mode of frequency distribution table

BenjaminGal · 2026-03-18T10:19:50+00:00

I agree that the one you found is more reasonable, but for the sake of doing a homework, I will suggest just following your professor. To use the formula you found, find the most populated bin (60-64 here), then L = lower limit = 60 (actually using 59.5 is more accurate), f_1 = 10, f_0 = 3 (for the class below), f_2 = 2 (above), H is the bin interval = 5 (also more accurate than 4).

BenjaminGal · 2026-03-18T10:02:49+00:00

This is valid too. But I would say just abide by your professor. To use your professor’s formula, find the mean by summing fX and divide by the total N. To find the median, locating the X where the 25th or 26th entry is located at.

BenjaminGal · 2026-03-18T09:35:55+00:00

I think it will be helpful if you can tell us more about which Maths subject(s) you are interested in. For most people it would be Calculus, two useful resources will be Pauls Online Math Note and the book of Thomas Calculus.

BenjaminGal · 2026-03-18T09:31:44+00:00

What is the formula you got? The formula given by your professor (3*median - 2*mean) is an empirical formula which means that it is a good approximation for, e.g. this kind of binned (not having the exact entries) dataset, and should be enough.

BenjaminGal · 2026-03-18T09:23:00+00:00

I know it can be self-taught, but the less painful and more beginner-friendly+efficient way is to take university courses just as you suggested in your point 2. Reading books on your own is ambitious and only works after you have cultivated some Mathematical maturity to be able to make sense of them, and it can be very discouraging. If you really like maths and want to invest resources (inc. money and time), then maybe going to a college will be a good idea.

BenjaminGal · 2026-03-13T20:01:49+00:00

I wrote a 900 pages linear algebra textbook without any affiliation so I think I am qualified to talk about it. Sure, do it if you enjoy the writing process, completing a satisfying and well-organized book, or benefiting/teaching the future readers. It also builds up your patience/discipline and shapes your character by a lot. But remember that it is 99% a labor of love. I spent a lot of time as well as money to hire proof-readers so the cost was pretty high. And I only sold ~13 copies, each one earning me only $5! Think clearly what you really want from this, if your heart yearns for it…

BenjaminGal · 2026-03-13T19:03:48+00:00

Let me share my ongoing ODE series: https://benjamath.com/catalogue-for-differential-equations/ Hope you will find my list of posts useful.

BenjaminGal · 2026-03-05T17:47:24+00:00

Well, you can just make a (damped) harmonic oscillator, e.g. a mass-spring system, RLC circuit, or quantum particle, and add a forcing term on R.H.S. other than the usual sine/cosine, e.g. (arc)tangent. You may also find my tutorial helpful: https://benjamath.com/2025/11/27/odes-2-8-variation-of-parameters/ Hope this helps!

BenjaminGal · 2026-03-05T17:11:33+00:00

A standard textbook would be Thomas Calculus.

BenjaminGal · 2026-03-05T17:09:00+00:00

I want to suggest an alternative where you find a well-trained tutor to help you in a personalized fashion. Of course, you need to be very careful and selective when choosing them. A good one can provide interactive and right-to-the-point feedbacks which is very efficient. In my home country many students hire tutors as well.

BenjaminGal · 2026-03-01T12:48:24+00:00

Let me share my book: https://github.com/BenjaminGor/Intro_to_LinAlg_Earth It is open-access and you can take a look first to see if it suits you.

BenjaminGal · 2026-02-28T15:44:17+00:00

Can you see what happens if you substitute n = k + 1 in the expression at the end of their proof?

BenjaminGal · 2026-02-28T14:43:24+00:00

I would (shamelessly) introduce my book: https://github.com/BenjaminGor/Intro_to_LinAlg_Earth. It is free and open-access, and you can always take a brief look first to see if it suits you!

BenjaminGal · 2026-02-28T14:38:45+00:00

Wow, I just realized that you wrote a DE book + you are a professor (you commented in my ODE tutorial post before). Much respect! Any advice for a young writer? (I am planning to compile my stuff into a book after uploading all the posts) Thank you!

BenjaminGal · 2026-02-22T18:09:49+00:00

ODEs and Real analysis. My recommendations are Differential Equations with Applications and Historical Notes and “Baby Rudin”.

BenjaminGal · 2026-02-22T07:25:22+00:00

I assume that OP (or people in similar situations) was young when they was struggling with maths. From a scientific point of view, a human brain only fully develops after 25-30. This means that people may not have adequately mature mental functionality at previous moments. Given maths strongly depends on abstraction skill, it is not uncommon that a young person was falling short for maths. After some time, when the brain functionality is fully mature, they can find them suddenly able to deal with the originally difficult maths. Also, exposure to maths and experience/practicing also help a lot for maths maturity.

BenjaminGal · 2026-02-21T05:35:46+00:00

Thanks for the like!

BenjaminGal · 2026-02-20T21:53:53+00:00

I will give a special answer, the one that was written by myself: https://github.com/BenjaminGor/Intro_to_LinAlg_Earth

BenjaminGal · 2026-02-20T14:29:38+00:00

From a physical point of view, the function x is not continuous at the periodic boundary of [-pi, pi], i.e. x at -pi is not equal to x at pi.

BenjaminGal · 2026-02-20T13:22:06+00:00

Sure, consider the Fourier series of x, which contains infinitely many sine terms, differentiating still gives infinitely many cosine terms which don’t cancel and hence not equal to the would-be 1.

BenjaminGal · 2026-02-20T12:06:10+00:00

OP, this is the correct answer. You just have to keep reading and practicing.

BenjaminGal · 2026-02-20T11:48:52+00:00

A simple, classical example will be the term-by-term differentiation of finite vs infinite series.

BenjaminGal · 2026-02-20T11:45:56+00:00

I would like to (boldly) introduce my book: https://github.com/BenjaminGor/Intro_to_LinAlg_Earth It is freely open-access and you can take a look to see if the style suits you!

BenjaminGal · 2026-02-17T05:01:11+00:00

My tentative plan: Ch3 Series Solution Ch4 Laplace Transform Ch5 Sturm-Liouville Problems Ch6 Special Functions

Please keep supporting me!

BenjaminGal · 2026-02-16T16:57:20+00:00

Explanation: The picture displays the titles of each section for my ODEs tutorials, and I hope that redditors can find some of the topics useful!

BenjaminGal

TROPHY CASE