Questions tagged [mean]
The expected value of a random variable; or a location measure for a sample.
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How to calculate mean and SD between $T_1$ and $T_2$ based on mean and SD from $T_0$ to $T_1$ and $T_0$ to $T_2$?
I am performing a meta-review about the transition of control in semi-automated cars, for which I am trying to retrieve specific means and standard deviations. I am not sure if I am using the right ...
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1answer
47 views
How can I shift the average probability keeping constraint (0.0:1.0)?
I have a large datasets of values that range from 0 to n. I am interpreting the values as probabilities for a later pseudo-random selection process. To make the values serve as probabilities, I ...
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Significant T-test with small mean difference but large standard deviation
I have recently run some analyses to test whether those participants lost to follow up are significantly different from those who stayed in the study. N= 590 for those who stayed and N=258 for those ...
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100 views
+100
Sampling distribution of the mean of the discrete-power law distribution
For a certain problem I wish to generate random integers $k$ so that their distribution follows $p_k \sim k^{-\alpha}$ for $k \geq k_{\text{min}}$, $k_{\text{min}} > 0$. I am following the ...
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3answers
329 views
Where does the expected value definition come from? [duplicate]
The definition of the expected value on the domain $[a,b]$ is given by
$$E[X] := \int_a^b x f(x) \, \mathrm dx $$
I understand what the mean is, but I don't fully understand how this specific equation ...
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25 views
What is the expectation of absolute difference
Given:
E(|X-R|) =2.5
E(|L-X|)= 3
where X, R, L are assumed to be normally distributed and independent. Standard deviations of |X-R| and |L-X| are known.
what is E(|L-R|) ?
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4 views
giving the sample covariance formula I want to show that they are equal [closed]
I want to understand how to move from the first formula of sample covariance in the image attached to the one below as indicated by the arrow
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1answer
20 views
Standard Error of the Mean: Do I use the main dataset's SD, or the sample's SD?
There's a nationwide dataset of the average scores on test, by school (each school has one entry in the dataset). There are significant differences between the means and SDs among the states. A subset ...
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1answer
46 views
Probability of a sample mean higher than population mean
I have solved this question but I am not sure if what I did is correct:
It is found that the population mean and standard deviation for the paper are 45.292 and 18.761 respectively. Find the ...
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0answers
23 views
Is it valid to compute the Spearman rank correlation's p-value on summarized (mean/median) data?
I have a dataset generated as follows: On each day for 30 days, a measurement is made for each individual. Individuals are separated into two groups. Each group contains 5 individuals.
Is it valid to ...
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1answer
31 views
variance of theoretical mean of y at given value of x in regression [duplicate]
Could someone tell me where I might find information on deriving the standard error used in confidence and prediction intervals of y at a given value of x on a regression line. I can't find anything ...
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Can I log-transform the sample variance estimated from an originally log-transformed data?
I have a dataset that is log-transformed to meet the assumptions of normality. I have estimated the mean and variance of each individual. I understand that the obtained mean is log-transformed. My ...
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9 views
Combined Variance through Several Linear Functions
Apologies in advance if my terminology isn't correct for everything I'm about to write
I am dealing with a corner-cased problem and I'm trying to figure out if my derivation is correct.
I have a large ...
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12 views
What is the difference between using SDs away from the mean and SEs away from the expected value?
I've always learned about the bell curve concept as having units in SDs away from the mean. For example, if the mean is 5 and the SD is 2, then the curve is centered around 5, and, for example, a data ...
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28 views
How to separate the relationship between mean and standard deviation, mean and coefficient of variation?
I have again a similar question related to my previous posts. Please consider the following scenario:
Mean and standard deviation of A are positively correlated.
Mean and coefficient of variation (CV)...
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17 views
Calculate minimum detectable effect
I need to calculate analytically the minimum detectable effect when comparing two-sided 2 sample proportions z-test for given sample size (different sample size per group), significance level and Type ...
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19 views
How to calculate the mean and standard deviation of combined series?
A company produces two products. It sells the product P1 per month and the product P2 per season. The revenue of the product P1 over one year (with monthly frequency) is stored in A.
...
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2answers
390 views
Effect of nonlinear transformations on the mean
Suppose I have a continuous random variable $X$ and a random variable $Z = f(X)$, where $f$ is a nonlinear monotonic transformation. How can I prove the following relation between the mean and the ...
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Distribution where mean and mean of reciprocal are both 1 [duplicate]
Is there a non-trivial distribution for a positive r.v. $X$ such that $\mathbb{E}(X) = \mathbb{E}\left(\frac{1}{X}\right) = 1$? If possible, I'd like the distribution to support (have positive ...
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1answer
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Sample size required for a given margin of error in sample mean when population standard deviation is not known
I have trained a regressor to predict the revenue generated when users click on an ad impression. Only few clicks eventually lead to positive revenue. As such, I have used the Tweedie regression in ...
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63 views
Is estimation of Coefficient of variation (CV) misleading when sample mean and standard deviation is negatively correlated?
I have a dataset with 145 individuals and two traits measured in 12 environments. I want to measure the variation among individuals i.e. individuals with high performance in one environment and low ...
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How to interpret results of survey with more options to select and find mean, median, modus
From mini-survey of 8 system users was found that:
1 Uses website
4 iPhone app
7 Facebook
2 Twitter
2 E-mail subscription
1 user can use more communication platforms.
How can I say: “From this ...
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34 views
The quantile of prob=0.05 and mean
What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution?
In other words, I would like to understand the relationship between ...
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1answer
43 views
Can I use the sample mean to check whether non-normally distributed populations are different?
I've run a user-test of a tool where 86 users participated and scored the a according to the System Usability Scale. The scale goes from 0-100, with 0 being the worst and 100 being the best. The ...
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2answers
54 views
Should I use 'median' instead of 'mean' for nonparametric distributions?
I have a dataset that I determined was nonparametric. If I want to do calculations like '% change', and find the average percentage change, should I really find the median percentage change instead of ...
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1answer
15 views
I want the mean of a group of means where some instances have multiple means. Should I include all scores, or only one mean per instance?
I have a list of mean usability scores for different tools. Some of these tools have been tested separate times, giving different scores. I now want the mean score for the entire group of tools - what ...
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15 views
How to compare factor levels when more than one categorical variable is present?
I have 2 categorical variables in my data: g1 and g2.
g1 has 5 levels:0,1,2,3,4.
g2 has 2 levels:0,1.
Below you see the coefficients and their errors and individual p-values and so on. I was wondering ...
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1answer
19 views
Telling which group's mean value is higher using lm()?
We have groups A,B,C and we try to see if their means are different. Below are the summary of the linear model fitted.Below you can see group A is the reference group.Can I say checking coefficient ...
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12 views
replacing nas when 50% or more of the data is missing
I have to perform a linear regression on a dataset. However, I am having trouble figuring out what type of imputation I should do on the data because in some cases the majority of the the data is ...
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1answer
37 views
Sampling distribution of sample means question (Newbold)
6.3 from Newbold (8th ed.):
A population contains 6 million 0s and 4 million 1s. What is the approximate sampling distribution of the sample mean in each of the following cases?
The sample size is n ...
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2answers
91 views
Calculating the Mean of an Ordinal Variable Question
I have distributed and analyzed a survey regarding teaching quality. For some of the questions, I ask how often a given teaching method is used. When doing this I ask them to select one of the ...
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1answer
24 views
How do you find the asymptotic distribution of a function of the sample mean?
There are a number of questions on this site that ask for the asymptotic distribution or moments of some function of the sample mean for IID data (see e.g., here, here, here, here and here). All ...
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1answer
29 views
Number of samples needed to estimate population mean to given margin of error
The population distribution is unknown, but is probably multi-modal. The required margin of error is given in advance. Any number of samples can be drawn from the population.
Given enough samples, ...
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10 views
How to calculate an average from three distinct but related samples?
I am trying to find out how to average price information stemming from three different types of products belonging to three distinct groups: Red Cars, White Vehicles and Blue Vehicles. The information ...
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1answer
320 views
What are good methods to deal with outliers when calculating mean of data?
I have a dataframe with yearly energy uses of buildings over 5 years. In order to have a representative yearly energy use for data modelling, I'll have to take the mean of those data. As the data can ...
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2answers
170 views
How would you find the mean of the zero truncated Poisson distribution? [closed]
Given the probability mass function is,
$f_T(y)=P(Y=y|Y>0)= \frac{1}{e^\lambda -1} \cdot \frac{\lambda^y}{y!}, y=1,2,3,\dots$
Where,
$f(y)=\frac{e^{-\lambda}\lambda^y}{y!},y=0,1,..$
How would ...
4
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3answers
124 views
Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate]
https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#In_least_squares_regression_analysis
I was reading this page and came across the fact that the mean of the predicted target values for an ...
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1answer
184 views
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37 views
What's the relationship between $\frac{1}{n}\sum_{i=1}f(X_{1i},X_{2i})$ and $\frac{1}{n^2}\sum_{i}\sum_{j}f(X_{1i},X_{2j})$?
Suppose $(X_1,X_2)$ is a bivariate random vector following distribution $G$. $f(x_1,x_2)$ is a known bivariate smooth function. Suppose we are interested in estimating $E[f(X_1,X_2)]$ using a random ...
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2answers
48 views
What estimation method establishes sample mean and sample variance as estimators of mean and variance?
Sample mean and sample variance can be derived as MLE estimators for the mean and variance of a normal distribution.
For a distribution in general, what kind of estimation method leads to sample ...
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14 views
Relative Median Absolute Deviation
For example, the CV (coefficient of variation) is the relative standard deviation (sd divided by the mean).
Now is there a relative MAD (Median absolute deviation https://en.wikipedia.org/wiki/...
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8 views
In a One-Way MANOVA, can one of the levels of the IV have a mean of 0 with a standard deviation of 0 on one of the dependent variables?
I realize that this sounds like a very stupid question, but I need to make sure—please stick with me.
The project in question is a quantitative content analysis; for the sake of this example, let's ...
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2answers
624 views
Is there a name for the midpoint of a sum (not a mean or median)?
I have a set of purchases with $ values like this: {1, 1, 1, 2, 7, 8, 10, 10, 20, 20}. Sum: 80. Mean: 8.
I had thought that if you split this into equal sums (of 40), this would occur at the mean (8)...
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1answer
26 views
Exhaustive list of techniques used to estimate population mean and variance?
In beginning stats, we were told that:
$\bar{x}$ is an unbiased estimate of $\mu$
$\frac{1}{n - 1}\sum(x - \bar{x})^2$ is an unbiased estimate of $\sigma^2$
As I am reading more, I have learned that ...
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4answers
418 views
Does Bayesian statistics bypass the need for the sampling distribution?
Let's take the classic case where the population follows a normal distribution, observations are iid, and we want to estimate the mean of the population.
In Frequentist stats, we calculate the ...
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1answer
22 views
Independent t-test for between 2 samples, using function other than Mean
I have 2 sample groups of n = 1000 individuals for each group. Each individual rates the quality of a product on a scale from 1 to 10, and these rating are the ...
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2answers
22 views
How to calculate therical `mean`,`sd` based on given distribution paramters in R?
Example: gamma distribution with shape=4,rate=0.05.
Checked wikipedia,In ...
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2answers
20 views
How to approximate sample mean age of people in a survey from grouped data
I am trying to calculate the approximate mean age of people that participated in a survey.
I have 4 age groups: $[0,15);\,[15,35);\,[35,55)$ and $[55,75).$
For each group age I have the number of ...
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0answers
18 views
How to calculate the threshold value for a variable
In a question-answer platform, in each week the platform releases a new question. In total there are 15 questions.
There are these three types of users.
Log in every week, and answer in the correct ...
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14 views
Mean of target values at different time points as predictor in multiple regression
I've received regression model that predicts crop yield based on data collected at 3 time points (years).
Input data contains multiple attributes and crop yield in the given year for a given location....
