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The problem is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need

by pps43 10y ago

The problem is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need derivatives and integrals. These days you can solve many practical statistical problems with Monte Carlo, but understanding why those curves look the way they do is still very useful.

danielmorozoff 10y ago
Though i think pdfs are useful, they may be a bit advanced. Perhaps linking integrals/derivatives into stats could be done from a more discrete approach as opposed to a continuous one first. For example: Starting with a representation of an integral as sum of areas of rectangles (something most students can do) and then saying what happens if the width of all the rectangles gets smaller and smaller. A la Riemann This could then tie into the pdf quite reasonably?
patrickthebold 10y ago
There's a difference between defining the integral,then taking about how it's estimated numerically and to use some software to get numbers. Vs Trigonometric substitute to solve analytically. For example.
krschultz 10y ago
That's a good point. I'm not an educator and it's been a while so I can't recall the sequence of stats 101, calc 1, more stats, more calc, etc. It all blurs together at some point.
analog31 10y ago
I had kind of a strange experience. While in college, I worked as a math tutor. Since I had taken one semester of stats, the tutoring center decided I was qualified to run a tutoring session for the non-calculus stats course. I was happy for the money, and had been reasonably successful with other tutoring assignments. When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data are recorded to two decimal places, and are reasonably bounded, for instance they are between 0 and 100. That's a discrete distribution. All of the data in the examples and problem sets were fixed-point. I literally couldn't justify to someone who had never taken calculus, why a wholly different kind of distributions with its own collection of formulas, was necessary or useful. The teacher had never explained it either.
- rocqua 10y ago
  The chance of choosing 0.5 from the interval 0 to 1 is 0. So if you want the change of choosing between 0.4 and 0.6 in that interval, you can't just sum all chances between 0.4 and 0.6 you'd have infinity x 0 which isn't 0.2 . Instead, to deal with this 'a lot of really small things' we need a slightly different approach. Then draw a pdf, and talk about area under the curve. Perhaps relate this to the discrete case where the curve is just really blocky.

by pps43 10y ago

danielmorozoff 10y ago

Though i think pdfs are useful, they may be a bit advanced. Perhaps linking integrals/derivatives into stats could be done from a more discrete approach as opposed to a continuous one first. For example: Starting with a representation of an integral as sum of areas of rectangles (something most students can do) and then saying what happens if the width of all the rectangles gets smaller and smaller. A la Riemann This could then tie into the pdf quite reasonably?

patrickthebold 10y ago

There's a difference between defining the integral,then taking about how it's estimated numerically and to use some software to get numbers. Vs Trigonometric substitute to solve analytically. For example.

krschultz 10y ago

That's a good point. I'm not an educator and it's been a while so I can't recall the sequence of stats 101, calc 1, more stats, more calc, etc. It all blurs together at some point.

analog31 10y ago

I had kind of a strange experience. While in college, I worked as a math tutor. Since I had taken one semester of stats, the tutoring center decided I was qualified to run a tutoring session for the non-calculus stats course. I was happy for the money, and had been reasonably successful with other tutoring assignments. When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data are recorded to two decimal places, and are reasonably bounded, for instance they are between 0 and 100. That's a discrete distribution. All of the data in the examples and problem sets were fixed-point. I literally couldn't justify to someone who had never taken calculus, why a wholly different kind of distributions with its own collection of formulas, was necessary or useful. The teacher had never explained it either.

rocqua 10y ago
The chance of choosing 0.5 from the interval 0 to 1 is 0. So if you want the change of choosing between 0.4 and 0.6 in that interval, you can't just sum all chances between 0.4 and 0.6 you'd have infinity x 0 which isn't 0.2 . Instead, to deal with this 'a lot of really small things' we need a slightly different approach. Then draw a pdf, and talk about area under the curve. Perhaps relate this to the discrete case where the curve is just really blocky.