i'm still struggling with the median? help please?

Question

click the lick below and scroll the histogram where it says "best estimate for the median".
http://cs.uni.edu/~campbell/stat/histrev.html
can somebody please explain how they got the answer?

well, i know that but how do they do it mathematically?

Answer 1

The third guy has a pretty good answer, but I thought I would fill in a few details. This is pretty tricky -- it took me awhile to figure it out. The total area of the histogram is 1375, so the median is the value of x such that eaxactly half of the area, or 687.5, is to the left (and to the right). There is no really slick way to find this other than just walking from left to right until you find the bar that contains the median and figuring or where it is in that block.

Since the first three bars have areas of 25*10 = 250, 25*12 = 300, and 25*20 = 500, you know the median 687.5 lies between 550 and 1000 and is this in the middle bar. The first two bars have area 550, so we the median is the value of x such that 687.5-550 = 137.5 area of the middle bar is to the left of x. Since the bar is of height 20, we know that the width of the portion of the middle bar that is to the left of the median is (687.5-550)/20 = 6.875. So the median is 6.875 to the right of the left edge of the middle bar. So, since the left edge of the middle bar is at 137.5 (halfway in between 125 and 150), the median is at 137.5 + 6.875 = 144.375.

I hope that helped!

Answer 2

THe median is defined as the middle value of a given set of data. Suppose you have 15 values in numerical order within a certain set, the 8th value (the middle value) will be the median.

In the example given, the median is estimated by finding the location on the histogram at which the area beneath the histogram on teh left is equal to the area of the histogram on teh right. Thereby having the "middle" value, or the median...

"In probability theory and statistics, a median is a number dividing the higher half of a sample, a population, or a probability distribution from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there are an even number of observations, one often takes the mean of the two middle values.

At most, half the population have values less than the median and at most half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median."

Answer 3

i'm not quite sure what this refers to, probably a distribution of data.
the median is calculated by using the area of each block representing the occurrence of data.
the idea is to divide the middle block so that on each side you have the same amount of data (the sum of all left side areas = the sum of all right side areas).
by calculating the areas of the blocks you should be able to get to the difference between the total area on the left and the total area on the right side.
use this difference to divide the middle block, by giving each side the amount it's needed. this will give you two blocks (like the green and pink in the histogram) that you can use to find the coordinate of the median point, after adding all the bottom coordinates of the left side blocks and the coordinate of the beginning of the first left block and the side length of the green block that you obtain by dividing the middle.

Answer 4

They estimated that the "area" (area of a rectangle is width*high) under the the left and right graphs is about the same.