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

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3
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1answer
68 views

Identifying whether some drivers are not collecting boarding passes

Here's the problem. I work for a transportation company and we're trying to prove the following hypothesis: Drivers are allowing passengers on the vessel without taking taking their paper boarding ...
0
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0answers
266 views

How to plot mean plus/minus standard deviation for histograms?

I have a set of grayscale images, where the pixels may have values in the range $[0, 255]$. From each image, I calculate a histogram, which shows how many pixels have the value $0$, $1$, $2$, and so ...
9
votes
1answer
471 views

Is the median a “metric” or a “topological” property?

I apologize for the slight abuse of terminology; I hope it will become clear what I mean below. Consider a random variable $X$. Both the mean and the median can be characterized by an optimality ...
1
vote
0answers
148 views

How to calculate mean and standard deviation of a range variable (grades) when the raw data is based on frequency categories?

Results of an exam indicate that: 13% of the class earned an A 20% earned a B 48% earned a C 10% earned a D 9% earned F's The grade C ranges from 70-79%. Assuming that the data is normally ...
1
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4answers
98 views

How many samples needed to approximate true mean?

If I have some arbitrary random variable with true mean $\mu$ how many samples from its distribution do I need to take such that the empirical mean $x$ approximates $\mu$ within an error of less than ...
5
votes
1answer
668 views

Efficient way to compute distances between centroids from distance matrix

Let us have square symmetric matrix of squared euclidean distances $\bf D$ between $n$ points and vector lengthed $n$ indicating cluster or group membership ($k$ clusters) of the points; a cluster may ...
1
vote
1answer
518 views

Making the most of Standard Deviation and P value — graphing?

I have a question or two in regard to getting the most out of the statistics of my data. By way of background, my qualitative observations of two distinct populations that are uniformly regarded to be ...
0
votes
1answer
2k views

In SPSS, should I calculate the mean score or the total sum score?

Are there any differences between mean scores and total sum scores? I know how to calculate both, I just don't know if there is one of them that is preferable? Also, the scores will be used for ...
1
vote
1answer
36 views

How do you run correlations on mean values?

I have five random variables measured on units in four sites, and I'm interested in comparing between sites to determine if there are significant differences. I'm extremely interested in the ...
3
votes
1answer
862 views

Is it correct to use plus or minus symbol before standard deviation?

I have represented standard deviation as "±SD" before in publications. But I like to have opinions on this. Is it appropriate to use the notation '±' with SD ? Or is it only for Standard error ?
0
votes
1answer
29 views

Hypothesis significance better than Mean Average Precision?

Consider I have two search engines, one (B) with Mean Average Precision higher than the other (B). Now, can this metric be enough to say that the first search engine A is better than the second one B? ...
0
votes
2answers
302 views

How to test if one mean is greater than the other in R?

What would an appropriate test be for testing whether group 3 has a larger vital capacity than group 1 from the vitcap dataset in the ISwR package. This is what I was thinking so far, but I'm really ...
1
vote
1answer
43 views

Is this the correct way to calculate the mean and variance of $(X-n)/(2n)$ where $X$ follows a Chi-squared distribution with $n$ degrees of freedom?

Let $X_n$ follow a Chi-squared distribution with $n$ degrees of freedom. I would like to study the variance and mean of $$\lim\limits_{n \rightarrow \infty} Y_n := \frac{(X_n-n)}{(2n)}$$ I would also ...
1
vote
1answer
230 views

how to calculate expected sample scale mean and sd based on the means and sd's of its dichotomous items?

I am developing a new psychometric scale consisting of a several dichotomous items taken from a larger item bank. The p values (item means) are known. Now I need to calculate the expected mean and ...
5
votes
3answers
607 views

Expected number of dice Rolls require to make a sum greater than or equal to K?

A 6 sided dice is rolled iteratively. What is the expected number of rolls required to make a sum greater than or equal to K? Before Edit ...
4
votes
2answers
450 views

Approximate mean from .25, .5, .75 percentiles

If I have median (.5 percentiles), and the .25 and .75 percentiles, what is the best guess of the mean? If the .25 and .75 percentiles are in the middle of a probability mass with weight .5 (.25 on ...
0
votes
1answer
53 views

Deriving the mean from a raw and standardized score

My son has received 52 marks in a test. This has been standardized, using a mean of 100 and a standard deviation of 15, as 102.27 What is the mean mark, and how many marks would he have needed to get ...
0
votes
0answers
51 views

Descriptive and Inferential Statistics

I am doing a time series analysis (stock market returns) and I am currently looking at the summary stats. I know the definitions of the individual stats but the one I am stuck on is the relationship ...
1
vote
1answer
554 views

Calculating Mean and Standard Deviation From Frequency Chart

I have only a frequency table like that below. How can I get the mean and standard deviation? ...
2
votes
0answers
30 views

Distribution with fixed mean and closest to a given distribution

I was wondering if this problem has been tackled in some way in the probability/functional analysis literature: Given a pdf $f$ such that the expectation is zero and $\mu\in\mathbb R$, find the ...
2
votes
1answer
97 views

How do I calculate PERT stddev if I use custom weight factors?

According to (for example) http://tynerblain.com/blog/2006/04/13/foundation-series-basic-pert-estimate-tutorial/, the PERT mean estimate is $$\text{meanA}=(\text{optimistic}\ +\ 4 \times ...
18
votes
4answers
3k views

How to tell if my data distribution is symmetric?

I know that if the median and mean are approximately equal then this means there is a symmetric distribution but in this particular case I'm not certain. The mean and median are quite close (only ...
0
votes
0answers
125 views

Meta-Analysis Data Extraction Process - Reporting of Outcome Measures

I am conducting a Meta-Analysis of a clinical intervention in randomised trials. I am using the RevMan Software of the Cochrane Foundation. The problem regards the extraction process of relevant ...
1
vote
1answer
139 views

How to compare means, variances and standard deviations of durations for statistical significance

I am trying to compare multiple mean values, variance and standard deviation values for statistical significance. For example I have the following data: Data 1 Mean: 0.01304 Sample ...
3
votes
1answer
144 views

Confidence Interval For Mean By Bootstrapping

The standard deviation in my original sample is very large, about 100 or so. I took many bootstrap samples, found the mean of each bootstrap sample and then took the mean of these means. I found the ...
1
vote
0answers
80 views

How to calculate E(1/Y) when Y is Inverse Gaussian distributed?

The Inverse Gaussian Distribution density is : $$\frac{\phi^{\frac{1}{2}}}{\sqrt{2\pi y^3}} exp[\frac{-\phi(y - \mu)^2}{2\mu^2y}]$$ Got to this integral: $$\int_0^\infty \frac{1}{y} ...
2
votes
2answers
202 views

Is recoding a categorical variable into a continuous variable possible?

I'm trying to see if it's possible to recode a categorical variable into a continuous variable. The data would probably not permit it but what if I really needed to find the mean and SD? Is there ...
1
vote
1answer
29 views

How to identify a binary model with varying mean and variance

I have the following model, Yi = 1.( Xiβ + εi > 0) where εi~ Ɲ(Ziδ,1). or Yi = 1.( Xiβ + εi > 0) where εi~ Ɲ(0, (µ + Ziδ)2) with a binary model, can i identify β and δ in such a model? How? and ...
1
vote
1answer
104 views

Is it possible to compute the mean/median of an variable by a contingency table?

A contingency table contains the frequencies of two discretized variables. To be more specific, the discretization is done by splitting the spectrum of a signal into equal width intervals. Is it then ...
0
votes
0answers
33 views

Can anyone help interpreting this equation?

The following is a portion of text from the Heckman, Ichimura and Todd (1997) paper about propensity score matching in ReStud The matching methods discussed in this paper focus on estimating an ...
0
votes
1answer
22 views

Estimating population mean when using biased sampling?

Say you had a sample of 50 items that was constructed by taking selecting values that were in the top 75% (not in the first quartile), and you had to take 61 items to find those 50 (11 were in the ...
0
votes
1answer
42 views

Using the average as a cut off to group data and compare groups?

I measured cell size of human muscle and I wanted to examine the effect of age on the parameter. I graphed my data as a scatter plot and calculated Pearson's correlation coefficient but then also ...
0
votes
0answers
21 views

Time-partitions of sample size

I am struggling with explain something I read in a Whitepaper. The essence is as follows. Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X ...
2
votes
2answers
1k views

Which is better, replacement by mean and replacement by median?

I'm doing a project that involves replacing missing values in a set of data (first time doing this). This is involves using to methods "replacement by mean" and "replacement by median" to fill in the ...
0
votes
1answer
308 views

Mean vs. Standard deviation for data ranging between 0 and 1

If e.g. 100 people can rate a subject between 0 and 1 than the dispersion (e.g. standard deviation) among the 100 raters is potentially largest for a mean of 0.5 (50 people rate 0, 50 people rate 1) ...
9
votes
2answers
354 views

Does a prediction interval have to contain the mean?

I am having a huge problem with a conceptual problem that I came up with. Say a company has a distribution that is highly skewed. Something similar to an exponential or lognormal only more extreme. ...
0
votes
0answers
17 views

comparing time ratios

I have two different implementations of an algorithm and would like to compare their runtimes on test data. The test data consists of multiple instances. I run every algorithm on each instance and ...
2
votes
2answers
308 views

Which notation should be used for the mean, SD, and median: mean±SD or mean (SD)?

I usually use mean±SD notation for reporting values. I know that many people use mean (SD) notation and I understand why. Right now in the document I am writing I am also reporting medians but I ...
0
votes
0answers
39 views

Anova Post Hoc Test

I am running an anova in SAS on the average hours worked for a country. With those countries grouped into 3 regions. When I run the anova I get a F value of 3.64 and P-value 0.0379. With these ...
1
vote
0answers
15 views

Accuracy of reported measurements

I take three measurements: 71, 72 and 74. Each of the three measurements have 2 significant digits. The mean of my three measurements is 72.33 (rounded to 4 significant digits). Because my ...
2
votes
1answer
74 views

What is the relationship between the mean of a continuous variable and expected value?

What is the relationship between the mean of a continuous variable and expected value? How are they connected?
3
votes
1answer
119 views

Why is the CI in the median larger then the CI in the mean?

if I generate sample of normally distributed values (N=100, Mean of 10, STD 2.5) Then I calculate the mean with confidence intervals and the median with confidence intervals of the sample I get: A ...
0
votes
2answers
85 views

SEM Interpretation

Standard error of the mean (SEM) represents the accuracy of the mean. Here's my question/doubt. Does higher the SEM mean higher the accuracy of the mean? To be more precise, what indicates ...
2
votes
1answer
26 views

Non neglible instrument error associated with a mean

I have N samples, that have mean X and standard deviation sigma. So far so good. I know that each sample has been measured with a measurement error e. Because the data is real world data the ...
1
vote
1answer
62 views

Unbiased Estimators

So I've been banging my head against the wall trying to figure out where to go with these problems, and I'm looking for a little direction. Suppose that $Y_1, Y_2, Y_3$ is a random sample where the ...
2
votes
3answers
152 views

Standard error of a population

I measure the weight of 100 people and pick 20 lots of 5 people from these 100. Therefore n = 5, repeated 20 times. The 100 people represent the population and groups of 5 people represent samples ...
-1
votes
1answer
65 views

Binomial distribution [closed]

folks! The problems is Suppose you can make free throws at a 70% rate. Let X be the number of free throws you make in 20 tries. Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] ...
-2
votes
1answer
55 views

What is the Mean Squared Error for this estimator?

I understand that to find the MSE, i must find the variance and bias and add them together. I've had trouble calculating either of these so a breakdown would be immensely helpful. The estimator is: ...
2
votes
2answers
160 views

The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
1
vote
2answers
67 views

How should I determine an average from a set of averages

I have a set of lines. I measure their length each 5 times, and then take the mean of their lengths (as I measure them). I also take the standard deviation. I want to know the 'average' line length. ...