exemplars

[Rob Campbell]

The NZQA have it right this time.

Suppose you had a list of numbers (like measured thicknesses of single
sheets of paper.)  You add them up and take the mean, which happens to be
0.2 mm.  Should that be 0.20, 0.200, or maybe 0.2 ?

You don't know unless you have the standard deviation.
In Y13, we assume that devices like callipers can be read to +- one scale
division, which looks as if it must be 0.1 mm here. 
Not +- .05 since you have to subtract the zero uncertainty.
Okay.  So the mean thickness value is 0.2 and the s.d. of single readings is
0.1 (sort of.)

Stacking the sheets into a pile is a painless way of averaging thickness.
It also means you're working with a sample of bits of paper, not individual
sheets.  And the s.d. of the sheets arrived at from measuring a sample is:

        s     
SD = -------
     Sqrt(n)

S  = s.d. of sheets measured on their own
SD = s.d. of sheets deduced from the sample measurement
n  = # of sheets in the sample: 10
sqrt (10) = 3.2
(Sorry about the crappy maths presentation.)

The precision of that measurement from a sample is about three times that
from measuring a single sheet.

And the gain in accuracy is real.  It's your prize for adopting an improved
measuring technique. 

Cheers,  Rob Campbell


-----Original Message-----
From: phys-teach-talk-bounces at nzip.org.nz
[mailto:phys-teach-talk-bounces at nzip.org.nz] On Behalf Of
andydyson at actrix.co.nz
Sent: Tuesday, 25 May 2010 2:36 p.m.
To: Phys-teach-talk at nzip.org.nz
Subject: exemplars

Just been reading the exemplars for internally assessed AS on the NZQA
website.


http://www.nzqa.govt.nz/ncea/resources/physics/exemplars.html

They have really clarified a number of points for me just as we are coming
into our major assessment time. A great resource that I recommend everyone
reads.

One tiny point I saw which I'm unsure of though was in the level 2
measurement

Student # 5
Grade: Merit / Excellence
Thickness of 10 pages = 2 mm. Therefore thickness of 1 page = 0.20 mm. 
Appropriate use of significant figures.


I thought that dividing by 10 did not change the number of sf but just
increased the number of dp. Answer 0.2mm, same sf, extra dp.

What do the rest of you teach?

Andy Dyson, HoD Physics, Kerikeri High School in the relatively dry
winterless Far North.


_______________________________________________
Phys-teach-talk mailing list
Phys-teach-talk at nzip.org.nz
http://nzip.org.nz/mailman/listinfo/phys-teach-talk_nzip.org.nz