Can someone explain the definitions of mean, median and variance in relation to probabilities?
2006-07-25 09:27:02 · 5 answers · asked by darcy_t2e 3 in Science & Mathematics ➔ Mathematics
The mean is the expected value of your variable. To calculate this for a probability distribution, you would take ∑(x*P(x)) for all possible x, where x is a possible value of your variable and P(x) is the probability of that value occurring. The statistical definition of the mean ((∑x)/n, where x is the value of a data point and n is the number of such points) is a special case of this, where each point in the data set is considered to have equal probability.
The median is the point that divides your probability distribution in half. More precisely, it is any number m such that P(x>m)=P(x
Variance is the expected value of (x²-μ), where μ is the mean of your probability distribution. It can be shown that this is equal to the expected value of x² minus the square of the mean, or ∑(x²*P(x))-μ². Again, the statistical definition is the special case where all data points have equal probability.
2006-07-25 09:59:23 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
Mean is the average. Add up the total value of all samples and divide by the number of samples. The median is the value exactly 50% of the way from the first to the last sample in the probabilitiy distribution.
The variace is a measure of distance of from the center of the distribution, as is the standard deviation. For example, in humans over two standard deviations right of the median is considered genius in intelligence. The variance is the standard deviation squared. The mode is the most commonly occuring value. If one value, say 15, occurs six times, and no other vaue occurs more than five, 15 is the mode.
http://www.en.wikipedia.org/wiki/statistics
2006-07-25 16:41:22 · answer #2 · answered by helixburger 6 · 0⤊ 0⤋
Say you have a data set 1,2,2,4,7,9, 12.
The mean is the average so (1+2+2+4+7+9+12)/(7) = 5.286
The median is the number right in the middle of the data set when they are arranged from low to high. So 4 would be the median in our example.
Variance (I forget the mathematical formula) is a measure of how spread out the data is in reference to the mean.
The variance of 1,2,2,4,7,9,12 would be greater than the variance of 3,4,4,5,6,6,8 (they both have about the same mean, but in the first one the numbers are further away from the mean).
2006-07-25 16:34:11 · answer #3 · answered by Steve S 4 · 0⤊ 0⤋
In terms of probability (versus statistics, there are some slight deviations), the mean is the average number that comes up. The median is the number that is in the center (this is the same as in statistics). Variance is the range of possible results, the same in prob and stats.
2006-07-25 16:30:53 · answer #4 · answered by biosafety_level_4 2 · 0⤊ 0⤋
mean is the average, median is the middle number and variance is how much the value varies from highest to lowest
2006-07-25 16:31:51 · answer #5 · answered by mi_gl_an 4 · 0⤊ 0⤋