1. Fundamentals Data processing concepts
Averaging

2. Two variables

3. Mean and perturbation quantities

4. Introducing
Variance
Standard deviation

5. What does standard deviation mean?
In probability theory, standard
deviation is a measure of the
variability of a data set. A low
standard deviation indicates that
the data points tend to be very
close to the mean, while high
the data are spread out over a
large range of values.
Example: observations 2, 4, 4, 4, 5, 5, 7, 9
Mean: 5
Standard deviation: 2

6. Rules for normally distributed data
Range
Confidence interval

7. Two variables
covariance
Correlation coefficient

8. Example 1

9. Example-2
Example-3

10. Example-4
Scientific meaning of covariance

11. Sensible heat flux z z 1 1 2 2 daytime nighttime T T
Specific heat at constant pressure
Kinematic sensible heat flux, sh z z 1 1 2 2
daytime
nighttime T T
Sensible heat flux, SH

12. Significant figures
Rules for identifying significant digits when writing or
interpreting measurements:
1. All non-zero digits are significant.
123.45: 5 significant figures
20, 300?
2. In a number without a decimal point, only zeros between
non-zero digits are significant.
101.12; ;
3. Leading zeros are not significant
; 0.12;

13. 4. In a number with a decimal point, all zeros to the right
of the first non-zero digit are significant.
; ; ; 120.
5. The significance of trailing zeros in a number not
containing a decimal point can be ambiguous.
(a) A decimal point may be placed after the number;
for example "100." indicates specifically that three
significant figures are meant
(b) Using scientific notation

14. Rule of arithmetic computation
For multiplication and division, the result should have as many
significant figures as the measured number with the smallest
number of significant figures.
Example: A sprinter is measured to have completed a m race in seconds, what is the sprinter's average speed?
A calculator gives: m/s.
Superfluous precision!
Applying significant-figures rules, expressing the result would be m/s
For addition and subtraction, the result should have as many
decimal places as the measured number with the smallest
number of decimal places.
Example: =53.8

15. Example: Let's calculate the cost of the copper in an old penny that
is pure copper. Assuming that the penny has grams of copper,
and copper cost 67.0 dollar per pound. How much it costs to make
the penny? 1lb=453.6 gram

16. = = = =
x 2.5 =
/ =
x 273 =
8. (5.5)3 =
x (4x ) =
x 3.00 =
x x 102 =
12. What is the average of , , , , and ?

17. = 268.1 = =
= 129.
x 2.5 = 5.0
/ = 114.7
x 273 = 0.87
8. (5.5)3 = 1.7 x 102
x (4.x ) = 4.
x 3.00 = 1.4 x 102
x x 102 = 3.0 x 105
12. What is the average of , , , , and ?
Answer =