SD -- standard deviation

sum of (each datum - mean)^2
divide by n-1
sqrt

It's so important that you should calculate one manually.
Data   x-mean   (x-mean)^2
----   ------   ----------
 1
 2
 3
 4
 5
 6
 7
 8
 9    
               ---------
             Sum=_____      Sum/(n-1)=______   Sqrt(sum/(n-1))=s=________
Which of these datums hae the bigget effect on the Sum (and thus on the SD)?_____
So, in general, the datums that are _______ from the mean have the bigget effect on the SD.

Now add a 1 and a 9 to the data, mean stays the same; 
increases the Sum by their squared difference from the mean 
             Sum=_____   Sum/(n-1)=______   Sqrt(sum/(n-1))=s=________

****************************************************************************
freq dist, histogram, stats ***
https://davidwills.us/math103/freq_histogram.html

Type in five 1's.    1 1 1 1 1
SD=_________   mean=_____
i.e. all the data is the same, there is no variation.
it is all [clustered] at the mean. (This is the only way for the SD to be 0.)
Boxplot is unusual? __Y __N
Sketch histogram from 0 to 10, Y max 10, class width 1.








Clear
Type in five 9's.     9 9 9 9 9
SD=_________    mean=_____
Again, no variation.


ADD five 1's          9 9 9 9 9 1 1 1 1 1
SD=________     mean=_____     
this data is maximally spread out, it is perfectly bi-modal, so
  SD (sigma) is one half the range: range=____   sigma=_____
BTW, the mean is usually said to be the "typical" datum. Is that the case here?:___
Boxplot is unusual? __Y __N
Sketch histogram from 0 to 10, Y max 10, class width 1.








Clear
Type one 1, 8 5's, one 9:   1 5 5 5 5 5 5 5 5 9
mean=_____ (same as the 10 1's with 10 9's)
SD=______  (much smaller than the previous data set)
Boxplot is unusual? __Y __N
Sketch histogram from 0 to 10, Y max 10, class width 1.










Clear
1 2 3 4 5 6 7 8 9  
mean=______
SD=_____     SD is not directly related to the number of different numbers.
Sketch histogram from 0 to 10, Y max 10, class width 1.