The area of statistics that provides descriptions of data, may it be samples or the population. This includes graphical representations and numerical indicators. No information is inferred from samples about the population, as in inferential statistics.

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How to do sampling for the following problem. [on hold]

There are 200 students with a mathematics exam marks. According to marks students are divided into five categories 0-20,20-40,40-60,... and I want to choose two random sample with 25 for a group. ...
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12 views

Prove the expression for standard deviation

Problem Let $x$ be a variable assuming the values $i=1,2,\ldots,k$ with frequencies $f_i$ and let $F'_i$ be the corresponding cumulative frequencies of the greater-than type, while $F''_i$ are ...
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7 views

A statistics problem on proving an inequality

Problem Let $R$ and $s$ be respectively the standard deviation and range of a set of $n$ values. Then prove that $\dfrac{R^2}{2n}\leq s^2\leq \dfrac{R^2}{4}$. I have tried using the ...
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1answer
52 views

The Largest Gap

If I have an X amount of randomly generated positive numbers, what type of algorithm could I run to find the following: Precisely where the largest difference exists between two of the numbers? How ...
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1answer
29 views

question on normal distribution [closed]

A mean of 25 mpg and a standard deviation of 5.8 mpg for highway driving. Assuming that a normal distribution can be applied. a) What gas mileage would put a car in 85th percentile for all cars? b) ...
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12 views

Curve 'anti-correlation' detection

If I have a data set, what algorithm can I use to detect when one curve moves in clear opposition to the majority of curves? For example: At point 15, the purple line moves up in opposition to the ...
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21 views

Statistics: Eliminating the effect of one parameter

a quick statistics question. Consider having a conveyor band inside a black box. A test-object is pulled through the black box at different speeds whilst gathering sensor data (temperature ...
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2answers
12 views

Population Variation with two variables

I have a dataset with two variables. I want to treat my dataset as a population not a sample. I am wondering if I can just use the formula for population variance as below: ...
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8 views

Is there a measure that monotonically changes as we change a normal distribution to a bimodal distribution?

Is there a measure with values varying monotonously from -1 to 1 (or 0 to n) as we change a bimodal distribution (or say a reverse normal distribution) to a normal distribution? Will the same work if ...
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2answers
39 views

Is there a measure of 'evenness' of dispersion?

I looked up on the web, but couldn't find anything helpful. I'm basically looking for a way to measure how 'evenly' a value is distributed. As in, an 'evenly' distributed distribution like X: and ...
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1answer
76 views

Analysis of IQ scores given mean, median, sd, quartiles

The statistics below provides a summary of IQ scores of 100 children Mean: 100 Median: 102 Standard Deviation: 10 First Quartile: 84 Third Quartile: 110 About 50 of the children in this sample have ...
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74 views

Joint PDF of Chi-Square & Normal Distribution

Let the independent random variables X1 and X2 be N(0,1) and $\chi^2(r)$, respectively. Let $Y_1$ = $X_1/sqrt(X_2/r)$ and $Y_2$ = $X_2$ a) Find the joint pdf of $Y_1$ and $Y_2$. b) Determine the ...
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1answer
38 views

Low Leverage in Residuals, Logistic Regression

I am doing an interpretation of logistic regression and I have an observation withh high residuals but low leverage. I thought that means that it is an outlier(bad prediction) but not ...
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1answer
21 views

calculating upper and lower quartiles

The 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 ...
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1answer
55 views

Distribution Weibull

I'm trying to find the parameters of the weibull distribution, the only thing that they gave me were the mean=EX=40 and the standard deviation=VX=35^2 I have gotten there so far but I'm stuck, have ...
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2answers
12 views

Calculating Quartiles Dilemma

When I am calculating the lower quartile and upper quartile, why am I taking (n+1)/4 and 3(n+1)/4, instead of n/4 and 3n/4? According to me, if total number of observations are n, then that should ...
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1answer
47 views

How to calculate lower & upper quartiles?

I'm sure this has been asked many times before but it's confusing me a lot so hopefully someone can help! I am given this data set: 0.28 0.30 0.42 0.59 0.71 1.67 1.82 2.39 4.71 4.79 4.89 5.00 5.00 ...
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37 views

Proof that data-processing selection process is statistically independent of the sample?

I hope to replace a proof of my own, in a paper explaining that the "no free lunch" theorems for optimization actually address sampling and statistics, with a reference to an existing result on ...
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1answer
175 views

Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...
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1answer
30 views

What can be said about usefulness of two regression lines?

How one can say that the regression equation $y$ on $x$ is more useful than the regression equation $x$ on $y$ as a predicting formula?
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1answer
82 views

Implications of Standard Deviation > Mean

I have a numerical dataset in which the standard deviation is larger than the mean and I am interested to know what this fact can tell me about the dataset. I have drawn the following conclusions on ...
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2answers
42 views

income distribution from N, min,max and mediansalary, and total compensation

My goal is to obtain a reasonable approximation of the Gini index of a company (UBS). I need to obtain an estimate of the salaries distribution from publicly available data: Nuber of employees=60205 ...
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1answer
38 views

Question about Logistic Regression - 7

I am currently studying Logistic Regression. I am facing a problem with understand the sentence in the red circle below. I am trying to figure out what he/she means by the sentence. Please let me have ...
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28 views

Question about Logistic Regression - 6

I am studying Logistic Regression and I have come across to understating the paragraph below. I kind of can understand, but it makes me confused when I read the sentence in the red circle, "It also ...
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1answer
35 views

Question about Logistic Regression - 2

How should I tell the difference between those two formulas in the circles below. I am studying logistic regression and I have faced two different formulas from two different documents. I don't know ...
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1answer
21 views

Question about Logistic regression-1

As I am currently studying Logistic regression, but I am still new to this. I have encountered a sentence and a word below in red circles that I can only image but not with my own clear ...
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2answers
39 views

Question about Logistic Regression - 4

I am currently studying on logistic regression. So I have found a document on the Internet explaining about it. Somehow, it explains Bernoulli distribution in the beginning and I am having a problem ...
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3answers
54 views

Question about English sentences in statistics?

Can somebody help me interpreting the red circled sentences in planer English? I understand "We view $y_i$ as a realization of a random variable $Y_i$ that can take the values of one and zero" but ...
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1answer
27 views

How to get a Gaussian curve fitting a given range of values?

I was trying to find a way to make a gaussian function out of a range of values: $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13\ 14\ 15\ 16$ I want the mean to be the most probable value, $8$ and the ...
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1answer
270 views

Measuring Variance of 2D Data Points

I have a list of weighted data points on a 2D plane in the form $(x, y)$. I believe the mean can calculated as $\left(\frac{\sum{x_i\times w_i}}{\sum w_i}, \frac{\sum{y_i\times w_i}}{\sum ...
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1answer
72 views

How to calculate new mean if population is unknown?

I have three values Mean (population mean, not from sample) $\bar{x} = 3$ Number of elements in population (number of values in original set) $n = 15$ A new value $x_{(n+1)} = 7$ What is ...
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21 views

Statistical Term for a Ratio of Percentages

In short, what's the name for a statistic that is a ratio of two percentages? I'm assessing the code quality of a developer using two metrics: Lines of Code and Number of Violations. Legitimacy of ...
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15 views

Help With Cross-Sectional Analysis

I am in an undergrad Econometrics class, and we are covering Repeated Cross Sectional and Panel Data analysis. The notes are not very clear, and I was wondering if anyone could link me to helpful ...
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1answer
21 views

Addition of two box plots

I have two box plots that I'd like to add together to form one box plot representing both plots in one. Here's an example of two box plots: At a school 200 boys and 200 girls participated in a test. ...
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44 views

Calculating the median when the sample size is even

In statistics the median is a point that divides an ordered data into two equal parts. By definition if $n$ is odd the median is $\frac{n}{2}{th}$ data point that is simply the middle point of the ...
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2answers
50 views

Finding correlation coefficient

Two dice are thrown. $X$ denotes number on first die and $Y$ denotes maximum of the numbers on the two dice. Compute the correlation coefficient.
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1answer
45 views

Basic business statistics [closed]

In 2009, the average charge for tax preparation by Hilda was $\mu=187$. Assuming a normal distribution and a standard deviation of $\sigma=20$, what is the probability that a randomly selected ...
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1answer
19 views

some knowledge about comare means of two group

I'm studying a bout statistic. I can compute very well. But i don't really know well. I want to know clearly about theory. And i have this problem: ...
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1answer
56 views

How do I find $\theta$ with bootstrap?

I have two vectors of known values $x$ and $y$. And the relationship between them is $y=\sin(\theta \cdot x)+\epsilon$, $\epsilon \sim N(0,1) $ . The question is how do I estimate $\theta$ with ...
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1answer
36 views

Smallest sample to produce n%

Q: A Statistic is published that 31% of people think it is okay to smoke in public. What is the smallest sample that could have been interviewed to get this result. A: 13, with 4 "yes" and 9 "no" ...
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1answer
20 views

Comparision between two random samples

I have the following simple random samples which denote the scores obtained by some students over $10$: Random sample A: 3.5 4.5 4.813 5.065 5.252 5.438 5.547 5.586 5.937 6.025 6.025 6.345 6.375 ...
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1answer
52 views

Need help understanding the approach to this question

At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their ...
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1answer
36 views

Problem related to the exact distribution and the CLT

I'm trying to solve a pretty straight forward problem but i can't find good info on the subjects necessary to solve it so i'm terribly stuck. I'll present it as follows and later try to explain my ...
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1answer
205 views

Change in single observation of data set and how it will affect sample variance

Q/ Consider the sample of size n=10, where the sample mean is 6 and the sample variance is 12. Consider a second sample that is exactly the same as the first except that there is an additional ...
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2answers
54 views

Why does variance divide by $n-1$? [duplicate]

The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ I read that $n-1$ is used instead of just $n$ when we are measuring the variance of a sample taken from a bigger population. I don't ...
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7answers
108 views

Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
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3answers
39 views

question about Mean absolute deviation formula

$$\frac{\sum_{i=1}^{n}(x_i-\bar x)}{n}$$ This method will not work for calculating the mean deviation. Instead we have: $$\frac{\sum_{i=1}^{n}|x_i-\bar x|}{n}.$$ I'm not quite understanding why ...
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43 views

How to convert a histogram into a failure rate distribution?

I have a histogram in which the frequency of failures are charted in the y-axis, the bins in the x-axis are time pockets in hours. This is from my historical data. The y-axis is the number of failures ...
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46 views

Question about Bernoulli Distribution calculation

can sombody explain the above calculation in the red circle marked with "why?"? I am studying MLE with Bernoulli Distribution, and in the middle of a video clip, the lecturer says $ 1\over{n} ...
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1answer
53 views

Confidence level of random sample from continuous distribution

Let X1,X2,⋯,Xn be a random sample from a continuous distribution with median μ. If [Xmin, Xmax] is used as a confidence interval for μ, what is its confidence level? What is the confidence level if ...