Download Notes Standard Deviation by Hand

Standard Deviation by Hand
I. Standard Deviation:
A) Shows how much the data “speads” from the
mean (center).
1) Symbol is σ.
2) If the standard deviation is small, then the
data values are close to the mean (center).
3) If the standard deviation is large, then the
data values have a large range.
4) Most data falls in 1 standard deviation from
the center (68%), 95% are within 2 std dev.
& 99% are within 3 std dev. of the mean.
Standard Deviation by Hand
II. Calculating Standard Deviation: by hand.
A) Find the mean (the average – the center).
B) Find the difference between each data point
and the mean, then square that difference.
C) Find the average of all those squared
differences and square root that value. This is the
simple standard deviation.
Example: 2, 4, 4, 4, 5, 5, 7, 9
mean = 5
Difference between data & 5 = 3,1,1,1,0,0,2,4
Squared is 9, 1, 1, 1, 0, 0, 4, 16: mean = 4
Square root the differences mean & you get 2. SD = 2.
Standard Deviation by Hand
III. Calculating Standard Deviation: on TI-84 calculator.
A) Press STAT & enter. Put the data #s into L1.
B) Press STAT  Calc  1 var stat. Enter.
C) The calculator tells you everything.
1) Mean (symbol = x ) and Median (Med)
2) The sum of all the data points (  x )
3) Standard Deviation (symbol = σx)
4) How many data points are in the sample (n)
5) Max and Min values
6) Q1 & Q3 values (for box & whiskers graphs).
Standard Deviation by Hand
IV. Displaying Data Charts on the TI-84 calculator.
A) Enter in your data in L1 like before and press
STAT  Calc  1 var stat. Enter.
B) Press 2nd y= and choose 1:Plot 1 On/Off
1) Turn plot “on”. Choose how to display data
(scatterplot, histogram, box & whiskers).
C) Press ZOOM. Choose 9:ZoomStat
1) Change the window to “fix” the data display.
a) Window: Adjust Xmin and Xmax and
press graph. Keep making adjustments
until you get a graph that looks right.
b) You can fix bad displays using
Window: Xscl (make Xscl = 1).