THE AVERAGE DOES NOT EXIST

The statisticians used to tell these jokes.
1. We humans have 1.999... legs on the average. It will happen when we take into account physically challenged people.
2. We have only one testicle. Again this will result when all women are taken into account.
3. In a survey, men were asked how many girl friends they have. Most of them reported one. But a few reported 5 to 10. Some even 100. If we take a simple average, the answer will be shocking and misleading.
We have to use not only average -mean, but also mode and median at the appropriate places. Let us explore.

MEAN: The average we use every day. It is got by adding all the items and dividing by no. of items. It is suitable for the data which cluster around a central value. Example: Height of male or female graduate students. Blood pressure values of persons in the age range 60-70.

MEDIAN: It is the number that lies in the middle when all the numbers in the data sheet are lined up in ascending order.Say, there are 51 students in a class. Marks are awarded for 100 in a particular subject. If the median of the marks is 75, it means that 25 students had scored above 75 and another 25 students scored below 75. It indicates a good performance. If the median is 23, we understand that the students had done badly.

MODE: It is the most common (occurring) number in the data set. In the case of average of legs, or number of wives,It is better to take the mode. We will definitely get 2 legs and 1 wife as average.

Normal temperature of the body, heart beats, BP value, sugar reading and other medical parameters are mostly average values. Today, we specify average range also.
Teachers teach not for highly intelligent students or the slow learners. But they teach for average students (who is not present in the class).
A state draws out finance budget for average man; A limited meal is designed for average appetite. A plane seat will fit only average sized man and so on.
In the world of averages we have to somehow fit ourselves in.
------------------------------------------------------------------------------------------------

Comments

LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

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. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

sciencecapsules

Search This Blog