Data Analysis & Statistical Methods Flashcards

Repeated refractometer readings on a calibration standard cluster tightly but are all 0.005 above the known value. How should the readings be described?

Answer: Precise but not accurate

Tight clustering shows precision, while a consistent offset from the true value shows inaccuracy.

Which of the following is an example of systematic error in gem testing?

Answer: An uncalibrated carat scale that always reads high

Systematic error biases every measurement in the same direction, as an uncalibrated instrument does.

How is the coefficient of variation calculated?

Answer: Standard deviation divided by the mean

CV = SD / mean, often expressed as a percentage, so you can compare variability across datasets with different scales.

In a normal distribution, about what percentage of values fall within one standard deviation of the mean?

Answer: 68%

The empirical rule gives roughly 68%, 95%, and 99.7% within 1, 2, and 3 standard deviations.

Emerald prices for a grade have a mean of $5,000 per carat and a standard deviation of $500. What is the z-score of a $6,000 per carat stone?

Answer: 2.0

z = (6,000 - 5,000) / 500 = 2.0.

Under the common diamond-trade weight rounding convention, how is a stone weighing 0.996 ct reported?

Answer: 0.99 ct

Carat weight is truncated to two decimals unless the third decimal is 9, in which case it rounds up, so 0.996 stays 0.99 and 0.999 becomes 1.00.

A parcel contains one 1.00 ct stone priced at $1,000 per carat and one 2.00 ct stone priced at $2,000 per carat. What is the weighted average price per carat?

Answer: $1,666.67

Total value is $5,000 for 3.00 ct, which gives $1,666.67 per carat.