The 95-minute beaker: an outlier that should not be deleted
Class VIII science at a mandal headquarters school has 40 students, three identical 250 mL beakers, one electronic balance that reads to the nearest gram, and no thermometer. For a lesson on factors affecting evaporation, the teacher asks eight groups each to put 20 mL of water in "a vessel", leave it wherever they like in the room, and time how long it takes to disappear. The results, in minutes, are: 35, 42, 38, 95, 40, 37, 44, 36. Group 4, which recorded 95, used a tall narrow test tube and kept it in a shaded corner. In the debrief, one student says, "Evaporation time is just random, sir"; another says, "Delete the 95, it is wrong"; a third asks whether the result would be the same on a rainy day. The teacher has one more period before the unit test, which contains a question on interpreting a data table.
1. Interpret the class data, identify the design flaws in the practical, and explain why silently deleting the 95 would be the wrong move even though it does not fit.
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Treat the numbers first. Sum of the eight times is 367, so the mean is about 45.9 minutes; the median is 39 minutes (the middle two values are 38 and 40); the range is 60 minutes, from 35 to 95. The mean is being pulled away from the typical result by one value - a useful, concrete lesson in why the mean alone can mislead.
Design flaws. (1) The teacher varied several things at once: vessel shape and surface area, position in the room (draught, sunlight, shade), and possibly water temperature. Group 4 used a narrow test tube in a shaded corner, which reduces surface area and air movement - so 95 minutes may be a perfectly correct measurement of a different set-up. (2) The wording "a vessel" and "wherever they like" made the variation invisible on the data sheet, so the class cannot interpret the table at all. (3) Measurement precision: 20 mL of water is about 20 g, and a balance reading to 1 g gives roughly 5% resolution, so small differences between groups would be invisible; "time to disappear completely" is also hard to judge consistently.
Why not delete the 95. Deleting data because it is inconvenient teaches students to hide evidence, which is the opposite of scientific practice. The defensible move is to record the conditions, show that the outlier came from a different set-up, and use it as the entry point to fair testing. Data may be excluded only with a recorded reason (equipment fault, wrong procedure), and the original value should still be reported.
2. Plan the next period as a fair test using the available resources, and show how you would use mean, range and a graph to make the reasoning visible to students.
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Question: does surface area change how fast water evaporates? Keep everything else the same: 20 mL of water, same position on the same table, same time of day, same vessel material.
Groups and replicates. Six groups, each doing two trials of the same set-up so that the class sees the idea of repeatability. Three set-ups are compared: a beaker, a beaker with a paper fan held at a fixed distance for one minute every five minutes, and a wider shallow dish if one can be borrowed. This gives one changed variable at a time.
Measurement. Use the balance: record mass lost every 10 minutes for 40 minutes, rather than time to complete drying. The mass-loss readings are more precise than a stopwatch judgement.
Maths made visible. Build a class table with every reading, then compute the mean of the two trials per set-up and the range within each set-up as a measure of reliability - a large range means "we need more trials before we trust this". Plot mass lost (g) against time (min) for each set-up on one graph; the steeper line is the faster rate. Discuss the third student's question explicitly: humidity and temperature are variables we are not controlling today, so the result is conditional on today's weather, and repeating on a rainy day is a genuine test, not a distraction.
3. What formative assessment questions would you use before the unit test, and how would you answer the student who wants to "delete the 95"?
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Questions that require reasoning, not recall:
- "Two groups measured 30 and 42 minutes for what they thought was the same set-up. Give two possible reasons, and say which one you could control next time."
- "You have a balance reading to 1 g and 20 mL of water. Is a 1 g difference between two groups a real difference or measurement noise? Explain."
- "Here is a table with one value far from the rest. List three things you would check before deciding the result is wrong."
- "A student says the result will change on a rainy day. Which variable is she describing, and how would you test it?"
Answering the "delete the 95" student: don't overrule; ask what the group actually did. When the test tube and shaded corner come out, the class can see the value is a valid measurement of a different set-up, not a mistake. Then set the rule together: we record every reading, we note the conditions, and we exclude a value only with a documented reason - and even then we report the original. Close by returning to the first student: "random" is what data look like when variables are uncontrolled; control them and the pattern appears. This links directly to the unit-test table-interpretation question.