Worksheet Grade 12 Science

Bexmoor Lead Sampling: The 90th Percentile Rule

A grade 12 statistics worksheet computing the median, mean, range, and the Lead and Copper Rule 90th percentile from a fictional utility's ten tap samples.

Grade: Grade 12
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

HSS-ID.A.3 Common Core Math

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers.

How this material aligns: Items 8 and 9 ask students to interpret how a single high outlier moves the mean and the 90th percentile, the outlier reasoning this standard names directly.

All materials for HSS-ID.A.3 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Items 1 through 7 keep every value in parts per billion and compare the computed percentile against the regulatory action level in the same unit throughout.

All materials for HSN-Q.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will compute the median, mean, and range of a set of lead tap samples.
Students will find the 90th percentile using the Lead and Copper Rule method and test compliance.
Students will explain how an outlier affects the mean and the 90th percentile.

Vocabulary

Action level: A trigger number in lead and copper testing. If too many homes test above this level, the utility must take steps like improving treatment and telling the public.
Corrosion control: Treatment that keeps water from slowly eating away at the inside of pipes. It helps stop metals like lead from getting into drinking water.

Also: 90th percentile, median, outlier

Teacher overview

Under the Lead and Copper Rule, a utility does not compare every tap sample to the action level; it computes the 90th percentile of its samples and compares that single statistic. This worksheet gives students one monitoring round from a fictional system and walks them through the median, mean, range, and the 90th percentile, then asks them to test the result against both the current 15 ppb action level and the 10 ppb level that arrives in 2027. A common error is treating the 90th percentile as the mean; students should see that the two statistics answer different questions and respond differently to one unusually high home.

Bexmoor Lead Sampling: The 90th Percentile Rule — Grade 12 Science

Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional Bexmoor water system collects lead results from ten household taps in one monitoring round. The values, in parts per billion (ppb), are:

8, 3, 21, 5, 11, 2, 13, 6, 9, 4

The current lead action level is 15 ppb, and it drops to 10 ppb in 2027.

Sort the ten sample values from least to greatest.
Find the median of the ten values.
Find the mean of the ten values. Round to the nearest tenth of a ppb.
Find the range of the sample.
Find the 90th percentile using the Lead and Copper Rule method: multiply the number of samples by 0.9 to get a rank, then read the value at that rank in your sorted list. Report the 90th percentile in ppb.
Compare the 90th percentile to the current 15 ppb action level. Is Bexmoor below the action level, and by how much?
Compare the same 90th percentile to the 2027 action level of 10 ppb. Would Bexmoor meet the stricter future level, and by how much would it pass or exceed it?
Identify the outlier in the sample. State how the mean and the 90th percentile would each change if that one home were removed, without recalculating exactly.
Suppose the 21 ppb home is resampled and the true value is 7 ppb, correcting a bad first reading. Recompute the 90th percentile with 7 ppb in place of 21 ppb.
Explain why the Lead and Copper Rule uses the 90th percentile rather than the mean to judge a system.
Bexmoor's 90th percentile is below the current action level, yet the utility keeps its corrosion-control treatment running. Explain why that decision makes sense.

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

Answer Key

Answer: 2, 3, 4, 5, 6, 8, 9, 11, 13, 21.
Listing the ten values in increasing order gives this sequence.
Answer: 7 ppb.
With ten values, the median is the mean of the 5th and 6th values: (6 + 8) / 2 = 7 ppb.
Answer: 8.2 ppb.
Sum = 2 + 3 + 4 + 5 + 6 + 8 + 9 + 11 + 13 + 21 = 82; 82 / 10 = 8.2 ppb.
Answer: 19 ppb.
Range = 21 - 2 = 19 ppb.
Answer: 13 ppb.
Rank = 10 x 0.9 = 9, so the 90th percentile is the 9th value in the sorted list, which is 13 ppb.
Answer: yes, by 2 ppb.
The 90th percentile of 13 ppb is below the 15 ppb action level, clearing it by 15 - 13 = 2 ppb.
Answer: no, it exceeds 10 ppb by 3 ppb.
The 90th percentile of 13 ppb is above the 2027 action level of 10 ppb, so Bexmoor would exceed the future level by 13 - 10 = 3 ppb.
Answer: The 21 ppb home is the outlier.
Removing it would lower the mean noticeably, because the mean uses every value. The 90th percentile would also drop, since the top of the sorted list changes, though the median near the middle would barely move.
Answer: 11 ppb.
With 7 ppb replacing 21 ppb, the sorted list is 2, 3, 4, 5, 6, 7, 8, 9, 11, 13. The 9th value is 11 ppb, so the 90th percentile falls to 11 ppb, still above the 2027 level.
Answer: The percentile protects most homes rather than averaging risk away.
A mean can look acceptable even when several homes are high, because low homes pull it down. The 90th percentile forces 90 percent of sampled homes to be at or below the limit, so a cluster of elevated homes cannot be hidden by averaging.
Answer: Some homes stay elevated, and the limit is tightening.
A passing 90th percentile still leaves individual homes above the level, and the action level drops to 10 ppb in 2027, which the current 13 ppb result would fail. Keeping corrosion control running protects those homes and prepares the system for the stricter standard.

Differentiation

Support

Provide the sorted list already completed for item 1 so students can focus on the percentile method, and give a worked percentile example with a different five-value data set before item 5.

Extension

Ask students to change one of the ten sample values so that Bexmoor's 90th percentile lands exactly on the 15 ppb action level, and explain which position in the sorted list they had to change to do it.

ELL supports

Pre-teach "percentile," "action level," and "outlier" with a simple number line showing the ten samples as points and the action level as a marked line. Allow students to answer items 10 and 11 using a sentence frame that contrasts the mean and the percentile.

Extensions

Have students find the 90th-percentile lead result reported in a real utility's Consumer Confidence Report, identify how many samples the utility collected, and discuss why larger systems must sample more homes than small ones.