Questions tagged [mode]
The mode is the most frequently occurring value in the data and can be used as a measure of central tendency for categorical data.
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Is there something like Z-score but for highly skewed distributions?
I'm analyzing my anki reviews answer times. Since I have a lot of data (over 14 years) with gaps between reviews and different study patterns I want to analyze this in cohorts.
One metric I want to ...
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What are the alternative summary measures of a maximum order statistic when the expectation of the underlying distribution is not finite?
Suppose, $n$ units are placed on a life test. The time-to-failure follows a continuous probability distribution with non-existing finite moments(like a lower-truncated Cauchy or inverse Lomax). Let, $...
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Can median or mode of the order statistics be obtained?
Suppose $X_1, X_2,\cdots, X_n$ is a random sample of size $n$ from a continuous probability distribution with cumulative distribution function (CDF) $F(x)$ and probability density function (PDF) $f(x)$...
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Retrieving beta distribution parameters, alpha and beta, from mode and variance
Is it possible to decide the parameters of beta distribution ,alpha and beta, when mode and variance are given? I know the two parameters can be decided from mean and variance as:
$E[X] = \dfrac{a}{a+...
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using mode or median
A survey is conducted among high school students, consisting of 30 questions designed to evaluate their levels of social media addiction. The responses to these questions are aggregated to calculate a ...
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Data mining for categorical variables that correspond to modes of a continuous variable
Is there a good method or test to find categorical variables associated with modes of a continuous variable?
Take the velocity of a car as an example. You would expect there to be at least two modes ...
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Game of guessing or is it! [closed]
I am trying to learn coding and want to create a simple game. The idea is that there are 20 different animals, and you have 5 rooms, each round 5 out of the 20 animals hide in the room, where behind ...
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Predict colours [closed]
I have very basic knowledge in statistical science and appreciate your patience. My problem is if you have a bag with seven differently coloured balls, you are allowed to blindly pick 3 balls every ...
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Fitting an arbitrary distribution to a given mean/mode/median
Given some combination of mean/mode/median, how would I go about generating a distribution that can fit an arbitrary combination?
For cases where mean = mode = median, I would just use a normal ...
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For log-concave densities, are joint and marginal modes consistent?
Suppose I have a probability density function $\pi(x_1, \ldots, x_n)$, which is the density of a vector-valued random variable $X$ in $\mathbb{R}^n$. Assume that $\pi$ is strongly log-concave, i.e., ...
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How to normalize the mode and respective bounds of the confidence intervals (percentages)
I have a dataset of the diet of a species, with the percentages that each individual ate of each prey.
My goal is to describe its diet and retrieve the percentage that the species eats of each prey (...
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Most probable value vs maximum of the distribution [closed]
Given a distribution p(x), there are two things that can be calculated.
Value of x for which p(x) is maximum.
Most probable value of x weighted over p(x).
Would these two values of x be the same?
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Verification of proof that a point of symmetry is mode (Casella-Berger 2.27)
I was solving the following problem 2.27 from Statistical Inference by Casella-Berger.
2.27 Let $f(x)$ be a pdf, and let $a$ be a number such that if $a\geq x\geq y$, then $f(a)\geq f(x) \geq f(y)$, ...
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Most likely counts of outcomes of a multinomial after N trials (mode of multinomial)
Given a categorical random variable $X = \{x_1,x_2,...,x_k\}$ with corresponding probabilities of each outcome $P = \{p_1, p_2,...,p_k\}$ (i.e. a multinomial):
What are the most likely counts of ...
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Inequality of $f(\mathrm{Mode}[X])$ and $\mathrm{Mode}[f(X)]$?
Say I knew the distribution of a continuous variable $X$. If somebody randomly picked out a single instance $x$ and asked me to bet on its value, I would go with the mode of the known distribution of $...
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How to analyse a right skewed dataset
I am trying to analyse several heavily right skewed datasets in order to determine their mode.
The story behind the sets is that they are calculations of performance data from marketing posts. The ...
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finding central tendency
The following table presents frequency distribution of teachers of 1 year:
Rank ----------Frequency
Professor ------------7
Assoc Professor ------4
Asst Professor--------3
Instructor -----------5
...
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In reinforcement learning/multi-armed bandits, why do we look at expected reward and not the most likely reward? [duplicate]
This is the dilemma that I have faced in applied probability in general. Say you have the choice to put your savings of $\$10$ in a deposit account with guaranteed retun of $\$100$ or buy a lottery ...
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How do we derive the conditional mode as the solution to linear regression, for uniform cost function?
I know that if the cost functions are respectively the least squares ($L^2$) and the absolute deviation ($L^1$), the solution to linear regression is the conditional mean and the conditional median ...
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Mean, Mode, Median of a histogram?
Based on my understandings, I would say for the below histogram that the mode is zero, the mean is between 0 & 1 and the median is 1. I'm I right?
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Mode for equal consecutive frequencies
I'd like to calculate the mode for the frequency distribution table:
...
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Understanding the Importance of "Sufficiency" within Statistics
I am trying to better understand what it means to be a "sufficient statistic".
"In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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Probability Distributions : "Mode" vs. "Expectation"
I have often heard the argument that in higher dimensions: the "mode" (most common value) of a probability distribution function does not correspond to the "expectation" (mean) of ...
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Suggestions for calculating peak times using entrance and exit times
I have a set of data containing the entrance and exit times/dates of visitors to a building and I need to calculate the peak time(s) of said building. With just this information is there a way to ...
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Likert data and Likert scales - ordinal or interval?
I was reading up on the use of Likert scales and how to analyse data. I found this bit of text confusing:
To properly analyze Likert data, one must understand the measurement scale represented by
...
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Mean, Median, Mode of Log Normal Distribution
Let $Y$ be Log-Normal with parameters $\mu$ and $\sigma^{2}$. So $Y=e^{x}$ with $X \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$. Which of the following statements is correct?
(A) The median of $Y$ is ...
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Test whether two samples have different modes?
I have a dataset with timed observations of an event across the day, in two different places. I am particularly interested in whether the peak in observation is significantly different between the two ...
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Can a sample average be multimodal?
Suppose $X_1,\ldots,X_n$ are iid with a well defined expectation. Is it possible for the sample mean $(1/n)\sum_{i=1}^nX_i$ to be multimodal for all $n$? Looking at simple examples I can see that for ...
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Why do we add an extra decimal place when we calculate the range in statistics?
From Mario Triola's textbook:
I understand that we add a decimal place when we calculate the median (it is possible to have (a+b)/2 ). I absolutely do NOT understand why we do that when we round off ...
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What are the terms involving the mode's frequency?
Suppose I have a finite multiset of $n$ elements (a "population" I guess we can call it). Suppose this set has a proper mode, appearing m out of $n$ times. What term(s) do statisticians use:
...
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Finding the mode given the probability of occurence
When a teacher asks a question, a student has a probability of 0.4 of being asked. Assume the occurrence is independent.
What is the mode of the number of questions raised by the teacher it takes for ...
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Can we use bootstrap to estimate Mode of the population?
I have known that bootstrapping can be used to estimate the population mean, Is it valid if we estimate the population mode too? Further, can we estimate any population parameter with the help of ...
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Does it ever make sense to average the median, mean, and mode?
Consider four subjects (A,B,C,D) competing 12 times in a game with 5 possible scores (5,6,7,8,9):
...
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Find the mode of the Weibull distribution
I am using the matlab curve fitting tool. It allows to use the Weibull distribution, using this formula:
$$f(x)=abx^{b-1}\exp(-ax^b). $$
Unfortunately this is not the formula that I found on Wikipedia....
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Expected value (Mean) of a joint distribution
I saw in a textbook that if we have a joint distribution $f(X,Y)$ that is a Gaussian distribution, then we have the mode equal to the mean. The mode is just the values of $X$ and $Y$ such that $f(X,Y)$...
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How do I know which way this sample is skewed?
I have a sample where n = 15 and the median = mean but the mode is less.
So I know to be:
Positively skewed (mode<median<mean)
Negatively skewed (mean<median<mode)
Symmetric (mean=median=...
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Mode in probability distribution
From what I know that mode is most frequent occurring value e.g. in
[1, 4, 51, 14, 12, 14, 2]
Mode is 14 because it occurs twice and most frequent.
However, in ...
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Does it make sense to impose a density curve over the bar plot and analyze the mode?
Suppose that my X variable for my probability bar plot is discrete (i.e. not continuous) and ordinal. If this is the case, does it make sense to impose a density curve (apparently this is possible by ...
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Finding the mode of multiple sample modes
I'm running an experiment where I'm collecting samples of different size (numeric data only) and computing the mean, median and mode of each sample. I'm interested in finding out the mode across all ...
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GLMs with skewed distributions - why use mean and not mode?
There's something that's a bit troubling for me. The unit deviance in GLM is defined as $2[t(y,y) - t(y,\mu)]$, when $t(y,\mu) = y\theta(\mu) - b(\theta(\mu))$ (theta being the natural parameter).
For ...
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Finding the most representative row in a dataset
Our goal is to model the hourly electric usage of a building given only building characteristics. We are running hourly energy models on hundreds of thousands of virtual buildings. We then take a real ...
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Computing Mode of Prior
How do you compute the mode of a prior with beta distribution $(\alpha, \beta)$?
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Is the mode considered a resistant statistic?
Is the mode considered a resistant statistic?
By the definition of resistant given in our text (i.e., not changed much by outliers), I would think the answer would be "yes."
On the other hand, the ...
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Standard deviation around mean rather than mode or median?
Why is standard deviation calculated from arithmetic mean and not from other measures of central tendency? I do get that standard deviation is to calculate dispersion, but why not use mode or median ...
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Is the mode of a Poisson Binomial distribution next to the mean?
A Poisson-Binomial variable $X\sim PB(p_1, \dots, p_n)$ is the sum of $n$ independent, not necessarily identically distributed, Bernoulli variables $X_1, \dots, X_n$:
$$
X=\sum_{i=1}^n X_i,
$$
with $...
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Median or mode for measurements with erroneous outliers
Background: I am working with real measurements that likely contain two sources of error, (1) measurements that were performed incorrectly, and (2) natural variability of the measured quantity and ...
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Conditional log-concavity and unimodality
Let $X$ and $Y$ be two random variables (or vectors)
with continuous and "smooth enough" joint distribution. Assume that the two conditional distributions $X|Y=y$
and $Y|X=x$ are log-concave for all $...
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What is a term to describe data where the mode represents a large proportion of all observations?
Below are some histograms of continuous variables, where 20-50% of all observations fall on the mode.
Are there any terms to describe data that exhibit this unusual concentration of observations on ...
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Best measure of central of tendency
I just started learning stats a few weeks ago well my question is that as we know that the mean, median, and mode is the central tendency of the data and its suggested that we shouldn't go with only ...
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Is mode a measure of central tendency?
I am just starting out with my stat basics and that’s where I came across measures of central tendency. In one of the books measure of central tendency is defined as a measure which yield information ...
