HOW MANY ARE BELOW YOU?

Your son has secured the fourth rank in the class. There are twenty students in the class. Hence 15 students are below him or 80% of students are below him. Now, your son is said to at the "80th percentile".

Percentile: The value below which a percentage of data falls.

Formula:

Percentile = (Number of values below "x"/total number of values)*100

In our case

=(16/20)*100

=80

Suppose, your son has scored 90% marks in math. But has percentile in math as 20. That means, only 20% of the students are below him. That is not impressive in spite of the high score. So percentile gives new meaning to data.

A total of 10000 people visited the shopping mall for over 12 hours.

Time (hours) people

0 0

2 350

4 1100

6 2400

8 6500

10 8850

12 10000

1. Estimate the 30th percentile

when 30% of the visitors had arrived

2. Estimate what percentile of visitors had arrived after 11 hours.

These questions can be answered by drawing graphs easily. But doing calculations is a bit difficult.

ADVT: DIY GARDENING KIT IN AMAZON

We draw a curve by taking hours in the x-axis and no. of people on the y-axis.

1. The 30th percentile occurs when the visits reach 3000 (since 30% of 10000 is 3000). Draw a horizontal line from 3000 until you hit the curve, then draw a line vertically downwards to read off the time on the x-axis.

the 30th percentile occurs at about 6.5 hours.

2. Draw a line vertically up from 11 until you hit the curve then draw a line horizontally across to read off the population on the vertical axis. So the visits at 11 hours were about 9500, which is the 95th percentile.

Uses:

Test takers can compare their performance to that of other students. Percentiles are used in children's growth charts (height, weight). This allows for an effective means of comparison so that parents can know if their child's growth is typical or unusual.

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