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.
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.
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...
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##...
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...
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...
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?
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...
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...
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...
<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...
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...
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...
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 ...
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...
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...
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...
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...
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...
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.
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...
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)...
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...
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...
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...
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)
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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
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...
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...
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...
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...
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.
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...
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?