A value representing the lowest $n$ percent of the values in a data set or of the possible values of a random variable.
Questions tagged [percentile]
153 questions
22
votes
1 answer
Is $50$th percentile equal to median?
Consider we have the $100$ distinct integers between $1$ and $100$ inclusive. The median and fiftieth percentile can be calculated as follows:
Data set: $1,2,3 ..... ,98, 99, 100$
The median is $(50+51)/2 = 50.5$
The $50$th percentile is $51$…
Cardinal
- 890
22
votes
3 answers
Percentile Symbol - does it exist or not?
Is there a standard symbol for percentile in mathematics, much like % is used for percentage? I have trying to get the right answer but only getting conflicting answers and logic.
Karthikeyan
- 237
5
votes
3 answers
What is the meaning of percentile?
I am confused by the term percentile.
Once my teacher told me that percentile means the percentage with respect to the score of the highest achiever.
This means that if in a competition I got $80$ out of $100$ and the highest score in that…
Singh
- 2,168
5
votes
2 answers
Definition of a percentile
I recently began a study of Introductory Statistics by Sheldon Ross. In the book, he defined a percentile as follows:
The sample $100p$ percentile is that data value having the property that at least $100p$ percent of the data are less than or…
Toba
- 345
5
votes
0 answers
What's the most accurate way to estimate a percentile from multiple partial percentiles?
There exists 3 sets of numbers. I have the 99th percentile (p99) of each set and the cardinality of the set, but not the values in the set themselves.
p99: 540, cardinality: 215
p99: 288, cardinality: 4
p99: 432, cardinality: 78
What is the most…
SGr
- 153
- 2
4
votes
3 answers
Why add one to the number of observations when calculating percentiles?
The CFA Quantitative Methods book uses the following formula for finding the observation in a sorted list that corresponds to a given percentile $y$ in a set of observations of size $n$:
$(n + 1)\frac{y}{100}$
It defines percentile as follows:…
dumb question
- 195
4
votes
1 answer
MLE and confidence interval of $\tau$ where $P(X < \tau) = 0.98$
Let $X_1,...,X_n \sim N(u; \sigma)$ Let $\tau$ be the .98 percentile, i.e. $P(X < \tau )$ = 0.98:
Find the MLE of $\tau$:
Find an expression for an approximate $1 - \alpha$ confidence interval for $\tau$.
My Attempt is as follows:
We know the MLE…
pavybez
- 103
4
votes
0 answers
How do you pronounce 0.1st percentile?
I'm analyzing some out of range values that are either really high (above the 99.9th percentile) or really low (below the 0.1st percentile). How would you pronounce 0.1st percentile?
ddx
- 141
4
votes
1 answer
Is there something like 700%?
I always see companies advertising their products as "700% effective " or "the product kills 900% germs".
But percent means "out of hundred". So how can the percentage be more than 100 like 700% or 900%?
pro neon
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4
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How to combine percentiles from different datasets
I'm trying to combine percentiles (50th and 90th) from 2 different datasets. I don't have access to the datasets at the time of combining. Apart from the percentiles I have the number of elements on each dataset.
Now, I know that any attempt at…
hortega
- 49
4
votes
1 answer
Median of Poisson Distribution
I've just taken Probability and Statistics exam and here is the question that becomes a hot debate among my friends in the classroom:
What is the median of a random variable that follows a Poisson distribution with parameter…
Venus
- 10,041
4
votes
1 answer
Finding Percentiles - How am I wrong?
So the problem goes:
There are 40 students and their test scores are:
30 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Find P85.
What I did:
Using the formula…
thes4s
- 171
4
votes
2 answers
How do I find percentiles of data sets (Even vs odd)?
Given the following data set with an even number of values:
$100, 100, 105, 113, 129, 132, 146, 152, 176, 200$
The value representing the 30th percentile, using the formula n(p/100) where n = sample size and p = percentile, is at position 10(0.30)…
Riptyde4
- 379
3
votes
1 answer
Why does the 90th percentile come out to be greater than the greatest number?
Why is the 90th percentile of the following numbers 0.193204884?
0.193111065
0.188885706
0.191501273
0.193298704
0.18895934
0.192364606How can the 90th percentile be greater than the greatest number in the set?
I used the formula -…
navneesi
- 31
3
votes
2 answers
Proofs that the median and a 50th percentile aren't always the same thing. Is my reasoning correct?
For our purposes we need to find at the least one case when a 50th percentile and the median aren't the same thing.
I will present three such cases.
Here the first case (proof) goes as this:
Suppose we have set of numbers {1,2,3}. Its median is 2.…
KarmaPeasant
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