Measuring Seedling Heights
Priya is measuring the height of five bean seedlings for a class investigation. She rests a plastic ruler on the rim of each pot with her eye about 20 cm to the left of the ruler, and records the number level with the tip of the tallest leaf. Her records are: 4.2 cm, 47 mm, 5.1 cm, 6.0 cm and 4.9 cm. The zero mark on the ruler has worn away, so the 1.0 cm mark sits level with the soil and she records the scale reading directly. Each pot is filled to a different depth below the rim, and one seedling has a bent stem.
1. Identify three sources of error in Priya's measurements. For each, state whether it makes her readings too high, too low, or whether the effect cannot be predicted from the information given.
Read the worked answer
1. Eye 20 cm to the side of the ruler (parallax). The leaf tip appears against a different mark than it would if her eye were level with it. This is a systematic error (same direction every time), but whether it reads high or low depends on which side of the scale the leaf tip sits, so from the description alone the direction cannot be predicted.
2. Worn zero, scale read directly. Because the 1.0 cm mark is at the soil and she writes down the scale number, every reading contains an extra 1.0 cm. All readings are too high by exactly 1.0 cm. This shifts all values equally, so differences between seedlings are still correct.
3. Ruler resting on the pot rim. Pots are filled to different depths, so the gap from rim to soil differs for each pot. Each reading is too high by a different amount, so the sizes of the differences between seedlings are distorted - this is the error that actually ruins the comparison.
A fourth issue: 'height' is not defined for the bent-stemmed seedling (tip of tallest leaf vs. length of stem), so she may be measuring a different quantity in that pot - effect unpredictable.
2. Priya's teacher says the five numbers cannot be compared with each other as they stand. Explain what the teacher means and describe the procedure Priya should use instead.
Read the worked answer
Comparison between seedlings is only valid if the same procedure was applied to each one, so that any error is a fixed offset (which cancels in differences) rather than a varying offset (which does not). The rim-based start point and the bent stem break this rule.
Better procedure:
- Use a ruler with an intact zero, or measure from the 1.0 cm mark and subtract 1.0 cm from every reading.
- Stand the ruler on the soil surface, not the pot rim, in every pot.
- Put her eye level with the top of the seedling before reading.
- Define height as soil surface to the highest point of the plant, using a straight edge across the top.
- Record all values in the same unit (mm is better than cm here, since the ruler is marked in mm).
- Measure every plant at the same time of day and take three readings per plant, averaging them.
3. Why is recording one height as 47 mm a problem when the other four are in centimetres? Support your answer with a calculation.
Read the worked answer
47 mm is the same as 4.7 cm. If the numbers are averaged without converting, the mm value acts like 47 cm and dominates the result.
Unconverted: (4.2 + 47 + 5.1 + 6.0 + 4.9) ÷ 5 = 67.2 ÷ 5 = 13.4 cm. Converted: (42 + 47 + 51 + 60 + 49) ÷ 5 = 249 ÷ 5 = 49.8 mm ≈ 5.0 cm.
The same data gives a mean about 2.7 times too large, purely from a unit mix-up. Mixing units also hides that the 47 mm reading came from a different scale division, so its precision differs from the others. All values must be converted to one unit before any calculation.