Questions tagged [types-of-averages]

Use this tag for questions about different types of averages / means / location measures.

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Choosing the right average method

The following tables shows the wall clock times of some programs. So, A means the time for one configuration and B means the ...
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10 views

Modify Bayesian Average for Multiple Quarters

I am currently calculating a bayesian average using Q1 data using the following equation: I would like to incorporate data from other quarters for several years back, i.e. Q4 2021, Q3 2021, Q2 2021, ...
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Average success rate when different number of attempts per participant

I have a group of participants who chose whether to attempt a task in 10 scenarios. So, some participants attempted the task once, some attempted in 3 scenarios, some attempted in all 10, etc. I want ...
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How can the sum of averages of my sample exceeds average of entire population? - market concentration

I want to see what percent of a market of listeners on a livestreaming platform my sample of top 100 musicians with the highest number of average listeners during a given month has. I only have ...
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1 vote
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average of geometric and harmonic means

I have a stochastic simulation model in which three types of mean (arithmetic mean, geometric mean, and harmonic mean) are calculated for three different variables. I run the simulation 1000 times so ...
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Need suggestion on average method to perform on ratios (harmonic, geometric, weighted)

Im looking at different cities which all have different population counts. For each of these cities im calculating the proportions of smokers. For example: ...
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39 views

Graphic representation of averages

I have a series of averages. One of these however turns out to take too high a value due to a N. low equal to 1. Let me explain better by means of an example: I have to calculate the averages of the ...
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24 views

Modal average in JMP Summary Statistics

The JMP Summary tool allows users to select mean or median for aggregated statistics, but does not include mode in the dropdown list. Is there some logical reason for this? Is there a way to do it?
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How to use averages with a changing sample size

I have some pilot study results of an app with an original total study size of 95 users. I want to accurately show the average usage over time (days). For example, the app was used for an average of ...
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3 votes
1 answer
247 views

expected value of sample from a skewed distribution

Let us say a market's prices are distributed with a skew. Given a sample of 10000 products, I can estimate the median, arithmetic mean and weighted average or any other statistic. Let us say I draw ...
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1 vote
2 answers
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Typical Customer Order Value

I am analysing some sales data and looking at the customer orders for 550 customers and want to answer the question "What is the typical customer order value", however, the orders are skewed ...
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  • 113
1 vote
1 answer
145 views

summary statistics of groups at different scales/units

I have these made up observations: ...
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2 votes
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Winsorized mean - trimming furthest points instead of both endpoints

I'm wondering if the Winsorized mean can be improved by trimming the 5% farthest points from the mean instead of trimming 5% on each endpoint. Concretely: Consider the Winsorized mean, where we ...
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What mean use when there is outliers [duplicate]

for a project I need to get a mean each time, this mean I then use it to compare it to a distribution under the null hypothesis H0. However sometimes some values (...
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4 votes
1 answer
388 views

Trimmed, weighted mean

The trimmed mean (or truncated mean) is a robust version of the mean, designed to be robust to outliers. I am wondering what is the right trimmed version of a weighted average. If I have a sample ...
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0 votes
1 answer
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Should You Take the Average of Two Test Score Percentiles?

I have two different tests that measure the skill of participants in two different fields, leading to two different test scores for each participant. I want to combine both test scores to get an ...
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2 votes
2 answers
112 views

Comparing yearly data that has different $n$ values per year?

I have been collecting soil moisture data at my research site for almost 20 years. However, I have not been consistent with the number of times that I have been taken these measurements. The problem ...
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2 votes
1 answer
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Meaning of phrases (median vs mean): Income of the average person in my city vs. The average income of people in my city

Hello Cross Validated, I have been discussing things like the average income of a person in my city, and have come to think there is a subtle but important difference in the phrases "Income of ...
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9 votes
2 answers
659 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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20 votes
2 answers
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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 ...
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25 votes
4 answers
4k views

Why does mean tend be more stable in different samples than median?

Section 1.7.2 of Discovering Statistics Using R by Andy Field, et al., while listing virtues of mean vs median, states: ... the mean tends to be stable in different samples. This after explaining ...
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16 votes
3 answers
3k views

Is there more than one "median" formula?

In my work, when individuals refer to the "mean" value of a data set, they're typically referring to the arithmetic mean (i.e. "average", or "expected value"). If I ...
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1 vote
0 answers
160 views

Arithmetic Mean Versus Geometric Mean for Environmental Measurements

The following comment was made by whuber in response to the question Which “mean” to use and when? ... in many cases the right mean to use is determined by the question we are trying to answer ...
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25 votes
3 answers
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What can one conclude about the data when arithmetic mean is very close to geometric mean?

Is there anything significant about a geometric mean and arithmetic mean that fall very close to one another, say ~0.1%? What conjectures can be made about such a data set? I've been working on ...
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1 vote
0 answers
49 views

What mean to use in odometer calculation based on model?

Im trying to figure out what would be considered a valid calculation. Imagine I have a dataset that looks like that: ...
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3 votes
2 answers
1k views

When to use mean or median?

I am asked to put together some KPIs. I'm breaking down what the general lifespan of our subscribers is by industry. There are some industries I feel outliers are impacting what the average would be, ...
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10 votes
2 answers
9k 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 ...
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22 votes
6 answers
2k 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} \text{...
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1 vote
0 answers
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Should I use arithmetic or geometric mean here?

So I have monthly indices (Consumer Price Indices for 12 months) for a given country. I want to calculate the annual average for each country in order to have an average Consumer Price Index for a ...
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33 votes
5 answers
29k views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
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33 votes
4 answers
86k views

How is finding the centroid different from finding the mean?

When performing hierarchical clustering, one can use many metrics to measure the distance between clusters. Two such metrics imply calculation of the centroids and means of data points in the clusters....
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8 votes
4 answers
10k views

What are the different types of averages?

I know there are three types of averaging methods in statistics: Mean, Mode and Median. Are there any other type of averaging methods that statisticians use? How do I know which method is best for ...
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218 votes
5 answers
87k views

Which "mean" to use and when?

So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean ...
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21 votes
4 answers
27k views

Mean and Median properties

Can somebody explain me clear the mathematical logic that would link two statements (a) and (b) together? Let us have a set of values (some distribution). Now, a) Median does not depend on every ...
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21 votes
7 answers
5k views

Is median fairer than mean?

I recently read the advice that you should generally use median not mean to eliminate outliers. Example: The following article http://www.amazon.com/Forensic-Science-Introduction-Scientific-...
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49 votes
14 answers
92k views

Why is median age a better statistic than mean age?

If you look at Wolfram Alpha Or this Wikipedia page List of countries by median age Clearly median seems to be the statistic of choice when it comes to ages. I am not able to explain to myself why ...
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91 votes
15 answers
146k views

What do you call an average that does not include outliers?

What do you call an average that does not include outliers? For example if you have a set: {90,89,92,91,5} avg = 73.4 but excluding the outlier (5) we have <...
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