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Calculating Water Contaminant Percentiles: Lead and Copper Examples, Study notes of Elementary Mathematics

How to calculate the 90th percentile of lead and copper contaminant levels in drinking water, using examples of 10 and 5 samples respectively. The document also covers different methods for calculating percentiles based on the number of samples collected.

What you will learn

  • How do you calculate the 90th percentile result for a system that collects more than 5 samples?
  • How do you calculate the Copper 90th percentile using interpolation?
  • What is the 90th percentile value for lead in a system with 10 samples?

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2021/2022

Uploaded on 09/12/2022

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Drinking Water Section
Calculating 90th Percentiles
How do you calculate the 90th percentile
result?
For systems collecting more than 5 samples;
Place Lead or Copper results in ascending
order.
Assign each sample a number, 1 for the
lowest value and rank.
Multiply the total number of samples
collected by 0.9
Example: 20 samples X 0.9 = 18
Therefore, the 18th highest ranked result
is the 90th percentile sample to be
compared to the Action Level.
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Download Calculating Water Contaminant Percentiles: Lead and Copper Examples and more Study notes Elementary Mathematics in PDF only on Docsity!

Calculating 90

Percentiles

• How do you calculate the 90

th

percentile

result?

– For systems collecting more than 5 samples;

• Place Lead or Copper results in ascending

order.

• Assign each sample a number, 1 for the

lowest value and rank.

• Multiply the total number of samples

collected by 0.

– Example: 20 samples X 0.9 = 18

– Therefore, the 18

th

highest ranked result

is the 90

th

percentile sample to be

compared to the Action Level.

Calculate the Lead 90

Percentile

10 samples collected

Site 1: 0.005 mg/L Site 2: 0.015 mg/L Site 3: 0.005 mg/L Site 4: 0.014 mg/L Site 5: 0.017 mg/L What is the 90 th percentile value? Site 6: 0.005 mg/L Site 7: 0.011 mg/L Site 8: 0.002 mg/L Site 9: 0.018 mg/L Site 10: 0.004 mg/L

Calculating 90

Percentiles

• Calculating 90

th

percentile result for system that

collected 5 samples:

– Rank results in ascending order and assign a

number to each with 1 being the lowest rank.

– Calculate the average of the 4

th

highest and

5th highest ranked results.

– The result of which is then compared to the

Action Level.

Calculating 90

Percentiles

Calculate the Lead 90 th Percentile 5 samples collected Order and Rank lead results from lowest to highest: Rank 1 – 0.001 mg/L. Rank 2 – 0.003 mg/L Rank 3 – 0.005 mg/L Rank 4 – 0.012 mg/L Rank 5 – 0.026 mg/L Multiply the number of samples by 0.9 : 0.9 X 5 samples = 4.5. Therefore, calculate the average of the 4 th (0.012) and 5 th (0.026) highest ranked result to get the 90 th percentile result to compare to the Action Level. 0.012 mg/L + 0.026 mg/L = 0.019 mg/L 2 Lead 90th percentile = 0.019 mg/l (Action Level is 0.015 mg/l)

percentile

Interpolation Calculation

Calculate the Copper 90 th percentile 7 samples collected Interpolate: 0.9 X 7 samples = 6.3. Therefore, interpolate to get the 90 th percentile result to compare to the Action Level.

  • Rank 1 – Result = 1.17 mg/l
  • Rank 2 – Result = 1.19 mg/l
  • Rank 3 – Result = 1.34 mg/l
  • Rank 4 – Result = 1.51 mg/l
  • Rank 5 – Result = 1.57 mg/l
  • Rank 6 – Result = 1.73 mg/l
  • Rank 7 – Result = 1.95 mg/l

percentile

Interpolation Calculation

Calculate the Copper 90 th percentile 7 samples ( th %) = 6.3 ranked sample First, subtract the difference between the 6 th (1.73) & 7th (1.95) ranks. 1.95 – 1.73 = 0. Second, multiply the answer by 0.3 since the 90 th percentile is 0.3 higher than the 6 th ranked result in this case. 0.22 x 0.3 = 0. Next, add 0.066 to the 6 th ranked result (1.73). 1.73 + 0.066 = 1.8 mg/l Copper 90 th percentile = 1.8 mg/l (Action Level is 1.3 mg/l)