Math 1 · Unit 12 · Lesson 1 · part 3 of 5

Shape: find the tail

The first of the three questions is shape .

Shape: find the tail

The first of the three questions is shape. Look at the dot plot or histogram and find the long tail.

SymmetricThe two sides roughly match, like a mirror. The center is in the middle and both tails are about the same length.

Skewed rightA long tail stretching to the right, toward the big numbers. Most values are low, and a few are much higher.

Skewed leftA long tail stretching to the left, toward the small numbers. Most values are high, and a few are much lower.

The tail tells you the name. Skewed right does not mean the pile is on the right; it means the tail points right. The songs data is skewed right: most students downloaded fewer than 20, and the tail reaches out to 88.

Why does data take these shapes? Think about the context.

Athletes' incomes: skewed right

Most professional athletes earn ordinary salaries, and a few stars earn far more than everyone else. The tail stretches right, toward the giant incomes.

Scores on an easy test: skewed left

Most students score high, near 100, and a few score much lower. The tail stretches left, toward the low scores.

Students' heights: symmetric

Most students are near the middle height, with a few taller and a few shorter, about the same number each way. The two sides match.

Where to go next

Next: Sort the shapesFind the tail. A tail toward the big numbers is skewed right; toward the small numbers, skewed left; two... All the partsPictures of Data and Their Shapes