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Questions tagged [mean]

The expected value of a random variable; or a location measure for a sample.

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1answer
24 views

How would I calculate the standard deviation of a sample given the sample size, mean, and sum of the data's squares?

For example, given: $\sum_{i=1}^n x_i^2 = 10$, $n=10$, and $mean = 10$, how would I go about calculating the standard deviation? The formula for standard deviation requires me knowing what $\sum_{i=1}^...
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13 views

Comparison of MAE and Mean to illustrate the error magnitude

I have predicted a time series with positive, zero and negative values. As error measurement I used the Mean Absolute Error (MAE). In order to give the reader of my paper a better understanding ...
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0answers
9 views

Back-calculation of the minimum sample size for an mechanical experiment [on hold]

I want to back-calculate the minimum sample size for an experiment. I have a known mean and standard variance of a statistical population. From the statistical population I chose two samples with ...
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3answers
3k views

Why do we use the Greek letter μ (Mu) to denote population mean or expected value in probability and statistics

According to this Wikipedia entry, "Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water". So, my question ...
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1answer
11 views

Error Propagation of standard devi

I have following problem: I do measurements with technical triplicates and biological dublicates. So I prepare the same sample two times and measure each one three times. This gives me an average ...
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0answers
15 views

Mean of repeated samples

Let's assume we have random variables $X_1\sim N(\mu_1,1),\cdots,X_n\sim N(\mu_n,1)$. Now we take one sample from each and get $X_1 = x_1,\cdots,X_n = x_n$. We order them and calculate the mean of top ...
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2answers
69 views

Computing the confidence interval for two samples but getting slightly different answers

Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
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0answers
20 views

Deriving the average and variance of number of runs in runs test

NIST states that the average and variance of a number of runs in the "runs above and below median" test as $$ \overline{R} = \frac{2n_a n_b}{n_a + n_b} + 1 \\ s^2 = \frac{2n_a n_b(2n_a n_b - n_a - n_b)...
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1answer
11 views

When to use Bessel correction and and does it alter the standard error?

is there any condition about when to use the Bessel correction as Python uses it to find the Standard Deviation by default. The standard error of the mean is $\...
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1answer
27 views

accuracy of the mean

I am doing a study on the performance of Aquifer thermal energy storage systems. During this study, I get results with consist of a normal distribution around a mean. What can I now say about the ...
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2answers
39 views

Is it reasonable to represent mean value without removal of the outliers?

At first, I want to say, I know that mean is outlier sensitive. Problem I have to talk about the lifestyle of the students, where the data is quantitative. Let's say I have to talk, how much time a ...
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1answer
15 views

How to modify the mean?

I have data collected in consecutive time periods using two sensors (i.e. sensor1 and sensor2) as follows. ...
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1answer
116 views

Calculate Mean and Standard Deviation, when given the confidence interval and sample size

How can I calculate the sample mean and sample standard deviation, given that I know the sample size and the confidence interval for the mean? For example, with the info provided below: Sample size ...
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0answers
23 views

How to plot minimum, maximum, and mean in r [migrated]

I've been reading how to plot points in r, but can't find anything that matches my problem. My data is a matrix; the rows start with a column called 'site' and it is followed by three columns ...
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1answer
15 views

Comparing Means of different Subscales

a friend recently asked me if she could compare the means in different subscales of one Questionnaire (measuring more or less distinct construct) in one sample. In concrete she has a sample of 100 ...
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1answer
42 views

How do I fit a distribution to summary statistics of population data?

I have a limited set of income data for CountryX. I have the mean, median and percentages (%) of the population that fall within various income brackets. I am trying to work out what percentage of the ...
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2answers
90 views

Is mean absolute deviation smaller than standard deviation for $n\ge 3$?

I want to compare the mean absolute deviation with standard deviation in general case with this definition: $$MAD = \frac{1}{n-1}\sum_1^n|x_i - \mu|, \qquad SD = \sqrt{\frac{\sum_1^n(x_i-\mu)^2}{n-1}}...
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1answer
46 views

Interpretations of time-series data with standard errors

I have plotted time-series data on estimates of pollutant emissions superimposed with standard errors of the means. See the figure below. In reality, quantities of emissions should be non-negative. ...
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2answers
1k views

Can someone give the intuition behind Mean Absolute Error and the Median? [duplicate]

I do not understand the intuition behind why the median is the best estimate if we are going to judge prediction accuracy using the Mean Absolute Error. Let's say you have a random variable X and you ...
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1answer
36 views

Inferences from a zero-inflated negative binomial distribution?

Frogs are generally known to spatially aggregate during egg-laying. I manipulated their egg-laying sites with different fertilizers ("Nitrogen" or "Phosphorous") that differed in their concentration ("...
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0answers
27 views

2 sample t test

I was thinking that a simple 2 sample t test is not that simple when dealing with skewed data. Considere 2 samples, each one with diferent skewness and kurtosis, both with a big sample sizes (say n > ...
2
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1answer
38 views

Under what circumstances would one expect a correlation between mean and stdev?

I have a distribution in which the standard deviation is positively correlated with the mean (0.9). The stdev increases as the mean increases. The data is count data without zeros. I'm interpreting ...
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6answers
339 views

How do I find the mean of counts of reported events when the last category is “5 or more”

I know that we can find mean (No. of errors per patient) from 0*5+1*30+2*56+3*15+4*10 But for 5 or more, what do I need to do?
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16 views

Appropriate sample size for model validation with RMSE errors

I have been looking over the internet for a way to determine the appropriate sample size for a validation experiment that validates the RMSE results from a deep learning (CNN) model. The network was ...
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1answer
29 views

How to determine whether a validation study produces acceptable results?

I have a method developed to predict results of a signal that outputs an root mean squared error (RMSE) for each subject. Combining all 40 subjects (2 samples for each subject), I get a mean RMSE of 5....
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1answer
30 views

Correct way to do a difference in means bootstrap

Say I want to find the confidence interval for the difference in means and I have these numbers: For A: c(1, 2, 3) and for B ...
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0answers
28 views

Calculate bounds of the sum of means of a normal distribution [closed]

I am not sure whether this question really belongs on this StackExchange or whether I should post it on a different one. Please indicate if this is the case. I am programming an algorithm (A1) and I ...
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1answer
20 views

Hypothesis test for the difference of two means, should I consider annualized or monthly returns?

I have 10 years monthly returns. I calculated annualized return multiplying the mean return over the period for 12. Then I calculated the excess returns as difference between the annualized mean ...
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0answers
18 views

Measures of Uncertainty in Higher Order Moments [duplicate]

Suppose I have a sample of data and compute the mean. I am able to quantity uncertainty in this by computing the variance. I am wondering if known methods exist for evaluating the uncertainty ...
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0answers
14 views

how do i annualize the mean of my monthly returns?

I'm getting really f'd up since two hours and almost deleted all of my code since this doesn't make sense to me. I got simple returns. I want to calculate the annualized mean. This would be my ...
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1answer
85 views

Formula to Calculate Confidence Interval of Marginal Means

What is the formula for the marginal means confidence interval in a regression analysis? Let us have the following regression $Y = b_0 + b_1X + b_2Z + b_3 XZ + b_4 Cov_1 + b_5 Cov_2$ If I get it ...
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1answer
19 views

why mean=50 instead of 0 and why is it even needed in this rnorm function? (From ISL book)

I'm new to the field of data science and I've started off by going through the Introduction to Statistical Learning book. In there I am going through the introduction to R section and have come ...
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2answers
74 views

I can see my two means are different. What information can a t test add?

Methods such as t-tests and anova find the difference between two means using a statistical method. This seems strange to a beginner like me, one could simply find the mean of two groups and ...
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1answer
42 views

How to derive Mean of Truncated Normal Distribution

How to derive Mean of Truncated Normal Distribution which is equation 17 below ? Note: Image screenshot is taken from L1-Norm Batch Normalization for Efficient Training of Deep Neural Networks
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1answer
23 views

significant mean difference over time?

I need help. I am looking at two data sets that come from two surveys asked of the same group with the same population over a year apart. Year one, the group was asked to rate 15 statements on a scale ...
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0answers
25 views

How to combine standard deviation of natural log and division equation?

I have two variables X_m and Y_m that are the mean of two data sets with standard deviations x_s and y_s. The equation I need to use is: A = |ln( X_m / Y_m)| How would I go about obtaining the ...
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2answers
313 views

Independence of Mean and Variance of Discrete Uniform Distributions

In the comments below a post of mine, Glen_b and I were discussing how discrete distributions necessarily have dependent mean and variance. For a normal distribution it makes sense. If I tell you $\...
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1answer
86 views

Central limit theorem and normal distribution confusion

So I'm trying to study for a test and I'm stuck on two textbook questions. I'm having trouble grasping the concept of sampling distributions and when to apply certain rules/when to categorize a ...
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1answer
39 views

How can I estimate the mean and standard deviation of the total duration of a family of tasks?

My current assignment at work deals with our in-house task system, which is largely responsible for executing operations and other work asynchronously from the usual HTTP request/response workflow. I ...
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1answer
37 views

Intuition for variance of mean sampling distribution

I'm having issues comprehending the reasoning behind the following formula: For a sampling distrubution $$\overline{X_1}, \overline{X_2},..., \overline{X_N},$$ The following is true $$ V(\overline{X})...
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1answer
51 views

Can a random variable/distribution have non-constant mean?

I have been asked that question, and it's very weird to me. I know how a random variable/distribution can basically not have a mean due to diverging integral of its expected value. But how is it ...
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1answer
59 views

How to change exponential distribution into Normal distribution? [closed]

We have random data, which is exponentially distributed. Data = exp($\lambda$), where $\lambda$ = 0.5. If it is possible to change exponential distribution into the normal distribution. Then what ...
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0answers
23 views

Intuition behind standard deviation greater than mean for all positive values [duplicate]

I am following through this example But it doesn't talk about what does it mean when the standard deviation is higher than mean when all values are supposed to be positive e.g. standard deviation of ...
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0answers
10 views

Is it possible to derive the median of a distribution from the mean and Gini Index?

I have some data on GDP, population, and the Gini index for various countries, and I would like to derive some median metric. To put it more broadly, given the sum $\sum_{i=1}^{n} x_i$ and size $n$ ...
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0answers
27 views

Average of correlations over time

I currently work on my bachelor's thesis and analyse the correlation between 13 countries over a time period of 117 years. I built a correlation table and now want to say somethin about the average ...
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1answer
32 views

t-test with negative and positive variable values?

I have two variables (A and B) that are correlations, i.e. with values between -1 and 1. I would now like to test whether variable A differs significantly from B. Can I use a t-test for this? Or ...
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3answers
43 views

T-test for two independent variable

This image show sample taken from LA and NY for apple price. When I want to do a hypothesis test if the mean of NY price > LA price, I was saying that my NULL hypothesis is H0 : μ_NY - μ_LA > 0, but ...
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1answer
76 views

Why does the mean for a beta distribution when input into the scipy beta cdf not return 0.5? [duplicate]

Very likely I am missing some fundamentals here, or my python coding is not up to scratch. When I use the standard formula to calculate the mean for a beta distribution ~ $B(\alpha,\beta)$ $$ \mu = \...
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2answers
489 views

Given mean and SD, can we approximate the underlying distribution?

I know the following info for values of a particular column for a dataset: [mean=4.989209978967438, stddev=2255.654165352454, count=2400088] Given just this, is it possible to approximate what the ...
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0answers
40 views

If Mann-Whitney U is a median test? Then what the heck is “unpaired pairwise median”?

Header: I am really sorry for the confusing title. I am going to edit it so it fits the responses I get based on Mann Whitney U. So I had this exact question on stack overflow about is the Mann ...