Hi, we just started density curves in AP Stats, and I am a little confused about one of the concepts.
It keeps saying that a density curve has to have an area equal to 1 below it...
1 of what?
I don't understand how you figure out if the area of your curve is 1, or what unit this "1" is in...
Sorry, and thanks!
If you understand that density curves are eventually used for calculating probabilities of certain events, they have to be normalized some how. Since the total area under the density represent the probability of all possible events, it would be convenient to normalize the area to unity.
A density curve is just another way of saying a pie chart. Its 100%, a whole. which is alonther word for saying its equal to 1. your different measurements with be equal to different percentages that you will mark in the density curv. All of them comprised will equal t. so for example..a measurement will be 60% of people. you will shade .60 and be left with .40. Together they will equal 1.
make sense?
Yes, I think so. Thanks :)
No problem! I can help explain the concept to you. In statistics, a density curve represents the probability distribution of a continuous random variable. It is used to describe the likelihood of different values occurring within a given range.
When we say that the total area under a density curve is equal to 1, it means that the sum of all probabilities of all possible values within the range is 1. This refers to the probability of all possible outcomes when we consider the entire range of the random variable.
To determine if the area under a specific density curve is equal to 1, you would need to integrate the density function over the entire range of the random variable. The unit of the “1” will depend on the units of the random variable itself. For example, if the random variable represents time in seconds, then the unit of the area under the curve would be seconds.
The area under a density curve can also be interpreted as probability. For instance, if you have a density curve representing the heights of a population, the probability of randomly selecting an individual with a height between a and b is given by the area under the curve between a and b. The probability unit will depend on the units of the random variable and will correspond to the probability scale being used (e.g., decimal, percentage, etc.).
I hope this explanation helps clarify the concept of the total area under a density curve being equal to 1! Let me know if you have any further questions.