Define the following terms: (a) Arithmetic mean (b) Deviation (c) Standard Deviation (d) Variance (e) Geometrical mean

(a) Arithmetic Mean:  
In the context of meteorology, instrumentation, and tribology, the arithmetic mean is a statistical measure that provides the central value of a dataset. It is calculated by summing all observed values and dividing the total by the number of observations. The arithmetic mean is commonly used in meteorology to determine average temperatures, rainfall amounts, or wind speeds over a certain time period. In instrumentation, it helps in calibrating sensors by averaging repeated measurements. In tribology, it may be used to determine the average wear rate, surface roughness, or friction coefficient.

For instance, in a meteorological study, if temperature readings over 7 days are: 28, 30, 27, 29, 31, 32, and 30°C, the arithmetic mean temperature is calculated as:

\[
\text{Arithmetic Mean} = \frac{28 + 30 + 27 + 29 + 31 + 32 + 30}{7} = \frac{207}{7} = 29.57°C
\]

This value represents the average temperature over the week. Similarly, in instrumentation, if a thermocouple gives slightly different readings for the same standard temperature during calibration, the arithmetic mean of those readings is taken to improve accuracy. In tribological testing, average values of surface hardness or coefficient of friction are determined using the arithmetic mean to compare materials or lubricants.

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(b) Deviation:  
Deviation refers to the difference between an individual observation and the central value (often the arithmetic mean) of the dataset. In practical applications, it gives insight into the variability or dispersion of data points.

In meteorology, deviation helps to identify anomalies or fluctuations in climate data. For example, if the average rainfall in a region is 100 mm and in a particular year it is 120 mm, the deviation is +20 mm. ___ ________ ________ ________ ________ _____ _______ __________ _______ _________ _____ ____.
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