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

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4
votes
2answers
435 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
527 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
94 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
2k 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
121 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
129 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
138 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
77 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
184 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
28 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
99 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
21 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
972 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
289 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
349 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
287 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
110 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
81 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
61 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
146 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
63 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
53 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
153 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
65 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. ...
0
votes
0answers
90 views

mean of log or log of mean

I'm interested in how indiviudals are influenced, by other individuals they are connected to. So mean values of connected individuals are included in a linar regression model. Some of my variables are ...
2
votes
1answer
77 views

Distributions with Median=Mode=Average?

Is there any important distribution with Median=Mode=Mean, apart from the Gaussian and Student's distribution?
6
votes
2answers
375 views

Trimmed mean vs median

I have a data set with all the calls made to an emergency service and the response times of the ambulance department. They admitted that there are some mistakes with the response times as there are ...
0
votes
1answer
28 views

How to compare the means of two populations that were subject to five treatments?

I have two populations that were each subject to 5 different treatments and I want to compare their means. This sounds like a great problem for multiple confidence intervals, but I don't want to make ...
1
vote
1answer
86 views

SPSS ANOVA or MANOVA or huh?

Me again asking the silly questions - this might belong here as I've been told it may belong in a software section somewhere..? Which I have still been unable to find. Here is a screenshot of my ...
5
votes
2answers
181 views

Can the difference between the means of two groups lie outside the confidence interval for the difference?

I received this question from a colleague which left me with a desire to find out a bit more about it. If you have two groups A and B with means--for example, 7.9 and 5.8--is it possible that the ...
0
votes
1answer
194 views

Question about probability of 0.99 that an average lies less than L years above overall mean

The duration of Alzheimer’s disease, from the onset of symptoms until death, ranges from 3 to 20 years, with a mean of 8 years and a standard deviation of 4 years. The administrator of a large medical ...
1
vote
1answer
74 views

Beta binomial mean different from actual mean

I have data that I am fitting a beta binomial distribution to. The VGAM package for R is being used to do this. However, the the mean of the fitting beta binomial distribution is vastly different from ...
1
vote
0answers
20 views

Calculating the highest of overlapping sets

My data set looks like the following: I have information about a large number of devices. For each device, I also have the data consumed by an application per day. Note however, all the devices ...
18
votes
6answers
805 views

Is the median a type of mean, for some generalization of “mean”?

The concept of "mean" roams far wider than the traditional arithmetic mean; does it stretch so far as to include the median? By analogy, $$ \text{raw data} \overset{\text{id}}{\longrightarrow} ...
5
votes
2answers
610 views

Reporting Results of Mann-Whitney U Test - Means vs Medians

I had a question yesterday that I got a bunch of great responses on. I have, hopefully, a quicker question here. There is a debate in the literature regarding reporting means vs medians in a ...
1
vote
1answer
281 views

2 discrete distributions with equal mean and variance

I need to compute 2 discrete distributions with equal mean and variance. One should be a distribution taking values x and y and the other one taking values z, 0, and y. The probabilities should take ...
8
votes
1answer
834 views

Which converges faster, mean or median?

If I draw i.i.d. variables from N(0,1), will the mean or the median converge faster? How much faster? To be more specific, let $x_1, x_2, \ldots $ be a sequence of i.i.d. variables drawn from ...
4
votes
2answers
274 views

How to properly state the average of a discrete number in a report?

I'm wording a report on the averages of a discrete variable, and am trying to get the most appropriate sounding wording. Consider the able below: ...
9
votes
1answer
3k views

Displaying Ordinal Data - Means, Medians, and Mean Ranks

I have some ordinal data that is not normally distributed, so I decided to do non-parametric testing using the Mann-Whitney U Test. I am looking at differences between groups for seven scores - these ...