Data Analysis & Statistical Methods Flashcards

Five refractometer readings on a tourmaline are 1.624, 1.625, 1.624, 1.626, and 1.624. What is the mode?

Answer: 1.624

The mode is the value that appears most often, and 1.624 appears three times.

A 2.50 ct sapphire sold for $10,000. What is its price per carat?

Answer: $4,000

Price per carat equals total price divided by carat weight: $10,000 / 2.50 = $4,000.

A sales dataset includes one exceptionally expensive diamond. Which measure of central tendency is least affected by it?

Answer: Median

The median depends only on the middle value, so one extreme outlier barely moves it.

What does a large standard deviation in a set of gemstone price-per-carat figures indicate?

Answer: Prices are widely spread around the average

Standard deviation measures how far values typically fall from the mean.

A stone gives refractive index readings of 1.544 and 1.553. What is its birefringence?

Answer: 0.009

Birefringence is the difference between the highest and lowest RI: 1.553 - 1.544 = 0.009, which is typical of quartz.

Diamond retail prices usually form a right-skewed distribution. How does the mean usually compare to the median?

Answer: The mean is higher than the median

In a right-skewed distribution, a few high values pull the mean above the median.

Three specific gravity readings on a quartz specimen are 2.65, 2.66, and 2.64. What is the range?

Answer: 0.02

Range equals maximum minus minimum: 2.66 - 2.64 = 0.02.