In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of a "typical" value. Median income, for example, may be a better way to suggest what a "typical" income is, because income distribution can be very skewed. The median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median is not an arbitrarily large or small result.
Homework Statement
You are asked to estimate of the most common level of a ace-inhibitor taken by patients who take the drug. Give your best estimate of central tendency.
These are the measurements
0.0 12.5 13.6 14.5 12.0 13.2
0.0 0.0 13.1 14.2 12.5...
Homework Statement
Given that:
f(x) = 2(1-x) for 0 < x < k
...0 for otherwise
sketch the graph of f(x) and find:
(i) the value of k,
(ii) the median of x
Homework Equations
The Attempt at a Solution
(i) I sketched the graph and got a line from (0,2) to...
Homework Statement
I have two sets of data, each with 30 distances and 30 results, I have the mean, median, mode, range etc, I have drawn histograms and cumulative frequency curves, got the IRQ for both sets of data.
Now I need to compare the data using standard deviations and also find...
Homework Statement
Hi, We know the famous central limit theorem for means.
I wonder if there is a central limit theorem for Median?
If so under what regularity condition, does the median converge to a normal distribution with mean and variance equal to what?
Homework Equations
The...
Homework Statement
IF X has an exponential distribution with parameter \lambda, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median.
Homework Equations
X.exp(\lambda)=\lambda e^{-\lambda x} for x>0
p=F(\eta (p)) =...
Homework Statement
P(r) = 1-(2r2+2r+1)e-2r
i know that p(r) is just the derivative of P(r)
to find the median i would just integrate from o to r and set that equal to .5
but when you integrate youre just going back to P(r) from 0 to r
so i get
1-(2r2+2r+1)e-2r = .5
how would...
Homework Statement
given distribution function F(t)=1-(1+t)^-c, 0<_t<_infinity, c>0. And that a company claim the median lifetime of a component is at least 7 years and that a component fails after 2.22. Using only this information test the claim that the median lifetime is in fact shorter...
Homework Statement
Hello, I have a set of data that is grouped into bins. The bin sizes increase logarithmically by 10% (1.1 x the previous bin).
Homework Equations
Bin
Mean
Radius Frequency
1.03 4924
1.10 9938
1.21 14009
1.32 12269
1.44 15813
1.58 18723
1.74 21471
...
Homework Statement
The probability density function is defined as
f(x) = (4/81)x(9-x^2) for 0 <= x <= 3
= 0 for every other value
Find the median value of the density.
Homework Equations
The median of a function is
integral from m to infinity of f(x)dx = 1/2
The...
Homework Statement
Given a set of sorted lists {X1, X2, ..., Xn} each Xi is in R^n , devise a divide and conquer algo that
finds the median of X1\bigcup X2 \bigcup ... \bigcup Xn efficiently.
(n * log(n), n^2 is not acceptable, also no probabilistic, expected runtime)
Also, Xi \bigcap Xj =...
Homework Statement
i have a few easy questions but i need some help with them:
1)
a) Why do we need averages?
b) Which average can have more than one value?
c) Which average represents the value when the total of all the sample values is shared out equally?
d) Which average has the same...
I recently learned that if you minimize these functions with respect to "a", you get the mean and the median respectively:
\sum (y_i - a)^2
\sum |y_i - a|
What would you get if you minimized an expression like \sum |y_i - a|^n for various n's? Do the resulting expressions have any use...
If I am given a frequency table, but instead of set scores, i am given classes, or a range of scores. So for example:
20-29 | 11
30-39 | 12
40-49 | 2
etc.
If asked to find the median of the set of data, should i give the midpoint of the class containing the median score, or should i...
i have a set containing 10000 data. i took 1000 samples of size 4, 16, 64, and 1024 and took the medians, means, and stadard deviations of each size. i graphed them sd of medians vs sample size, sd of mean vs sample size, and sd of s.d. vs sample size. for sample mean, i know from a textbook...
I was doing some last minute skimming through my book for my exam tomorrow and panic. Can someone please please tell me about finding the median by interpolation and perhaps an example of how it would could used or asked, i will be forever greatful :cool:
yasmin x
(i can only find a...
I am developing a rubbery serpentine wall as a highway median barrier and I need to know the tensile strength necessary to hold against a 4400 lb pickup moving 62.5 mph. Using an excel spreadsheet and iterations, I subtract the momentum of the wall from that of the pickup at 2 foot intervals...
Is it possible to have a set where the average is some number and the standard deviation from the average is equal to the median value of that same set? If so, could you show me such a set?