Step by Step Mode Calculation to Boost Your Math Skills

Recent questions in Mode
vomi2xn 2023-03-06

Mean of the squares of the deviations from mean is called the: Variance Standard deviation Quartile deviation Mode

Savanne1bo 2022-12-30

Tell whether the statement is true or false : A data always has a mode.

Annie French 2022-11-16

At the Faculty of Computing, 53% of the students are male and 47% are female. 35% of themales and 20% of the females from this group major in Computer Networking.Find the probability that a student selected at random from this group is majoring inComputer Networking.

Keenan Santos 2022-07-14

$X$ is a discrete uniform distribution on $1,2,\dots ,n$. I know that the median is $\frac{n+1}{2}$ for odd $n$. I need to find median when $n$ is even. Would it be $\frac{n}{2}$ or $\frac{n}{2}+1$, whichever is greater?Also, is every point mode as PDF has highest values there? So there are $n$ modes - $1,2,\dots ,n$?

glitinosim3 2022-07-09

A random variable, X, is defined as X ~ Geo(p). I know the mode is 1 as it is the value of X with highest probability.How do i show this? As this is a discrete R.V, can i be allowed to use Calculus?

Banguizb 2022-07-09

If we have $N$ sets, $\left\{{A}_{1},\dots ,{A}_{N}\right\}$, and we form a set $S$ by taking the sum of each element in the set with each element in the other sets, what can we say about the mode of $S$?Intuitively, I would like to think that we can simply take the sum of the modes, i.e:$\mathrm{Mode}\left(S\right)=\sum _{n=1}^{N}\mathrm{Mode}\left({A}_{n}\right)$However, this seems unlikely, especially as we would expect that $\mathrm{Mode}\left({A}_{n}\right)$ could potentially be a set of values, rather than a single value.So I was wondering if we'd be able to relax this condition to state that $\mathrm{Mode}\left(S\right)\subseteq \sum _{n=1}^{N}\mathrm{Mode}\left({A}_{n}\right)$, where we define $\mathrm{Mode}\left(A\right)+\mathrm{Mode}\left(B\right)$ as the set formed by taking the sum of each element in $\mathrm{Mode}\left(A\right)$ with each element in $\mathrm{Mode}\left(B\right)$, formally:$\mathrm{Mode}\left(S\right)\subseteq \sum _{n=1}^{N}\mathrm{Mode}\left({A}_{n}\right)=\left\{\sum _{n=1}^{N}{x}_{n}:{x}_{i}\in {A}_{i}\right\}$This seems to be true, but I was wondering if we could say anything stronger?

rjawbreakerca 2022-07-09

According to the definition I read, it came to my notice that the number with highest frequency has to be a mode for a given data set, but then what if I have all the numbers as distinct... In that scenario we won't have a particular number having a frequency more than other elements in the data set... Now if I consider a case when we have 2 numbers in a dataset with same max number of occurrences like:$2,3,4,5,3,2$Here 2, 3 both happen to have same maximum frequency and thus we say there are 2 modes... The above is stated similar in case we have 3 modes or multi modes ... So if there are all distinct numbers then we would have each number having the same maximum frequency as 1 ..so we can say all the numbers are modes...for that dataset...But then I have seen on some websites claiming that such data sets have "NO MODE".

Araceli Clay 2022-07-08

Five test scores have a mean of 91, a median of 93, and a mode of 95. The possible scores on the tests are from 0 to 100. a) What is the sum of the lowest two test scores? b) What are the possible values of the lowest two test scores?

prirodnogbk 2022-07-07

Given the mean, median and mode of a function and have to find the probability density function.mean: $\gamma -\beta {\mathrm{\Gamma }}_{1}$median: $\gamma -\beta \left(ln2{\right)}^{1/\delta }$mode: $\gamma -\beta \left(1-1/\delta {\right)}^{1/\delta }$Also given that${\mathrm{\Gamma }}_{k}=\mathrm{\Gamma }\left(1+k/\delta \right)$$\mathrm{\Gamma }\left(z\right)={\int }_{0}^{\mathrm{\infty }}{t}^{z-1}dt$$-\mathrm{\infty }0,\gamma >0$Now I understand how to calculate the mean, mode and median when given a probability density function. However I'm struggling to go backwards. I initially tried to "reverse" the process by differentiating the mean or median however I know this is skipping the substitution over the given limit.I then looked for patterns with known distributions and realised they are from Weibull distribution however $\gamma -$. Does this mean essentially this is a typical Weibull distribution however shifted by $\gamma$ and therefore the pdf will be $\gamma -Weibullpdf"$

spockmonkey40 2022-07-07

Consider random variable $Y$ with a Poisson distribution:$P\left(y|\theta \right)=\frac{{\theta }^{y}{e}^{-\theta }}{y!},y=0,1,2,\dots ,\theta >0$$P\left(y|\theta \right)=\frac{{\theta }^{y}{e}^{-\theta }}{y!},y=0,1,2,\dots ,\theta >0$Mean and variance of $Y$ given $\theta$ are both equal to $\theta$. Assume that $\sum _{i=1}^{n}{y}_{i}>1$.If we impose the prior $p\propto \frac{1}{\theta }$, then what is the Bayesian posterior mode?I was able to calculate the likelihood and the posterior, but I'm having trouble calculating the mode so I'm wondering if I got the right posterior:$P\left(\theta |y\right)=likelihood\ast prior$$P\left(\theta |y\right)\propto \left({\theta }^{\sum _{i=1}^{n}{y}_{i}}{e}^{-n\theta }\right)\left({\theta }^{-1}\right)$$P\left(\theta |y\right)\propto {\theta }^{\left(\sum _{i=1}^{n}{y}_{i}\right)-1}{e}^{-n\theta }$

lilmoore11p8 2022-06-30

The operation is of two step.1. Bin a data in 10 bins. (the distribution is unimodal) and2. Then find the bin with maximum density.In other words finding the mode of a distribution.

Bailee Short 2022-06-27

Suppose that ${X}_{1},{X}_{2},\dots ,{X}_{n}$ are IID Bernoulli random variables with success probability equal to an unknown parameter $\theta \in \left[0,1\right]$.Let $A$ and $B$ be nonnegative constants. If we impose the prior $\pi \left(\theta \right)\propto \left({\theta }^{a}\right)\left(\left(1-\theta {\right)}^{b}\right)$, then what is the Bayesian posterior mode?

freakygirl838w 2022-06-24

A formula to calculate the mode for grouped data's is given:Mode = $l+\frac{\left({f}_{1}-{f}_{0}\right)h}{2{f}_{1}-{f}_{0}-{f}_{2}}$Where, $l=$ lower limit of the modal class,$h=$ size of the class interval,${f}_{1}=$ frequency of the modal class,${f}_{0}=$ frequency of the class preceding the modal class,${f}_{2}=$ frequency of the class succeeding the modal class.Explain the derivation of this formula.

flightwingsd2 2022-06-21

The distribution is left-skewed if meanThe distribution is right-skewed if mean>median>mode.Can mode lie between mean and median?

rose2904ks 2022-06-21

Given is a lognormal distribution with median $e$ and mode $\sqrt{e}$. What is the variance of the lognormal distribution?Not sure how to solve this. A variable $Y$ has a lognormal distribution if $\mathrm{log}\left(Y\right)$ has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?

George Bray 2022-06-21

need to generate some random data from lognormal distribution, where I set the mode and standart deviation of that lognormal distribution. For this purpose I choose to use random numbers generator from lognormal distribution. This generator takes two numbers, that are mean and sd of underlying normal distribution.So far its clear I need to derive mean and sd of normal distribution, which is underlaying for lognormal distribution where I know mode and sd. I know the equations for derivation of mean and sd:NOTATION:$n\left(x\right)=$ mean of normal distribution$sd\left(x\right)=sd$ of normal distribution$n\left(y\right)=$ mean of lognormal distribution$sd\left(y\right)=$ sd of lognormal distribution$mode\left(y\right)=$ mode of lognormal distributionEQUATIONS:$n\left(x\right)=2\ast ln\left(n\left(y\right)\right)-\left(1/2\right)\ast ln\left(sd\left(y{\right)}^{2}+n\left(y{\right)}^{2}\right)$$sd\left(x\right)=-2\ast ln\left(n\left(y\right)\right)+ln\left(sd\left(y{\right)}^{2}+n\left(y{\right)}^{2}\right)$$mode\left(y\right)=exp\left(n\left(y\right)-sd\left(y{\right)}^{2}\right)$Here I stuck because I cant get the equation for $n\left(y\right)$ from these equations, that I need to compute $n\left(x\right)$. So far I ended:$mode\left(y\right)=exp\left(4\ast ln\left(n\left(y\right)\right)-3/2\ast ln\left(n\left(y{\right)}^{2}-sd\left(y{\right)}^{2}\right)\right)$$mode\left(y{\right)}^{2/3}\ast sd\left(y{\right)}^{2}=n\left(y{\right)}^{2}\ast \left(n\left(y{\right)}^{2/3}-mode\left(y{\right)}^{2/3}\right)$Can anybody help me to complete this derivation?

Sarai Davenport 2022-06-20