how would you find the median of a pdf picture

it basically is a triangle with points
(0,0)
(6,.2)
(10,0)

do i need to find the slopes to find equations for the lines?
thanks!

A triangle has three medians. You get them by drawing straight lines from each vertex to the midpoint of the opposite side. They intersect at the centroid.

http://www.mathwords.com/m/median_of_a_triangle.htm

One median goes from (6,2) to (5,0)

To find the median of a probability density function (PDF) graph, you don't need to find the slopes or equations of the lines in this case. The median can be found by considering the area under the PDF curve.

Here's how you can find the median of the given PDF graph:

1. Determine the base of the triangle: In this case, the base of the triangle is the line segment connecting the points (0,0) and (10,0). The length of the base is 10 - 0 = 10 units.

2. Find the midpoint of the base: To find the midpoint of the base, you can take the average of the x-coordinates of the two endpoints. In this case, the midpoint is (0 + 10)/2 = 5 units.

3. Find the height of the triangle: The height of the triangle represents the highest point on the PDF curve, which is the point (6, 0.2).

4. Calculate the area of the triangle: The area of the triangle can be calculated using the formula: Area = (base * height) / 2. In this case, the area is (10 * 0.2) / 2 = 1 unit.

5. Calculate the median: The median is the x-coordinate of the point on the base that divides the area of the triangle in half. Since the area of the triangle is 1 unit, the median is the x-coordinate of the point on the base that has an area of 0.5 units.

To find this point, divide the area of the triangle by 2 and divide the result by the length of the base. In this case, (0.5 * 10) / 2 = 2.5 units.

Therefore, the median of the given PDF graph is located at x = 5 + 2.5 = 7.5 units.

No need to find slopes or equations for the lines in this case, as the median is determined by considering the area under the curve.