# Statistics probelm

1. Sep 11, 2006

### MeatyDumplings

in population density graphs, the median is known to be the line where it splits the graph into two equal sections. And the mean, according to the textbook, is the 'balancing point" of the graph. What exactly is this "balancing point"? what are its properties and how do i calculate the coordinate/location?

sorry if this is in the wrong section, the Statistics section says not to post homework probelms there...

2. Sep 12, 2006

### Gokul43201

Staff Emeritus
What's on the x-axis?

The mean is the flat line drawn such that the (rectangular) area to the left of it equals the area to the left of the density curve.

Last edited: Sep 12, 2006
3. Sep 12, 2006

### MeatyDumplings

the density cirve looks like this, some line intersecting the x-axis at (x, 0) is the mean

4. Sep 12, 2006

### Gokul43201

Staff Emeritus
What do the axes represent?

5. Sep 12, 2006

### HallsofIvy

Staff Emeritus
Assuming that x (taking on values from 0 to b) is some random variable and y (taking on values of 0 to a) is the probability density, you can think of "probability density" as if it were a real "weight density". The "balancing point" would be where the total weight (integral of density) is the same on both sides. If the total weight were one, that would mean that the weight on each side of the balancing point would be 1/2. You are looking for x such that
$$\int_0^x f(t)dt= \int_x^b f(t)dt= \frac{1}{2}$$.