The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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13
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3answers
354 views

If my average speed is 50 mph, is it better to go 10% faster or 5 mph faster? (These are not the same)

BACKGROUND Suppose we have a journey between A and B where different sections of roads have different speed limits and our average speed is 50 mph. If when I repeat the journey I travel 10% faster ...
0
votes
1answer
58 views

Incremental averaging (different case)

I've seen the integer version $$m_n = m_{n-1} + \frac{a_n-m_{n-1}}{n}.$$ But how do I calculate it where there are amounts, which is $$A=[3, 5, 4]$$ and the corresponding quantities $$Q=[1.5, 2.5, ...
0
votes
1answer
222 views

alligation problem

Ravi lends Rs 3600 on simple interest to Harsh for a period of 5 years. He lends a part of the amount at 4% interest and the rest at 6% and receives Rs. 960 as the amount of interest. How much money ...
1
vote
3answers
47 views

Mean of a vector

Be a set of numbers $v=(a_1, a_2, \ldots, a_n)$ I want to form the following average vector $\mu = (\frac{\sum a_i}{n}, \frac{\sum a_i}{n}, \ldots, \frac{\sum a_i}{n})$. If I do it iteratively step ...
1
vote
1answer
147 views

Maximum and minimum average question

During a cricket match, India playing against NZ scored in the following manner: Partnership | Runs scored $1$st wicket$~~$ | $112$ $2$nd wicket | $58$ $3$rd wicket$~$ | $72$ $4$th wicket$~$ | $9$ ...
1
vote
1answer
300 views

problem in understanding overall change in average

The average weight of 5 men is decreased by 3kg when one of them weighing 150kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the ...
2
votes
2answers
46 views

Estimated wait time for a library book

A library has 20 copies of a book that circulates for 3 weeks. All copies are out and there 40 people on reserve ahead of me. How do I estimate the wait time?
0
votes
1answer
39 views

Basic algebra problem for weighted averages

This question has me completely stumped for some reason, I would appreciate a bit of help. If you have 20 pounds of coffee for $1.80 a pound And then add X amount of coffee for $1.44 a pound How ...
0
votes
1answer
126 views

Mean of a discrete function

I have a set of finite variables (~20) which when plotted are forming a decaying exponential function. I want to know is there a better way to calculate the average of this function than by just ...
-1
votes
1answer
117 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
0
votes
1answer
40 views

Average value of function that converges?

I have a function $f$ that converges to a value: $$ f(x) = 1−s−A \beta ^ x $$ Where $A \in \mathcal{R}$, and $0< \beta <1 $, $0< A <1 $ I want to get the average value of for $ x > ...
0
votes
1answer
28 views

Average of Numbers

Consider the following problem: if $a \leq b \leq c \leq d \leq e \leq f \leq 101$ and if average of these(a,b,c,d,e,f) numbers is 100 then what could be the least value of a?
0
votes
1answer
26 views

How can I understand a formula written in this format. I am a beginner.

$$\bar{l}(\mathcal{P},\mathcal{L}) = \sum_{j=1}^n p_j l_j$$ I have just started studying this module and it describes the equation as the the average length of the code. Can you please break ...
0
votes
1answer
33 views

In data compression this equation describes the 'average length' of the code. Can someone please explain?

$$\bar{l}(\mathcal{P},\mathcal{L}) = \sum_{j=1}^n p_j l_j$$ I have just started studying this module and it describes the equation as the the average length of the code. Can you please break ...
0
votes
2answers
22 views

What is the Term for the Center of Mass Equation Structure

What is the term for the generic structure of this form of equation: SUM(Mi * Xi) / SUM (Xi) It is the same as the center of mass calculation.
0
votes
3answers
219 views

Average speed question of a car on an oval track

On an oval track, a car averages $30$ M.P.H. (miles per hour) for the first lap (a lap is $1$ mile around the track). At what average speed must that same car drive the 2nd lap on that same track so ...
1
vote
1answer
20 views

Simplifying an indefinite integral representing the calculation of an average

I have an equation for a term $z_i$: $$ z_i = \ln\frac{a_iR+p_i}{T_o* tan\theta_i } $$ This represents a value in a grid, at location $i$, with the grid representing a geographic area. To get the ...
2
votes
2answers
38 views

A Percentage of Averages

A company brags about the speed of their service, "75% of our assignments are completed in an average of 20 days." Is this a meaningful claim? Or is it kind of like saying, "60% of the time, it ...
0
votes
1answer
63 views

How do i find weighted normal vector?

How do I find the weighted average of a normal vector. Heres a phrase from my book a weighted average might be used where the weights are determined by the areas of the polygons (e.g., polygons with ...
1
vote
3answers
302 views

Probability of two normal random variables when random samples are taken from a population

This is sort of second section to my previous question, I should have included both together, but I forgot to. Sorry for any inconvenience. X= random height of a male Y= random height of a female X ...
1
vote
2answers
169 views

Probability of a normal random variable added to a number being greater than another normal random variable, and distribution of average

$X$= random height of a male $Y$= random height of a female $X$ and $Y$ are independent of each other For $x$, $\mu=180\text{ cm}$ and $\sigma^2= 16\text{ cm}^2$ For $y$, $\mu=170\text{ cm}$ and ...
1
vote
2answers
75 views

Calculate the average as numbers arrive

So, suppose you have to calculate the average of a set of numbers, but you don't know the whole set yet. Someone is providing you one number after the other and you cannot use more than the current ...
2
votes
0answers
33 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...
2
votes
1answer
129 views

Average question GRE

The average daily temperature from 9th to 16th January(both inclusive) was 38.6 C and that from the 10th to 17th January(inclusive) was 39.2 C. what was the temperature on 17th January? I am able ...
1
vote
1answer
57 views

Meaningful statistic measure of data pairs

I have a dilemma. I have pairwise data, (a,b), that represents some form of speed, whether it's miles/hour or megabits/second. Let's say that we have the following set of data from measuring the ...
0
votes
1answer
48 views

Funny problem. How to average over periodic numbers

I'm want to calculate the average day and respective month that a specific event happens in a sample of countries. So for each country I have the date (one per year) of the particular event. Now my ...
1
vote
2answers
37 views

statistics z score

I'm curious what the phrase "on average" means. Here is an example: On average, 30% were further than ___ kilometers away when they had their accident. Is $30\%$ a $z$-score or is it a mean? ...
0
votes
1answer
26 views

Fair distribution

I have an user, who received one score in 3 different things for example in A, B and C. I ...
5
votes
1answer
460 views

Find center of mass of triangle with varying density

My objective: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines $y= 7x+3$ and $y= 36-4x$. Assume that the density is given by $\delta(x,y) = 7x+2y+2$. In ...
1
vote
4answers
123 views

Percentages not adding up

I have a series of percentages: 132/220 (60%) and 88/220 (40%). Now when I break them down into subcategories and then recalculate the percentages them come out 5% different. 81/140 (58%) and ...
0
votes
0answers
56 views

What is the confidence level of a curve fitted moving average forecasting next element in time series?

Suppose I got a time series X={X1,X2,X3,...,Xn}, and i got a Moving Average of any kind, it doesn't matter. The moving average is curve fitted to the timeseries of n elements, to fit exactly and most ...
0
votes
1answer
28 views

Calculate the average grade Leslie must make in order to receive a B for the math class?

Leslie is taking a math class. This is how the class is graded. Test 1 13% Test 2 13% Test 3 13% Lab 1 10% Lab 2 10% Lab 3 10% Lab 4 10% Final Exam 21% She received a 93% on Lab 1, 70% ...
3
votes
1answer
234 views

How to find the function $f$ that satisfies $f(x, y) = f(x^{-1}, y^{-1})^{-1}$ and $f(x, y)$ is $\approx$ $average(x, y)$?

Fist of all, I'm a programmer, not a mathematician, and I'm sorry for my non native English. And I'm sorry if the question is not appropriate, it is my first time here. Or if the question has no ...
0
votes
1answer
215 views

calculus integration, average height of point on semi circle

i was recently watching a single variable calculus video of mit 18.01, lecture 23. in that it is said that average height of a point on semicircle with respect to arc length is 2/pi.I have a hard time ...
0
votes
3answers
218 views

How to compute Final Grade with assignment weightings?

I have just finished the Final for my Computer Hardware course, and I'm trying to figure out where my grade currently stands. The way the class is broken up is 50% weight for the homework, 25% for the ...
0
votes
2answers
47 views

Suppose the height $(m)$ of a ball is modeled by $s(t) = -4.9t^2 + 24.1t + 2$ where $0 \le t \le 5$ [closed]

Suppose the height $(m)$ of a ball is modeled by $s(t) = -4.9t^2 + 24.1t + 2$ where $0 \le t \le 5$ Find the time when the ball is 1m off the ground What is the function for average velocity from 1m ...
1
vote
0answers
320 views

About Bayesian formula and rating system

I'm building a scoring system with score from 0 to 5) and I would like to sort products according to the number of reviews and their scores. After some research on the Internet I have found two ...
0
votes
1answer
21 views

Getting the average of values with errors.

I have five data values each with an associated error. I want to find the mean of these values but also take the errors into account. How do I do this? Lets say the data values and errors are: ...
0
votes
1answer
35 views

Statistics question regarding mean of exponential distribution

So I have a question in front of me which reads: 'If component lifetime is exponentially distributed with parameter,obtain an expression for the proportion of components whose lifetime exceeds the ...
3
votes
2answers
262 views

Expressing a summation using matrix algebra

Consider the $r \times n$ matrix $$\begin{pmatrix} X_{11} & X_{12} & \cdots & X_{1n} \\ X_{21} & X_{22} & \cdots & X_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ ...
0
votes
1answer
120 views

Unweighted Mean of Percentages

I have come across an interesting problem, which I'm sure there must be a standard solution to, but lots of Googling hasn't yielded much (which may mean I'm well off track...). I am trying to ...
0
votes
2answers
39 views

Magnitude of Average Velocity

A train travels 100 miles toward 37 degrees northwest and then 90 miles north. The whole journey takes 2 hours. What is the magnitude of the average velocity of the train?
1
vote
3answers
87 views

Find the average test score for each of three groups, given overall averages

I've been working on this question for the last hour and cannot determine a solution. Q: 100 children, 200 teens and 300 adults write a test and an average is computed for all three groups. The ...
1
vote
2answers
149 views

Where should I use median instead of average?

Is there a general law, or rule of thumb, or rationale, when to use median and when average? Although I know the difference and how they are computed, when I try to translate to simple English I ...
0
votes
2answers
82 views

What exactly does the Geometric Mean actually mean ? When should I use it?

I am working signal demodulation and the RC value requires to be the geometric mean of the periods of the message signal and the carrier wave. I wonder why I need the geometric mean for this or why ...
0
votes
1answer
45 views

Estimating how much two probability distributions differ

I have two probability distributions A and B. First I would like to estimate how much they differ. In this regard I use as metric the Jensen–Shannon distance (i.e. the square root of Jensen–Shannon ...
0
votes
1answer
22 views

In the loop average computation

I want to compute the average of a set of number, which is constantly increasing. I guess it's simple, but I'm struggling here: Let's say: 1st iteration: m(i)=a+b/2 2nd iteration: m(i+1)=a+b+c/3 ...
0
votes
1answer
303 views

Help with creating a formula to calculate grade needed on test to pass?

This is probably a simple math question and yet I'm struggling to understand it, any help would be extremely appreciated. Say if I have 2 test results, 50% on Test 1, test worth is 10% of final ...
0
votes
2answers
49 views

Using difference of average for identifying features in an image

I'm working with this paper: Textural Features Corresponding to Visual Perception, by Tamura, Mori, and Yamawaki. There's a part where you have to calculate neighborhoods of one image (matrix of, for ...
0
votes
4answers
2k views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...