What is Median: Definition and 68 Discussions

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.

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  1. chwala

    Find suitable value of Median and Range for given box-whisker plot

    I do not seem to understand this question nor the Ms. I understand the box-whisker plot and its relationship to quartiles of which ##Q_2## is the Median. This question is from an As level- statistics past paper question.
  2. dextercioby

    I Connection between mean and median

    I have 100 random real (even rational with only one decimal, like average temperatures of months at a particular weather station) numbers. With them I compute the arithmetical mean and the median. It is a (very) small probability they are the same number within let's say 0,1 or 0,2. Question...
  3. chwala

    Find the mode, median and mean of the number of children

    See attached question and markscheme. Solutions Now they give the Mode as ##1## i am not getting this... My understanding 'maybe its the English used' is that we have ##0## children living in 3 houses, 7 houses have ##1## kid each bringing total number of kids to 7!, 5 houses have ##2##...
  4. marcophys

    A Recalculate a range by variable 'Median'?

    Hello everyone :) I'm struggling to wrap my head around recalculating a data set based upon median. The data set represents a fixed distribution pattern of population to income group. There is no data available for 'population to income group' at differing medians, hence we accept the...
  5. M

    Expected value of median of rolling three fair dice

    Hi, I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand. Question: Calculate the expected value of the median of rolling a die three times. Attempt: I read the following answer on math stack exchange here "As already noted in a comment, the...
  6. N

    Median and mean when there are 2 variables

    Here's a list of six numbers written in order of size 4, 7, x, 10, y, y The numbers have a median of 9 a mean of 11 Find x and y? So I've gone to do: (4+7+x+10+2y)/2 = 11 I get x+2y = 45 What do I need to do from here?
  7. chwala

    Finding the median in a bar graph problem

    i do not understand the language used in part a, otherwise i would indicate the number of children the women have in order as ##1,2,3,4,5## and ##6## now for part b) this is where i have a problem. To find the median assumably for the number of children, we have to find the total number of...
  8. Mr Davis 97

    Length of median is less than half of adjacent sides

    Homework Statement ##ABC## is a triangle, the midpoint of ##AB## is ##H##. Prove that ##2CH < AC+CB##. Homework EquationsThe Attempt at a Solution Note that by the triangle inequality that ##CH \le HA + AC## and that ##CH \le HB + BC##. Adding these two inequalities gives $$2CH \le HA+HB+AC+CB...
  9. Mathman2013

    Median vs. Second Quartile question

    Homework Statement Lets say I have a list of numbers. income=[17000, 11000, 23000, 19999, 21000, 10000] I sort them income_sorted=[10000, 11000, 17000, 19999, 21000, 23000] Calculate med 2nd Quartile. Homework Equations Median_formula = (n+1)/2 The Attempt at a Solution The second...
  10. Umaxo

    Find Length of Median in Triangle via Cosine Law

    <Moderator's note: Moved from a technical forum and thus no template.> Hi, i am quite embarrassed to ask this question, but i am really stuck. i want to derive length of median of triangle from cosine law and i am getting wrong results. I cannot spot the mistake. So let's have a triange with...
  11. J

    Calculating Mode and Median for Non-decreasing Series | Stats Homework Solution

    Homework Statement Consider non-decreasing series of numbers: 1, 8, 8, 13, 14, 14, x, y, 18, 20, 31, 34, 38 and 40. Median is 15 Calculate mode Homework Equations Median is middle term for odd number of terms and it's average of middle 2 terms for even number of terms. 3 Median = Mode + 2 Mean...
  12. Monoxdifly

    MHB Calculating Median in a Class with B, D, A, and C Scores: Findings and Solutions

    In a class, Budi's score is greater than Doni's. The sum of Adi's and Doni's scores is greater than the sum of Budi's and Coki's scores. Meanwhile, Doni's score is greater than two times Budi's score substracted by Adi's score. Determine the median of those four students' scores. All I know...
  13. R

    MHB Which measure of center is most accurate for the batting averages of a team?

    The rainfall (in inches) in the month of June for 7 years is recorded below. 20, 24, 53, 13,0, 43, 36 What is the best measure of center ?The batting averages of 10 players of a team are 0.338, 0.234, 0.256, 0.321, 0.333, 0.290, 0.148, 0.222, 0.300, 0.276 What is the best measure of center ...
  14. S

    How to do a running median in n*log2(n)?

    So I came up with the following solution which is n*log2(n) since the input is n elements and I use a binary insertion and calculating the median is constant time. This is passes all the test cases in the tests that don't time out. I need to figure out how to make it faster so I beat the...
  15. W

    MHB Median, mode, normal distribution

    In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assumed that a bit is received in error is 1×〖10〗^(−5) . if 16 million bits are transmitted, What is the probability that more than 150 errors occur? Find the...
  16. FallArk

    MHB Find Median Value in Data: Algorithm & Question

    Recently, I encountered a problem asking that I am very confused, since the mode and "anti-mode" (least frequent value) can be more than just one number, is it still possible to find the median of a list of integers? I was thinking that median is the number which half of the list is bigger...
  17. M

    MHB Right triangle, feet of altitude, angle bisector and median

    Let $\triangle ABC$ be a right-angled triangle with $\angle A = 90^{\circ}$, and $AB < AC$. Let points $D, E, F$ be located on side $BC$ such that $AD$ is the altitude, $AE$ is the internal angle bisector, and $AF$ is the median. Prove that $3AD + AF > 4AE$ My solution. Can you check it is...
  18. reddvoid

    I Most effective of 1000 groups given mean median mode and N

    Hi, For a SoC project I am working on I need to select one cell which is most critical. example, If a bus is going through 1000 stops 1000 times I have mean median mode of delay contribution of that stop compared to the total delay to reach from start to stop point and N (number of times bus...
  19. Julio1

    MHB Laplace equation and Median Value Property

    Suppose that $u$ is the solution of the Laplace equation $u_{xx}+u_{yy}=0$ in $\{(x,y)\in \mathbb{R}^2: x^2+y^2<1\}$ $u(x,y)=x$ for all $(x,y)\in \mathbb{R}^2$ such that $x^2+y^2=1.$ Find the value of $u$ in $(0,0).$ Use the property of median value.
  20. D

    Survey Results: 100 Respondents, 5 Colors - Mean, Median & Mode?

    1. hi there I am a bit confused, I am doing a survey of 100 respondents. ive asked them 5 colors to choose from ( red, green, blue, yellow and black) ive got these results from my survey of 100 respondents red = 21 green = 36 blue = 19 yellow = 10 black = 142. is my sample size 100? or 5? how...
  21. D

    Finding the median of a distribution

    Homework Statement Suppose X has the Uniform (0,1) distribution. Find the median of the distribution of e^X correct to 2 decimals. Homework Equations F(X) = 0.5 F(X) = ∫f(x) The Attempt at a Solution I am not entirely sure what to do here, I know to find the median you need to find when F(X)...
  22. Drakkith

    Finding the Median Volume of a Sample in Chemistry Lab

    Homework Statement A question in my chemistry 151 lab book: A student measures the volume of water displaced by the same metal sample as 5.4 mL, 5.8 mL, and 5.5 mL for his three determinations. Determine the median volume. Homework Equations Unknown or N/A The Attempt at a Solution How do...
  23. B

    Calculating mean from 5 number summary

    It seems like it should be possible to calculate the mean (usual average) from a 5-number summary of a set of numbers (min, first quartile or Q1, median, third quartile or Q3, and max). You should be able to calculate roughly what a percentile is, then by taking each discrete percentile and...
  24. G

    Sum of deviations from median

    Dear Friends! Is sum of deviations from median always minimum,in comparison to deviations from mean,mode or any other observation?Why?
  25. P

    MHB Determining the Median of Five Median Numbers

    Problem: My goal is to show the median income among five different groups of people, where the median income for each group has already been determined. Is it as simple as choosing the median income of $ 45,615 since there are five numbers? Here is the information: Group One's Median Income...
  26. evinda

    MHB Finding the $p$ Closest Elements to Median of Set $M$ in $O(m)$ Time

    Hello! (Wave) I want to describe an algorithm with time complexity $O(m)$ that, given a set $M$ with $m$ numbers and a positive integer $p \leq m$, returns the $p$ closest numbers to the median element of the set $M$. How could we do this? (Thinking)
  27. C

    MHB How to find if there are outliers, given mean, median, etc

    Hi guys, I'm getting ready for a stats exam and one of the questions looks like this If I'm not given a histogram, how can this be solved?
  28. L

    Determining the Median for Hours Studied and Slept | Interpretation of Graph

    Homework Statement Attempt : I think I am interpreting the graph wrongly, the median for the Number of hours studied should be 3 since only There are people who studied from 1~5 hrs, and for Number of hours slept it should be (7+6)/2 = 6.5 since people only slept for 4~9 hrs...
  29. S

    Formula for median of a set (sorted)

    Now i think i derived this correctly, but I'm not sure if it's correct, can anyone give me a confirmation? ##n-1/2=x## Where ##x## is the result of subtracting 1 from the observations and then dividing by 2. Then ##x+1=Median## Thank you :) Edit: Oops, this is the handicapped...
  30. U

    Triangle with median and altitude

    Homework Statement In triangle ABC with A as obtuse angle, AD and AE are median and altitude respectively. If BAD = DAE=EAC, then sin^3(A/3)cos(A/3) equals Homework Equations The Attempt at a Solution CE = a/2. Let DE = x. Then BD = a/2 - x. Let AE = p, AD = q. For ΔADB \cos...
  31. 3

    Mean with standard deviation or Median with IQR?

    Hi guys, I hope someone is able to help me with this, I'm currently stuck on a problem. 1. I was given some data (in continuous, grouped form) regarding phone call times for a call center agent and asked to represent the data using the most accurate form of average. I initially calculated...
  32. 3

    MHB Which is better? Mean with standard deviation or Median with IQR?

    Hi guys, I hope someone is able to help, I'm currently stuck on a problem. I'm having trouble justifying which representation is more accurate for my data; either mean with standard deviation or median with IQR. I've calculated both averages for the my data, however I was advised by someone...
  33. M

    What is the correct way of describing this change - mean or median?

    Hi, Please see the attached Excel file. The list shows the old and new values of a set of variables. I am trying to understand what is the best way – average or median - to describe the change the values of the set. I want to describe the true central tendency of the change. 1. I...
  34. P

    How can I calculate the median of a terabyte dataset efficiently?

    Hi all I am working with a huge dataset that it to large to store in memory all at the same time. I have been looking at estimating the median of this dataset and how found things such as the median of medians etc but these methods still require me to store a lot of the data. For...
  35. karush

    MHB Q_1, Median, and Q_3 of A,B,C,D & E

    A=18 (first data in list) B=19 Q_1 C=23 (median of list) D=31 Q_3 E=36 (last data of list) altho the problem doesn't ask for it, but W|A says the interquartile range is 11 but here Q_3-Q_1 is 31-19=12?
  36. J

    Find the median of two sorted arrays

    Well ... I completely failed that job interview. That was one of the programming questions. He said I answered it completely wrong.
  37. P

    Probability distribution and finding the median

    Homework Statement Suppose that x measures the time (in hours) it takes for students to complete an exam. All students are done within 2 hours and the density function for x is given by f(x)={(x^3)/4 0<x<2 {0 otherwise Compute the median of this distribution. (Give an exact...
  38. P

    Find the median of the probability distribution

    Homework Statement f(x) = C|x-2| for 0 <= x <= 3 f(x) = 0 otherwise Homework Equations The Attempt at a Solution Solved for C, found it to be (2/5). So.. I'm confused how to set up my integral here. I tried integral(2/3(x-2)dx) from m to 3 = 1/2. That didn't yield the correct...
  39. E

    What is the median number between zero and one?

    Hi, is there a median number between zero and one? There are countless numbers between zero and one - an infinite set. If we pick any number at random (say 0.2) then could we always say it is the median as there is an infinite set of numbers on either side? What if I pick another...
  40. L

    95% confidence interval - median

    To calculate the 95% confidence interval of the mean of a normal distribution you calculate 1.96 χ standard error on the mean. what do you do if you want to calculate the 95% confidence interval on the median of the distribution, for a distribution that is most definitely skewed and not...
  41. R

    Reconstructing dataset given mean, median and Stdev

    Wondering if it is possible to reconstruct a dataset if I give you the mean, median, standard deviation and N of a dataset. For example, if there are 20 students in a class. The mean of their exam score is 80, median is 85, standard deviation is 14. Of course the maximum score for the exam...
  42. M

    Median geometric distribution

    Homework Statement How do you find the median of the geometric distribution? Homework Equations M is median if P(X>=M) >= 1/2 and P(X<=M)>=1/2. The Attempt at a Solution I have found this inequality using the geometric series: (m-1)*log(1-p) >= 1/2
  43. N

    Any Two Sample Median Tests (for differences) in R

    Hey, Is there any Two Sample Median Tests (for differences) in R. I tried searching for hours, and I got not luck. The closest ones I can think of is: mood.test wilcox.test but they are not really testing for median differences. The sign test, on the other hand, does tests for median...
  44. N

    Tests for Difference in Mean VERSUS Tests for Difference in Median

    Sup everyone, Assume I have two sample observations. I am wondering when I should use a test for a difference in mean and when I should use a test for a difference in median. Should I test for mean if both the distribution of both the samples are normal? Should I test for median otherwise? I...
  45. D

    Image Median Filtering (Selection Algorithm)

    Homework Statement I started working on a C++ image median filter for fun... I'm supposed to read a 30x30 16-bit grayscale binary image and apply selection algorithm. 3x3 kernel. Please help output is messed up and i don't know where to start fixing it. Homework Equations using...
  46. A

    How to calculate median of grouped data if group size is variable

    I learned in school that Median = L + (n/2-cf)*h/f where L = lower limit of median class n = no. of observations cf = cumulative frequency of class preceding the median class, f = frequency of median class, h = class size (assuming class size to be equal). I used to use this formula for...
  47. M

    How many values of x make the mean and median of a set of numbers equal?

    Let f(x) be the mean of five numbers: 4, 5, 7, 9 and x. Let g(x) be the median of the same numbers. For how many values of x, a real number, is f(x) = g(x)? I only got 2. x = 0, 10 There are 3 though. Perhaps someone can help me find the other one.
  48. M

    How to find x if we know the median amount?

    Homework Statement {3.2,4.6,5.8,2.4,x,5.7} mediant amount is 4.8litres Find x ? Homework Equations The Attempt at a Solution forgotten Thxx
  49. Femme_physics

    Finding the minimum length of a median in a triangle

    Homework Statement In a right triangle ABC, AD is a Median to BC (see drawing) Given: AB+BC = 4 A) Mark BD with an x, and express the lengths of the adjacent and opposite through x. B) Find the x for which the length AD is minimal http://img641.imageshack.us/img641/6798/abctriangle.jpg The...
  50. G

    Which Generalized Mean Best Approximates the Median?

    Which of the generalized means (like http://en.wikipedia.org/wiki/Generalized_mean and more general) do you think is most suitable to approximate the median?