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Project Grade 11 Math

Vireo Lake Plant: A Chlorine Residual Control-Chart Study

A four-session grade 11 statistics project building a control chart from a fictional plant's 20-day records and writing a compliance memo to a water board.

Objectives

  1. Students will compute the mean, median, and standard deviation of daily water-quality readings.
  2. Students will construct a control chart with a center line and limits at the mean plus and minus two standard deviations.
  3. Students will judge whether a treatment process meets regulatory limits and write a compliance memo.

Vocabulary

Key words: control chart, standard deviation, control limits, statistical control, outlier

Teacher overview

Treatment operators record daily readings and also watch for signs that a process is drifting out of its normal range before it becomes a violation. This project has grade 11 students turn 20 days of records from the Vireo Lake Water Treatment Plant, a fictional plant, into a control chart, then judge the plant against regulatory limits and report to a fictional water board. The driving question is whether the plant's disinfection is in statistical control and meets the rules. Students build a histogram, compute the mean and standard deviation to set control limits, flag unusual days, and write a short compliance memo, which mirrors how a real plant reviews its own performance.

Vireo Lake Plant: A Chlorine Residual Control-Chart Study — Grade 11 Math
Name: ____________________________ Date: ______________

Project Brief

Driving question: Is the Vireo Lake plant's chlorine residual in statistical control, and does the plant meet its regulatory limits?

Scenario: The Vireo Lake Water Treatment Plant is a fictional plant. Its board has asked a student analysis team to review the last 20 days of finished-water records and report whether the disinfection process is steady and compliant.

The data (a fictional 20-day record):

Day Chlorine residual (mg/L) Turbidity (NTU)
1 1.0 0.08
2 1.1 0.10
3 0.9 0.09
4 1.0 0.12
5 1.2 0.11
6 0.8 0.10
7 1.0 0.09
8 1.1 0.08
9 0.9 0.15
10 1.0 0.10
11 1.0 0.11
12 1.1 0.09
13 0.9 0.10
14 1.0 0.40
15 1.2 0.09
16 0.8 0.08
17 1.0 0.10
18 1.7 0.11
19 0.9 0.09
20 1.0 0.10

Constraints:

  • Use only the provided 20-day data set; do not add outside numbers.
  • Set the control limits at the mean plus and minus two standard deviations of the chlorine residual.
  • Compare each chlorine reading against the usual 0.2-to-2.0 mg/L distribution range, and compare the turbidity readings against the finished-water standard, which requires at least 95 percent of readings at or below 0.3 NTU and none above 1 NTU.
  • The chlorine maximum residual disinfectant level is 4.0 mg/L.

Final deliverable: A one-page compliance memo to the fictional Vireo Lake Water Board, plus a labeled control chart, stating whether the process is in statistical control and whether any day broke a regulatory limit.

Milestones

  1. Session 1 (Organize and summarize): Compute the mean, median, and standard deviation of the 20 chlorine-residual readings, and draw a histogram of them. Output: a summary-statistics table and a labeled histogram.
  2. Session 2 (Build the control chart): Plot the 20 chlorine readings in day order, draw the center line at the mean, and draw upper and lower control limits at the mean plus and minus two standard deviations. Output: a labeled control chart.
  3. Session 3 (Flag unusual days): Mark any chlorine reading beyond the control limits or outside the 0.2-to-2.0 mg/L range, and mark any turbidity reading above 0.3 NTU, then check whether the record meets the 95 percent turbidity rule. Add a box plot of the chlorine residuals to check the flagged points as outliers. Output: an annotated chart and a short outlier note.
  4. Session 4 (Report and present): Write the one-page compliance memo to the fictional water board and present the control chart and findings to the class acting as the board. Output: the finished memo and a brief presentation.

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

Rubric
Criterion Emerging Developing Proficient Advanced
Statistics and data display Mean or standard deviation is missing or wrong, and no histogram is shown The summary statistics are computed but the histogram is unlabeled or misread Correct mean, median, and standard deviation, with a clearly labeled histogram All statistics correct and clearly connected to the shape shown in the histogram
Control chart construction No control limits, or limits not based on the mean and standard deviation A chart with a center line but incorrect or unlabeled control limits A labeled chart with a center line and limits at the mean plus and minus two standard deviations A precise, labeled chart that also explains what the limits mean in plain terms
Compliance interpretation No comparison to the regulatory limits Compares to one limit but misses the high chlorine or high turbidity day Correctly flags the out-of-control chlorine day and the day-14 turbidity reading above 0.3 NTU, and checks the record against the 95 percent turbidity rule Flags every unusual day and explains, using the data, which are statistical signals versus regulatory violations
Memo and presentation Memo is incomplete or draws a conclusion the data do not support Memo states a conclusion but gives thin evidence Memo clearly answers the driving question with evidence from the chart Memo answers the question, cites specific days, and recommends a next step the board could take

Differentiation

Support

Provide the mean and standard deviation of the chlorine data already computed so teams can focus on drawing and reading the control chart. Give a partially drawn chart with the axes and center line in place, and a checklist of which limits to add.

Extension

Ask teams to recompute the control limits with the day-18 spike removed, then explain how dropping one unusual point changes the limits and whether that change would hide or reveal a real process problem.

ELL supports

Pre-teach "in control," "limit," "center line," and "compliance" with a simple labeled chart showing points inside and outside a band. Provide a memo template with headed sections (finding, evidence, recommendation) and sentence frames for each so students write shorter, structured entries.