Graph draft

H1: original paper run; actual bench inputs pending

This is original paper simulation. Do not load liquids, open iodine, use tips or operate a timer from this lesson. The objective still includes the actual run; this practice does not complete it.

The real run needs the teacher’s starch stocks, assigned base concentration, coded sample, exact iodine formulation and Safety Data Sheet. Actual permission, equipment, plate and posted class records are also missing.

Teacher instructions must confirm PPE, eyewash access, spill response, compatible waste collection and cleanup. Do not improvise a reagent-specific response or disposal route from these notes.

The recorded row has six wells but only five transfers: 1 to 2, 2 to 3, 3 to 4, 4 to 5 and 5 to 6. Six halvings would require another well.

The recorded amounts would leave 100 microliters in each sample well before iodine after the stated final discard. One unspecified drop changes final volume; post-iodine concentration is not established.

All concentrations below are nominal starch concentrations before indicator addition. The model assumes an identical effective visual rule for every row. It is not a validated iodine method or instrument detection limit.

E1: half concentration and a declared visual rule

For ideal dilution with no material loss, concentration times volume is conserved during dilution. Equal sample and diluent volumes halve the concentration. OpenStax explains this conservation relationship.

Original rule: a nominal well concentration at or above 1 milligram per liter is called positive, meaning darker than the blank. A value below 1 is called negative, matching the blank.

The threshold T equals 1 milligram per liter only in this invented model. It is not a measured classroom threshold, an actual stock specification or a health limit.

For starting concentration C, wells 1 through 6 have C, C/2, C/4, C/8, C/16 and C/32. The endpoint is the last positive well when calls are monotonic.

Monotonic here means all positives precede all negatives. A positive after a negative breaks this model and must be flagged, not forced into a clean endpoint.

Before reading D1, copy the predicted claim: doubling a start should move an uncensored endpoint one well farther under this ideal rule. Predict the endpoint for an assigned original 8-milligram-per-liter row.

D1: complete original appearance and class-chart records

These are invented records, not actual teams, photographs or measurements. P means darker than the yellow-brown blank; N means matching that blank. All records share an assigned 60-second read point; no reaction took place.

BL contains zero added starch in the model and is yellow-brown. It defines the comparison appearance; it does not prove that every transfer or reagent worked.

Known A starts at 2 milligrams per liter. Wells 1-6: 2, 1, 0.5, 0.25, 0.125, 0.0625. Calls P P N N N N; endpoint 2.

Known B starts at 4 milligrams per liter. Wells: 4, 2, 1, 0.5, 0.25, 0.125. Calls P P P N N N; endpoint 3.

Known C starts at 8 milligrams per liter. Wells: 8, 4, 2, 1, 0.5, 0.25. Calls P P P P N N; endpoint 4.

Known D starts at 16 milligrams per liter. Wells: 16, 8, 4, 2, 1, 0.5. Calls P P P P P N; endpoint 5.

Repeat C2 has the same nominal 8-milligram-per-liter row as C. Its supplied calls are P P P N N N; endpoint 3. This deliberately anomalous record disagrees with the ideal rule; no cause is established.

Repeat C3 has the same nominal 8-milligram-per-liter row as C. Calls P P P P N N; endpoint 4. Retain all three 8-level records separately.

Coded unknown U has no revealed starting concentration. U1-U6 calls are P P P P N N; endpoint 4. Its concentrations remain U, U/2, U/4, U/8, U/16 and U/32 until constrained by the model.

The complete pooled chart is A:(2,2), B:(4,3), C:(8,4), D:(16,5), C2:(8,3), C3:(8,4). Each pair is start in milligrams per liter, then endpoint well number. Do not average or delete the flagged row.

E2: choose axes that match the doubling structure

The known starting concentration is the independent variable. Endpoint well number is the dependent variable. Use a scatter plot for their relationship, with concentration on the horizontal axis and endpoint on the vertical axis.

Equally spaced starting values 2, 4, 8 and 16 are not equal numerical gaps. Use a base-two logarithmic horizontal scale, or a linearized doubling-index axis.

For our linearized axis, x equals log2(C/T), where T is 1 milligram per liter. The ratio has no units. Calculate x for each of the four starts.

Log2 names the power of two giving that ratio. For example, 128/1 equals 2 to the seventh power, so log2(128/1) is 7. Write both the index and its concentration equivalent at each tick.

Plot all six records from D1. Where two records share one position, mark it as two records. Plot and flag C2.

The four ideal reference anchors A-D lie on one straight line. Write its rule in terms of e and x, and draw that reference segment only from the lowest to the highest anchor x. It is not a fit claiming every pooled record agrees.

Actual endpoint is a stepwise category: a band of concentrations can have the same endpoint. The straight anchor line is a reading guide, not proof of continuous exact concentration or a validated regression.

Your graph is today’s product, so no finished graph is shown; E2 and D1 supply every axis rule and plotted record. Do not draw a straight reference line on evenly spaced numerical concentration values and call it the same model.

E3: recover an interval, including censored cases

For an interior endpoint e, the last positive gives C / 2^(e - 1) >= T. The next negative gives C / 2^e < T. Here ^ means raised to a power.

Together, T * 2^(e - 1) <= C < T * 2^e. The star means multiplication. The lower bound is included; the upper bound is excluded.

For U, substitute its endpoint e and T=1 into these bounds. Mark the lower-bound anchor on the line and label the full interval; do not report an exact U value.

The upper bound is twice the lower bound. This is a multiplicative window, not a plus-or-minus range or a symmetric error bar around the lower bound.

The interval depends on an ideal threshold and correct calls. C2 shows disagreement, so a real pooled experiment could be less certain. Do not claim this is a statistical confidence interval.

Endpoint 0 means no well is positive. Use well 1’s call and threshold T to write the one-sided bound on the start; it need not be zero.

Endpoint 6 means the last available well is positive. Use well 6’s call and threshold T to write the lower bound; no next negative sets an upper bound. Do not invent endpoint 7.

Your lowest and highest known starts set the calibrated range. Do not extrapolate the reference line for endpoints 0 or 6. Those are model boundary checks, not calibrated unknown estimates.

R1: keep variation and limitations visible

NIST describes calibration as relating measurement scales and requiring uncertainty assessment. The ideal original line here illustrates that idea; it is not a laboratory calibration certificate.

C2 is a candidate outlier relative to the ideal anchors. Retain and flag it. Mixing, transfer volume, labeling or visual scoring are possible explanations, not established causes.

Reusing a tip can carry material forward; it does not guarantee a shift of exactly one well. Unequal indicator drops or read times may change comparability even with fresh tips.

At the 8 level, find the observed minimum and maximum of the three endpoints. You may show this range if labeled as three original records, not a confidence interval.

Other known levels have one record each. They cannot establish repeatability or precision by themselves. Do not invent error bars for unreplicated levels.

Write a trend sentence that says how endpoint changes as the known start doubles, followed by because the data shows and specific D1 pairs. Then state that the flagged repeat limits agreement.

The simulated association and model do not prove a real causal effect or a human health result. Actual interteam evidence needs matched methods, records and teacher review.

Q1: graph choices and a complete time-series check

Warmup 1 asks about water samples taken each week for ten weeks. Week is an ordered time variable; use a line or connected points to emphasize change. Warmup 2 asks for a title, axis labels, units or a readable scale.

No real Cleveland lead chart is supplied. Use this original arithmetic example instead: bars for 9 and 11 starting at 8 have visible lengths 1 and 3. Their values did not triple.

The exact self-check asks: Your data is monthly air-quality readings for one year. A classmate plots them as a bar chart with the y-axis starting at 40. Name the two problems and fix them.

Original twelve-month PM2.5 inputs, in micrograms per cubic meter: Jan 42, Feb 44, Mar 43, Apr 45, May 47, Jun 46, Jul 48, Aug 50, Sep 49, Oct 47, Nov 46, Dec 45. These are invented monthly averages, not Cleveland data.

V2 supplies the truncated bars and a clear line version with the same twelve values. The bars encode lengths from 40 and exaggerate relative sizes. Rebuild bars from zero, or use a clearly labeled line chart.

Graph type is the other decision to explain, not an automatic error. Monthly columns can validly compare levels; a line emphasizes the sequence. Defend the choice using the intended message.

Line and scatter axes need not always start at zero, but their scale must be clear. Broken bar axes do not repair misleading bar lengths. ONS recommends zero baselines for bars.

For extension, plot the same monthly values as zero-based columns and as a line; compare what a skeptical reader learns. Identify the overall rise to August and later fall without inventing a cause.

A recovery graph can start with five or six points. D1 supplies six records, so that small graph can still include the full original calibration dataset and unknown interval.

P1: authentic run, async and official work

If actual class endpoint records are posted, use them for the assigned asynchronous graph and uncertainty sentence. They require the actual stock, blank, method and coded unknown inputs. The D1 route is labeled recovery, not that class record.

Keep your predicted claim, assigned known, known endpoint, BL result, all pooled records, titled graph, unknown interval and one interteam limitation in one record. A graph alone is incomplete.

Today, open Activity 4.1.3 Testing the Waters and draft the graph in Data Tables as the current Problem 4 graphing activity. Confirm the exact assigned portion and portfolio route with your teacher.

The 4.1.3 procedure uses eleven tests on two waters, its Student Resource Sheet, actual results, health-effects notes, research and peer/remediation comparison. This starch endpoint practice does not replace that procedure.

The actual iodine formulation, stock concentrations, water-test match and blank are teacher inputs. No earlier practice series is a validated detection limit for this run.

April 15 is the next class day. No actual U concentration or reveal is supplied, and any later practice value stays separate from a real sample result.

April 12 L1 was a separate six-halving illustration. This six-well row has five halvings. Your teacher will confirm when any bench work happens; do not add a well or assume permission.

Submit the endpoint table and graph only through the teacher-confirmed enrolled BI section and current Problem 4 portfolio. Open the linked BI assignment and check its posted requirements and deadline. Save the same full original record if unavailable and record pending status.

Predict and check readiness

Read H1 and answer both Q1 warmups. Copy the ideal doubling claim and predict known C before reading D1.

The actual laboratory branch remains pending. Six wells provide five halvings.

Build the complete endpoint record

Label K1-K6, U1-U6 and BL. Copy or calculate the four known concentration rows, all six pooled records and U calls. Identify variables and control meaning.

D1 supplies every original value and call. Unknown concentrations stay symbolic; no real reveal is invented.

Draft the calibration graph

Use E2 and D1 to plot every pooled record with titled/scaled axes, source status and C2 flag. Explain the doubling-index ticks and ideal reference line.

Keep both overlapping records visible by their count. Do not treat a straight line as an exact continuous endpoint law.

Mark the unknown and limits

Mark U on the guide and write its full included/excluded interval, factor-of-two width and interteam limitation. Explain endpoints 0 and 6 as E3 boundary checks.

State the ideal-rule condition and observed disagreement. These limits are not a statistical confidence interval.

Defend graph choices and outliers

Write the trend and because-the-data-shows claim with a causal limit. Answer Q1 and flag rather than delete C2.

Use all twelve monthly values for the Q1 graph comparison. If ready, produce zero-based columns and line versions and defend their different messages.

Preserve original and actual status

Check the entire product and P1. Use actual posted class records for the async task when available; otherwise label the full D1 recovery.

Keep table, prediction, blank, graph, U interval, source and interteam limitation together. Actual stocks, SDS, run, official work and route remain pending.