Math  /  Data & Statistics

QuestionDescribe what the mean absolute deviation of the maximum speed of 8 roller coasters represents.

Studdy Solution

STEP 1

What is this asking? We need to explain what the mean absolute deviation (MAD) *means* in the context of the maximum speeds of a group of 8 roller coasters. Watch out! Don't confuse MAD with other measures of spread, like standard deviation or range!

STEP 2

1. Define Mean Absolute Deviation
2. Relate to Roller Coasters

STEP 3

Let's break down what "Mean Absolute Deviation" actually means.
It's all about how spread out a set of numbers is!
Imagine you have a bunch of numbers, like the ages of students in a class.
The MAD tells you, on average, how far each age is from the average age of the whole class.

STEP 4

Let's say the average speed of our **8 roller coasters** is x\overline{x}.
To calculate the MAD, we first find the *difference* between each roller coaster's maximum speed and x\overline{x}, and take the absolute value.
This gives us the *deviation* of each speed from the average speed.

STEP 5

Why absolute value?
Because we only care about how *far* each speed is from the average, not whether it's higher or lower.
So, whether a coaster is \(10 mph faster or \(10 mph slower than the average, the deviation is still just \(10 mph!

STEP 6

Then, we find the *mean* (average) of all these absolute deviations.
This gives us the **MAD**, which represents the average distance of each roller coaster's maximum speed from the average maximum speed.

STEP 7

Now, let's apply this to our roller coasters.
We have **8 roller coasters**, and we're looking at their **maximum speeds**.
The MAD of these speeds tells us how spread out those maximum speeds are.

STEP 8

A *small* MAD means the maximum speeds are clustered close to the average.
Imagine a bunch of roller coasters all going roughly the same top speed – maybe they're all pretty tame family rides.

STEP 9

A *large* MAD means the maximum speeds are more spread out.
This could mean you have a mix of super-fast thrill rides and slower, gentler coasters in your group of eight.

STEP 10

The mean absolute deviation of the maximum speed of 8 roller coasters represents the average distance of each roller coaster's maximum speed from the average maximum speed of all 8 roller coasters.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord