The following lesson summarizes the topics of central tendency including mean, median, mode, and range. Additional lesson units in the math toolbox provide additional detail and related exercises.

### DO YOU KNOW ANY GOOD SHORT CUTS TO CALCULATING THE MEAN?

#### Khan Academy (Mean, Median, Mode)

Mean/Median/Mode

Approximately 5 minutes video.

Range

Approximately 5 minutes video.

Histograms

Approximately 5 minutes video.

Pie Charts and Other

Approximately 5 minutes video.

#### Eratosthenes Part 5

Part 1 begins on the Introduction lesson page. This is the final part.

# The Story of Eratosthenes – Critical Thinking Adventure Part 5

Designing the experiment on the east coast with similar tools available to Eratosthenes may prove challenging. Unlike the flat desert, the terrain on the east coast is defined by hills and valleys and enormous variation all of which do not match the ideal surface of a sphere. Even if distance could be accurately assessed, you will have the challenge of finding level surfaces. Two points along the ocean might be more ideal than the desert, but alas the meridional lines tend inland and not along the coasts. The plains, midwest might be better suited for the effort.

The next question is what equipment did you consider using? Did Eratosthenes use a vertical stick as employed in our theoretical thought experiment earlier? Of course not. Not literally. He used a sundial and not just any sundial. He used the best astronomical equipment at the time which was a graduated skaphe or sundial with a hemispherical bowl and graduated meridian. Not only were no other methods better for centuries to come (and many were worse), this is the prototype for what is used today. His choice of equipment to eliminate some of the potential problems with measurements contributed in no small part to his accurate results.

In all, Eratosthenes was a clever scientist with some excellent ideas, but his success was not solely the result of his ideas, but in large part due to carefully designed, constructed, and executed experiments—all part of the scientific method in practice. He also stood on the shoulders of giants as Newton would remark about his own accomplishments many centuries after Eratosthenes’ time. Eratosthenes lived in a period that was ripe for intellectual advances from Pythagoras in 6th century B.C. through Plato and Aristotle right into 3rd century B.C. Eratosthenes used his education to put himself in a position of seniority at an intellectual hub in Alexandria working with other creative geniuses like Archimedes, and, with direct access to the greats of previous centuries, he used that opportunity to make his own mark. Can you draw parallels to the current day and age and the opportunity offered by educational institutions like the specialized high schools?