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Questions tagged [average]

Average most often refers to the arithmetic mean, but more generally to measures of central tendency that use most, or all, of the data values. Examples include trimmed mean, Winsorized mean, harmonic mean and geometric mean.

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How to calculate weighted average of hourly sales in a day

I have hourly sales data & want to aggregate it to a day level. Out of 24 hours, we are classifying 6 hrs as peak hours and 18 hrs as non-peak. Assume peak hr sales for a day as: $X_1,X_2,\ldots,...
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Calculating an average

Hi I’ve got a quick question. On statistics. I ran a survey in which I asked respondents how many hours of quality time they spend with their family per week . I also asked them what percentage of ...
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PCA as scaled average of original variables

Let $X_i=(x_{i1},...,x_{ip})$ be a vector of $p$-dimensional $n$ observations. Suppose that we apply principal component analysis and find the $p$ principal components. Also, suppose that the $p$ ...
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Average of marks in examinations

Is it statistically correct to find out final marks of a student in a paper by taking arithmetic mean only of 4 valuations of a single paper without an answer key, or any rectification measures for ...
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32 views

Estimating the population median from a kernel density estimator

I have a 1-d kernel density estimate in the form of two vectors: x_grid is a vector of x-values at which the density function was sampled ...
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How to penalize for empty fields in DataFrame?

I have to calculate the consistency of racing car drivers during the whole season. My DataFrame consists of 10 columns (10 circuit names) and for each of those columns I have the standard deviation in ...
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Statistical methods for assigning weights based on rank differences?

I have encountered methodological problem in my pursuit of my master's degree, and I hope you can help! I know exactly what I want to do, but I do not know which statistical area this is related to. I ...
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Assumption testing for a large amount of individual regression models and averaging R-squared?

I am running the following model for my thesis, a simple regression: \begin{equation} y_{i,t} = \alpha_t+\beta_tx_{p,t}+\varepsilon_{i,t} \end{equation} where Y is an observed variable (...
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28 views

Statistical uncertainty in average of continuous variable, where values are not expected to be the same

I have been trying to understand statistical uncertainties on measurements made, I have found many partial sources, but they seem to either deal with simply counting whether something happened or not ...
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How to weight values for a weighted average

I have 100 answers regarding production times in minutes of a certain product from 100 manufacturers around the country. I also know if these companies have met any of the 3 quality standards relating ...
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74 views

Weighted average of averages or average of weighted samples?

I have to estimate the average amount of goods that will be produced by machines per resource unit. Each machine will be working in one of two modes (A or B) and I know their proportions ($p_A$ and $...
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60 views

The correct formula for weighted average

The formula for a weighted average is: sum of values, multiplied by respective weights, divided by count of values. Right? That’s what I thought it was until I saw other variations, which are ...
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Given an average and a maximum, how determine the minimum range

Suppose that we have $k$ non-negative values. We know the average $A \in \mathbb{N}$ of these values and we know that the maximum value is $M$ (not necessarily $\in \mathbb{N}$) we don't know the ...
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Retrieving instantaneous information from average quantities

I have a very large vector containing instantaneous information on a quantity on the timescale of microseconds. I also have another vector of the same quantity containing the 10 minute max, 10 minute ...
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Best Way to Aggregate further and Analyze a Data Point that is Already an Average

I want to understand how much time (on average) each Customer Service Agent (CSA) is taking to reply to messages that are sent by a Customer on a single chat. E.g., "Charles took on average, 22s to ...
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38 views

What happens with my variance if I multiply observations by 5?

Suppose a dataset with observation values: 2 3 4 4 2 Variance of this observation, assuming this is the entire population, would be: Where the average is: 3. ...
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Given a list of standard deviation values, how do I find the overall standard deviation of the whole set?

I have a program which takes a set of images and collects various types of information about the colours within each image. One of the things it collects is the mean of each RGB colour value (in a ...
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Comparing Likert Data

I have several 5-item likert scales and would like to compare the results between different surveys. Is there any logical way to score the likert results and compare? Averages don't seem to capture ...
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Can I use averages to improve the forecast of a multiple regression?

I have a cross-sectional multiple regression that I have estimated and now I would like to apply it to make a simple forecast of the dependent variable. Take the data generating process $$y_i =\...
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Can I compare daily averages using a T test?

Pretend you had a sales group that was required to perform a bunch of administrative work for every prospect they contacted. E.g., entering the prospect's contact info into a CRM, researching the ...
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24 views

Most “statistically sound” method for finding the average of multiple different metrics [duplicate]

If I have 3 different metrics and I wanted to find an "average" (not necessarily arithmetic mean) of the 3 metrics so that observations can be ranked, what would be the most "statistically sound" ...
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Correlating with average of independent but values of dependent variable?

I want to correlate reef health (independent variable) with fish biomass (dependent variable). I have six location and at each location I determined reef health only once, but fish biomass was ...
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From unsupervised clustering to a weighted average?

I am in the process of writing my master's thesis, and have stumbled (as one often do..) upon an area of statistics that I am not familiar with. My setup is, that I initially have 2 features which I ...
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94 views

On average of percents

I have read some pages about how to calculate the average of percents. However, still I don't understand something... Assume data points are organized in the following manner: We have two categories ...
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Which test applicable to compare means across time series?

I am currently writing my Master thesis and seek some advise how to best analyse my data and what the appropriate test for significance would be. To give you some background: I want to analyse ...
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142 views

Calculating the variance of sample, knowing the mean of population

Suppose that I somehow know the mean of the population. And I want to calculate the variance of a sample. Should I subtract population mean or sample mean? Is there any situation in which I should use ...
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Which mean to use to find the average of measurements given in the form of “per period”

Let's say I made several measurements on my gas consumption. 2m^3 per day 1m^3 per day 1.5m^2 per day 2m^3 per day What is the average daily consumption of gas? I can take arithmetic mean and it ...
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340 views

Calculate Median Value of Likert Scale data

I have a dataset in a Likert Scale: strongly agree, agree, neutral, disagree, strongly disagree (see attached). (i) Is there an online calculator that can used to calculate the Median for each item ...
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how to calculate average tenure of a worker in any factory

I have tenure data for workers who have left the factory and also who are still working in the factory. I need to calculate average time spent by worker in the factory?. what data should i consider ...
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Interpretation of the ratio of two estimated population means

I have two datasets. Lets say average of 1st dataset is 10, and average of second dataset is 12. Is it acceptable to divide 12/10 and say that the relationship between both datasets is 1.2? I am ...
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How to calculate the standard average of a set excluding outliers? [closed]

I have a set of numbers, and I need to calculate their average excluding outlier values (which I don't know a priori). It came to mind that many years ago I studied Standard Deviation. Could I apply ...
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Median versus Harmonic Mean As Log Normal Data Summary

I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single ...
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2answers
55 views

Correct way to calculate an average

If I have the cost and number of days for several trips to Italy and I want to calculate how much an average trip costs to Italy per day. So my data would look like this: ...
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Name for (maximum+minimum)/2 and relationship to average?

Is there a common name for $c := \frac{max(X)+min(X)}{2}$? What is the relationship between $\tilde{x} := Avg(X)$ and $c$? What metrics or information can I derive from $\tilde{x}$ and $c$? If I ...
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Calculating mean of continuous time series

I'm calculating the arithmetic mean of values in a continuous time series, weighted by duration. Points in the time series are not guaranteed to be evenly spaced. Example data: ...
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71 views

How to compare sub-sample mean with the sample mean?

I have a dataset with 983 rows and two columns: Rent and Postcode. The mean Rent for the entire sample (983 rows) is 817.49. The mean Rent for the N1 postcode (23 rows) is 887.02. The N1 data is a ...
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What does “middle of the data” really mean?

I have some noisy time series data for different climate variables and I want to know overall if they are increasing or decreasing with time. From this Water Resources Statistics Guide, the LOWESS ...
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29 views

Robust estimator of a geometric average?

Is the geometric average of a sample the best robust estimator of the geometric average of a population, or is it something else like the median or trimmed mean or even the mode? Would it be correct ...
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43 views

Which data needs to be collected and what to do with it. I need step by step process with explanation for understanding.

I sell a given product through 1000 shops & average revenue for that product is 2400 dollars per week per shop, with a standard deviation of 3100 dollars. I want to analyze, the offer ' three for ...
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120 views

Is there a method to transform all z-scores into positive values?

During my calculations I need to use square roots but z-scores can be negative. Is there a trick to transform them into positive value without missing the usefulness of z-scores? What if I have not ...
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42 views

average number of tossing coins till 'Head-Tail-Head' series of observation comes up [duplicate]

I know that we use 'geometric distribution' to solve problems such as 'Expected number of tosses till first head comes up' or 'expected number of rolling dice till first 'number 6' comes up'. However,...
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Comparing averages of unequal population sizes

Imagine the following problem: I have 1000 plots of land. On each plot of land I plant 1000 Oak trees and 1 Elm tree. Each plot of land differs in multiple parameters (e.g. sunlight, soil type, ...
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42 views

Averaging Histograms

I am currently running experiments which include measuring concentrations throughout an environment, producing a histogram as such: Which shows the percentage of positions which have oxygen ...
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20 views

Error propagation in dividing the averages of two data sets

Let's say I have two data sets each containing 1000 points. I want to get the respective averages of both data sets, then divide the resulting averages. What is the best way to propagate the error (e....
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38 views

Effects of exclusion on averages

Given a set of data points, if a single point which is above/below the average is excluded, can it be said that the new average will surely decrease/increase? What if the average is the median instead ...
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What is the maximum entropy distribution given the median (instead of the mean)?

Given that the median seems to be a more robust statistic than the mean/average, I was wondering if there is a solution of the maximum entropy distribution given the median (or the median and some ...
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64 views

Standard deviation useful for indicating the spread of data when there are few outliers?

I have the following data set: 340 1680 1490 140 56 188 177 15 99 5 31 160 67 10 140 35 105 67 34 150 77 20 122 19 250 59 9 144 199 I calculated the arithmetic ...
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23 views

Show that these two sums involving sample means are equivalent

Let $C_{ij}$ be observations with indices where $i=1, \cdots, M_j$, $j=1, \cdots, J$. That is, there are $J$ groups and each group $j$ has $M_j$ observations so that in total there are $N=\sum_{j=1}^{...
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In what sense did “average” ever come to mean a statistical quantity?

I was researching the etymology of "average" to enlighten the debate as to whether "average" can in fact mean a "median" (or if the presenter was merely trying to sweep up their tracks so to speak). I ...
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Comparing population averages while accounting for changes in composition

I have two populations (i.e., men / women) with different average measurements (let's say height). I observe the combined average of their height decreases. I also observe the proportion of women ...