MEANING OF 'MEAN-VALUE'

A cricket game in progress. The batting team has scored 60 runs so far in 10 overs. Dividing 60 by 10 we get 6. 6 is the average number of runs per over taken so far. .That is , the team seems to have scored 6 runs in each over (Practically, they might have scored 12 runs in a over and zero runs in another over). 'Average runs' is also called run rate. If the rain bring the game to a halt, run rate is used to decide the winner. Remember, as the game processes, the run rate changes.

Toss a coin 5 times . 4 times you may get the head and 1 time tail may appear. So the mean is 80% for head and 20% for tail. Toss the coin 10 times. 6 times may be head. 4 times may be tail. Now the average is 60% and 40%.
Throw the coin for 1000 times. (A computer simulation helps). You may get the head 502 times and tail 498 times. The average of getting head or tail per throw approaches 50% or 1/2. When the volume of samples or trials go on increasing, the average approaches probability.

The normal values of blood sugar, blood pressure, life expectancy, normal height, normal rainfall, per-capita income,all are averages based on many samples and studies.

Take 10 persons. Measure their heights. Find their average height. Find at least 30 samples of 10 persons and calculate their average height(30 averages). Now draw a graph. Taking averages in X- axis and heights in Y- axis. A bell curve or normal distribution curve appears. The curve tells us that majority of averages are close to the universal average. Averages peak or accumulate at the center. That is the reason for bell shape. This concept is termed as 'central limit theorem'. This is applicable to all the natural attributes like height, weight, blood sugar, intelligence, courage and so on. So we may be average in many traits but best in a few traits.

Moving averages are used in stock market. Average price of a stock is calculated for a week. When the new week day is born, most old price value is shed from the list, the new day's price value is taken into account and fresh average price is calculated. The average price runs(changes) everyday. Investors can speculate using the running average and can decide to buy, sell or keep it.

The mean value is the safest value. When it is difficult to take a firm a decision, take shelter under average value.

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THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, ...

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. ...

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high ...

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