 # Lower quartile problems and answers

Recent questions in Lower Quartile Jaime Coleman 2022-05-09 Answered

### What is the lower quartile of the set of data?I came across this problem asking the lower quartile of the ungrouped data. My answer is 3, but other references say it should be 2.5. Here's the data:1, 1, 2, 2, 3, 3, 4, 4, 6, 7, 8, 10, 11, 14, 15, 20, 22What do you think? dresu9dnjn 2022-05-09 Answered

### Calculating the position of the medianI know this is a simple question, but I cannot find a straight answer anywhere.When calculating the medium of listed data, the formula is (n+1)/2. My Statistics teacher said for grouped data the position of the medium is n/2. However, this seems contradictory as for discrete grouped data, the data could be written in a list if the original values were known. Therefore two different values for the median are found.I know this question is probably going to get flagged as it has already been asked, however, it has never been answered. I find it frustrating that such a fundamental concept in Statistics, what is supposed to be precise and never subjective has a wishy-washy answer.Rant over, I think the position should be (n+1)/2 for discrete data and n/2 for continuous data. Moreover, this then leads into the obvious question of how we should calculate quartiles as well.It would be nice if everyone could agree on a certain method for calculating the medium as all my textbooks are saying different things.Someone please dispell the confusion and this statistical mess. spazzter08dyk2n 2022-05-08 Answered

### calculating upper and lower quartilesThe number of goals scored by a football team during a months worth of matches is recorderd.They scored $0$ goals $4$ times, $1$ goal $6$ six times and $2$ goals $3$ times. Calculate the lower and upper quartiles.Would it simply be this?: lower quartile is the $3.5$th value which is zero, and upper quartile is the $10.5$th value which is $2$? iyiswad9k 2022-05-02 Answered

### Probability and Statistics (Quartiles)Q: Find the upper and lower quartiles of the random variable.$f\left(x\right)=\frac{1}{x\mathrm{ln}\left(1.5\right)}$for $4\le x\le 6$I set $F\left(x\right)=0.25$ and $F\left(x\right)=0.75$ to denote $Q1$ and $Q3$This is what I got for the answers:For$F\left(X\right)=0.25,x=9.86$For$F\left(X\right)=0.75,x=3.28$However, these answers are wrong as compared with my textbook. It should be:For$F\left(X\right)=0.25,x=4.43$For$F\left(X\right)=0.75,x=5.42$Please help me. I don't know what I'm doing wrong. albusgks 2022-05-02 Answered

### Can anyone help me with statistics?Question: Following is the distribution of marks obtained by 500 candidates in the statistics paper of a civil services examination:+ marks more than: 0 10 20 30 40 50+ number of candidates: 500 460 400 200 100 30Calculate the lower quartile marks. If $70\mathrm{%}$ of the candidates pass in the paper, find the minimum marks obtained by a passing candidate.In the above problem, I am able to find the first part to calculate lower quartile marks but not able to find the second section.Anyone, please help I am a newbie to statistics.Thanks in advance, please ignore the bad English. Eve Dunn 2022-04-06 Answered

### $\mu =m=\frac{{q}_{1}+{q}_{3}}{2}$Let $X$ be a random variable with p.m.f./p.d.f. ${f}_{X}\left(x\right)$ that is symmetric about $\mu \left(\in R\right),$ i.e., ${f}_{X}\left(x+\mu \right)={f}_{X}\left(\mu -x\right)$, $\mathrm{\forall }x\in \left(-\mathrm{\infty },\mathrm{\infty }\right).$If ${q}_{1},m$ and ${q}_{3}$ are respectively the lower quartile, the median and the upper quartile of the distribution of $X$ then show that $\mu =m=\frac{{q}_{1}+{q}_{3}}{2}$How to prove.....any Hints. Peia6tvsr 2022-04-06 Answered