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Worksheet Grade 11 Art & Music

Redbank Well Nitrate Chart: Choosing an Axis Origin

Grade 11 students size bars for a fictional utility's nitrate chart, compare a zero baseline with a cut axis, and judge a newsletter claim built on the cut version.

Objectives

  1. Students will compare the center and spread of two sampling records.
  2. Students will calculate bar lengths for a stated axis range and column width.
  3. Students will explain how moving a chart's origin changes the comparison a reader makes.

Vocabulary

Key words: axis origin, baseline, encoding, column width, cut axis

Teacher overview

Community water systems publish an annual water quality report, and most readers take its charts at face value rather than working back to the sampling tables. This worksheet gives students that design decision, using a fictional utility, the Redbank Water District, and two of its monitoring wells. Students compute the summary statistics, size the bars for a chart with a zero baseline, then rebuild the same chart with the axis cut and compare what a reader takes away. The misconception addressed directly is that a cut axis is only a matter of taste, when in fact it changes the ratio a reader sees between two bars.

Redbank Well Nitrate Chart: Choosing an Axis Origin — Grade 11 Art & Music
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Redbank Water District samples nitrate at two wells four times a year. The readings are given in milligrams per liter.

Reading Well North Well South
January 3.2 2.0
April 3.6 2.4
July 4.4 5.6
October 3.8 4.0

The chart runs in a report column 90 mm wide. Bars are drawn horizontally, so a bar's length is measured along that 90 mm.

  1. What is the mean of the four Well North readings?
  2. What is the mean of the four Well South readings?
  3. What is the range of the four Well North readings?
  4. What is the range of the four Well South readings?
  5. The first draft runs the axis from 0 to 6.0 across the full 90 mm. How many millimeters represent one milligram per liter?
  6. Using the scale from item 5, how long is the bar for the Well South July reading?
  7. Using the same scale, how long is the bar for the Well North January reading?
  8. Divide the bar from item 6 by the bar from item 7. What ratio does a reader see?
  9. The second draft cuts the axis so it runs from 3.0 to 6.0, still across 90 mm. How many millimeters now represent one milligram per liter?
  10. On the cut axis, how long are the bars for the Well South July reading and the Well North January reading?
  11. Divide the longer bar from item 10 by the shorter one. What ratio does a reader see on the cut chart?
  12. Compare your answers to items 8 and 11. Explain what a reader gets wrong from the cut chart.
  13. A district newsletter runs the cut chart with the sentence "Nitrate at Well South is many times the level at Well North." Judge that sentence against the table. Say whether the data supports it and why.

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: 3.75 mg/L. The four Well North readings sum to 15.0, and 15.0 divided by 4 is 3.75.
  2. Answer: 3.5 mg/L. The four Well South readings sum to 14.0, and 14.0 divided by 4 is 3.5.
  3. Answer: 1.2 mg/L. The largest Well North reading is 4.4 and the smallest is 3.2, and 4.4 minus 3.2 is 1.2.
  4. Answer: 3.6 mg/L. The largest Well South reading is 5.6 and the smallest is 2.0, and 5.6 minus 2.0 is 3.6.
  5. Answer: 15 mm. The axis covers 6.0 across 90 mm, and 90 divided by 6.0 is 15 mm for each unit.
  6. Answer: 84 mm. Multiplying the 5.6 reading by 15 mm per unit gives 84 mm.
  7. Answer: 48 mm. Multiplying the 3.2 reading by 15 mm per unit gives 48 mm.
  8. Answer: 1.75. Dividing 84 mm by 48 mm gives 1.75, which matches 5.6 divided by 3.2.
  9. Answer: 30 mm. The cut axis covers 3.0 across the same 90 mm, and 90 divided by 3.0 is 30 mm for each unit.
  10. Answer: 78 mm and 6 mm. The July reading sits 2.6 above the new origin, and 2.6 times 30 is 78 mm. The January reading sits 0.2 above it, and 0.2 times 30 is 6 mm.
  11. Answer: 13. Dividing 78 mm by 6 mm gives 13.
  12. Answer: The reader sees a ratio of 13 where the data holds a ratio of 1.75. Bar length is read as quantity, so cutting the axis at 3.0 hides the shared portion of both readings and leaves only the difference on the page. The chart then reports a gap between the two wells that the samples never showed.
  13. Answer: The data does not support it. The two means, 3.75 and 3.5, are close, and Well South is higher than Well North in only two of the four readings. What the table does show is a wider spread at Well South, whose range of 3.6 is three times the 1.2 range at Well North. An honest sentence would describe the swing across the year rather than a difference in level.

Differentiation

Support

Provide the two column sums already computed for items 1 and 2, and a printed strip of the axis marked at every half unit so students can measure item 6 and item 7 rather than multiply. Work item 5 with a small group first, since every later bar length depends on it. Allow calculators throughout.

Extension

Ask students to design a third version of the chart that keeps the zero baseline yet still makes the wider swing at one well easy to see. They may add a range marker, a second small chart, or a plotted line, and they must state in writing which encoding carries the spread and why the zero baseline stays. Require one sentence naming what their version gives up in exchange.

ELL supports

Pre-teach axis, origin, baseline, and range against a printed chart with each term labeled on the drawing, and leave it posted. Provide a bilingual card pairing the words mean, range, and length with a small diagram. Allow items 12 and 13 to be answered with two labeled sketches and a short phrase, and offer the frame "The cut chart makes the reader think that ___."

Extensions

Have students redraw the chart as a grouped display with all eight readings shown in time order, then write a two-sentence caption for the report. The caption should state what the chart shows without repeating what the reader can already measure. Discuss why a caption that argues a point sits uneasily in a compliance report, and where a utility would put that argument instead.