Digital SATMath: Problem-Solving and Data AnalysisMedium
A scientist is testing a new fertilizer on a crop. She records the yield (in kg) for two plots: Plot A with fertilizer and Plot B without. After 10 harvests, the mean yield for Plot A was 50 kg with a standard deviation of 5 kg, and for Plot B was 45 kg with a standard deviation of 2 kg. Which of the following statements is best supported by the data?
- AThe difference in mean yields is not statistically significant.
- BThe fertilizer had a positive effect on the mean yield, but Plot B's yields were more consistent.
- CPlot B's maximum yield was definitely higher than Plot A's minimum yield.
- DPlot A consistently produced higher yields than Plot B.
Show answer & explanationAnswer & explanation
Correct answer: B. The fertilizer had a positive effect on the mean yield, but Plot B's yields were more consistent.
Plot A has a higher mean (50 kg vs 45 kg), suggesting a positive effect on yield. Plot B has a smaller standard deviation (2 kg vs 5 kg), indicating its yields were less spread out and thus more consistent.
Why the other options are wrong
- A. Without knowing the sample size (10 harvests is small but not enough to judge significance definitively without a statistical test) or performing a t-test, we cannot conclude statistical significance from just means and standard deviations.
- C. Standard deviation only describes spread around the mean, not absolute min/max values. We cannot make definitive claims about specific min/max yields without more data.
- D. While Plot A has a higher mean, its higher standard deviation means there could be individual harvests where Plot B yielded more than Plot A, so 'consistently' is too strong a claim.
Interpreting Mean and Standard Deviation
The mean provides the average value of a dataset, while the standard deviation measures the typical spread or variability of data points around that mean.
- Higher mean indicates a larger average value.
- Lower standard deviation indicates greater consistency or less spread.
- Standard deviation is sensitive to outliers.
Memory trick: Mean is the center, Std Dev is how far points stray.