# Get help with descriptive statistics problems

Recent questions in Descriptive Statistics
doturitip9 2022-07-10

### I want to ask about standard normal distribution. What is the highest and lowest value of $z$ score can be?From the table of standard normal, the value z score is only for -3.99 $\le$ $z$ $\le$ 3.99.Can it be higher than the range? Is there any programme or formula to compute the probability of standard normal distribution for the range outside -3.99 $\le$ $z$ $\le$ 3.99?

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?

vasorasy8 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?

glitinosim3 2022-07-09

### What is the difference between categorical (qualitative) data and numerical (quantitative) data?

Jamison Rios 2022-07-09

### Is age a discrete or continuous variable? Why?

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".

myntfalskj4 2022-07-09

### Write the general form of linear equation in two variables?

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 }$

delirija7z 2022-07-07

### I had a question about an instantaneous z score. The question reads as$P\left(z=2\right)$I think that this is 0, as z-score is the area under the curve and could be found by integrating the PDF over the range. As the range is 0, the area is also zero. Is that correct?

vasorasy8 2022-07-06

### In a given population, a score of X= 88 corresponds to z= +2.00 and a score of X= 79 corresponds to z= -1.00. Find the mean and standard deviation for the population.I know how to find X and z-scores as well as how to plug things into the z-score formula, but I'm not sure how to solve this one. It says to sketch out a distribution table and find where the mean and SD fall on it, but I'm not sure how to do that.

kolutastmr 2022-07-06

### The 2006 Statistical Abstract of the United States reports on a survey that asked a national sample of 80,000 American households about pet ownership. Suppose that one-third of all American households own a pet cat. The survey discovered that 31.6% of all the households sampled owned a pet cat. What is the z-score of this?From the standard deviation formula for a sample proportion, I found that standard deviation is 0.0016. From there, I plugged that into the z-score formula, and got (0.316-0.333)/0.0016 = -10.625. However, a z-score that high baffles me and I cannot imagine getting a z-score that high. Where did I go wrong?

Callum Dudley 2022-07-04

### I'm new to studying z-scores and I've been told that for a gaussian statistic, around 95% of the values lie within the area two standard deviations above and below the mean, which (in accordance to my interpretation) would imply,${\int }_{\mu -2\sigma }^{\mu +2\sigma }A{e}^{-\left(\left(x-\mu \right)/\sigma {\right)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=0.95\ast {\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}A{e}^{-\left(\left(x-\mu \right)/\sigma {\right)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x$Firstly, am I correct in my presumption? and secondly, is there any way to calculate the integral on the left to prove this point mathematically?

prirodnogbk 2022-07-02

### I have been reading a Statistics book and they show the following formula for z-score:$z=\frac{x-\mu }{\sigma }$And then they explain about the $\mu$ and the $\sigma$ in the formula like this:These are the mean and standard deviation of data containing the value x.But is that so ? I don't think the mean and standard deviation should contain the value x.

Sovardipk 2022-07-01

### On the first periodic exam in Statistics, the population mean was 70 and the population standard deviation was 9. How to determine the standard score of a student who got a score of 88 assuming that the scores are normally distribtued?

Pattab 2022-07-01