CGC Data Analysis & Statistical Methods 4

Question 1

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

Accepted Answer

Precise but not accurate

Answer

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

Question 2

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

Accepted Answer

An uncalibrated carat scale that always reads high

Answer

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

Question 3

How is the coefficient of variation calculated?

Accepted Answer

Standard deviation divided by the mean

Answer

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

Question 4

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

Accepted Answer

68%

Answer

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

Question 5

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?

Accepted Answer

2.0

Answer

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

CGC - Certified Gemstone Consultant Practice Test

CGC - Certified Gemstone Consultant Practice Test

CGC Data Analysis & Statistical Methods 4