a group of equal proportions - the definition of quantile is one of a class of values of a variate that divides the total frequency of a sample or population into a given number of equal proportions

A quantile.

Yes.

Usually the value of the lower quantile, median, and upper quantile are in ascending order, how if for the particular set of data, if all values are the same, then these three measures can be the same.

Victor Chernozhukov has written:

'Quantile regression with censoring and endogeneity'

'An IV model of quantile treatment effects' -- subject(s): Accessible book

'Rearranging Edgeworth-Cornish-Fisher expansions'

'L1-Penalized Quantile Regression in High Dimensional Sparse Models' -- subject(s): Regression analysis

'Instrumental variable quantile regression' -- subject(s): Accessible book

'Extremal quantities and value-at-risk' -- subject(s): Accessible book

'Estimation and confidence regions for parameter sets in econometric models' -- subject(s): Accessible book

In the context of "q125," the "q" typically stands for "quantile," which is a statistical term used to describe the division of a dataset into equal intervals. The number 125 indicates a specific quantile, often referring to the 125th quantile, which might represent a specific data point or threshold in a distribution. However, in many contexts, particularly in statistics, quantiles are usually expressed as fractions or percentages, so the precise meaning can vary depending on the specific application.

Quantile regression is considered a natural extension of ordinary least squares. Instead of estimating the mean of the regressand for a given set of regressors, and instead of minimizing sum of squares, it estimates different values of the regressand across its distribution, and minimizes instead the absolute distances between observations.

Lingxin Hao has written:

'Quantile regression' -- subject(s): Statistical methods, Regression analysis, Social sciences

The interquartile range is well known as a measure of statistical dispersion. It is equal to difference between upper and lower quartiles. The quartiles is a type of quantile.

According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 1 words with the pattern Q-AN--L-. That is, eight letter words with 1st letter Q and 3rd letter A and 4th letter N and 7th letter L. In alphabetical order, they are:

quantile

In statistics, a quartile is a type of quantile that divides a data set into four equal parts, each containing 25% of the data. For example, if you have a set of test scores, the first quartile represents the score below which 25% of the scores fall. Understanding quartiles helps in analyzing the distribution and spread of data.

In mathematics, ( Q_x ) typically denotes a quantile function for a random variable ( x ). It represents the value below which a given percentage of observations fall, effectively providing a threshold for probabilities. For instance, ( Q_{0.5} ) would indicate the median of the distribution. The specific meaning can vary based on context, so it's important to consider the surrounding definitions.

Qinglai Meng has written books in the field of Statistics, particularly focusing on mixed effects models, quantile regression, and other statistical methodologies. He has also published research articles in various statistical journals.

–adjective 1. Astronomy. noting or pertaining to the aspect or position of two heavenly bodies when 60° distant from each other. –noun 2. Astronomy. a sextile position or aspect. 3. Astrology. a sextile position or aspect, conducive to mental stimulation. 4. Statistics. a quantile for the special case of six equal proportions. from dictionary.com

If the exponential distributions have the same scale parameter it's known as the Erlang-2 distribution. PDF and CDF exist in closed-form but the quantile function does not.

If you're looking to generate random variates the easiest method is to sum exponentially distributed variates. If the scale parameter is the same you can simplify a bit: -log(U0) - log(U1) = -log(U0*U1).

Doryun Sok is an author known for writing about contemporary Korean art and modern art history. His work often focuses on Korean artists and their impact on the global art scene. Sok's writings provide insights into cultural exchanges and the development of art in Korea.

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +

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152

50

10 x 10=100. Would you rather go like this: 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100?

64

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10

1 1 1 1 1 1 1 1 1 1 5 5 5

1 1 1 1 1 1 1 1 1 1 5 10

1 1 1 1 1 5 5 5 5

1 1 1 1 1 5 5 10

1 1 1 1 1 10 10

5 5 5 5 5

5 5 5 10

5 10 10

12 ways

1+1+1+1+1+1+1+1+1+1+1+1+1=13 3 divided by 10 = 30

I assume by "square numbers" you mean perfect squares.

You didn't say how many of each were allowed:

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1²= 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 3² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 2² + 2² + 2² + 2² = 23

1² + 1² + 1² + 1² + 1² + 1² + 1² + 4² = 23

1² + 1² + 1² + 1² + 1² + 3² + 3² = 23

1² + 1² + 1² + 2² + 2² + 2² + 2² + 2²= 23

1² + 1² + 1² + 2² + 4² = 23

-29

1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1 and 1

and 1 and 1 and 1 and 1 and 1 and 1.

Or

1.1 and 1.1 and 1.1 and 42.7

or an infinite number of other possibilities.

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

(-1)3 = (-1)(-1)(-1) = -1

11111 x 11111 = 123454321

1 1 1 1 1

x 1 1 1 1 1

_______________

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

1 1 1 1 1

+ 1 1 1 1 1

_______________

1 2 3 4 5 4 3 2 1

[Legend: Each number represents the denomination (amount) of the coin.]

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+5+5 = 25

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+10 = 25

1+1+1+1+1+1+1+1+1+1+5+5+5 = 25

1+1+1+1+1+5+5+10 = 25

1+1+1+1+1+5+5+5+5 = 25

1+1+1+1+1+10+10 = 25

5+5+5+5+5 = 25

5+5+5+10 = 25

5+10+10 = 25

So the answer is 11!!!

I think you're missing 1+1+1+1+1+1+1+1+1+1+5+10 = 25 ?

20

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 is one example.

The answer is -1.

(1 + 1 x 1)/(1 - 1 x 1 -1) + 1 =

Follow the order of operations: parentheses/brackets, exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Numerator:

Simplify 1 x 1 to 1.

(1 + 1)/(1 - 1 x 1 -1) + 1

Simplify 1 + 1 to 2.

2/(1 - 1 x 1 - 1) + 1

Denominator:

Simplify 1 x 1 to 1.

2/(1 - 1 - 1) + 1

Simplify 1 - 1 - 1 to -1.

2/(-1) +1

Simplify 2/(-1) to -2.

-2 +1

Simplify.

-1

There are infinitely many possible solutions. One of them is

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 +

1 + 1 + 1 + 1 + 12

11

1+1 is 2 and 1-1 is 0 and 1*1 is 1 and 1/1 is 1

23

One possibility:

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 x 0

1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1x0=

They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

They are -1 and +1.

1 quarter, 2 dimes, 2 nickels, and 45 pennies

1+2+2+45=50

25+10+10+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=100

1 quarter, 2 dimes, 2 nickels, and 45 pennies.

1+2+2+45=50

25+10+10+5+5+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

The reciprocal of 1 is 1.

Proof:

a. 1*(1/1) = 1 because a*(1/a) = 1

b. 1*1 =1 because 1*a = a

c. 1/1 = 1 compare a. and b.

1+1-1+1-1+1-1+1-1+1-1+1-1+1-1*0+2

1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 19

1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 12 1 11 1 1 1

There are infinitely many possible answers.

One such is 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+16

It is negative infinity.