Frequency Distribution Formula

Monday 18th of February 2013 | By: Javed Ansari | Views: 336 | Comments: 0 | Rating: 3 Star Content3 Star Content3 Star Content3 Star Content3 Star Content |  

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A frequency distribution has shows the unorganized data which can be divide the data in a mutually exclusive in the number of occurrences. In the frequency distribution the tables can be consists of a classes with corresponds to the frequency of data values. We can be grouping the data value and data is known as raw data. The followings are some of the formula in the frequency distribution.

Formula for Frequency Distribution 1:

The followings are some of the formulas for finding the mean and cumulative frequencies of a frequency distribution.

Formula for the mean of discrete for frequency distribution:

The mean of frequency distribution   sum_(i=1)^nf i x i   / N

N = sum_(i=1)^nf i

Mean of Frequency Distribution:

The mean of a frequency distribution is a group of a average data. It consists of the frequency deviation values as x1, x2, x3…xn and the frequencies as f1, f2, f3….fn.

 

Formula for Cumulative frequencies:

Formula, F = m / (n + 1)

Where m = the mth value of the order of the series.

n = it is the number of the terms in the series.

f = it is the randomized value of the probability and the data value calculated for F.

 

Formula for Frequency Distribution 2:

The followings are some of the formulas for finding the continuous and ranking for cumulative frequencies of a frequency distribution.

 

Formula for Continuous Frequency Distribution Interval:

The continuous frequency distribution interval can be calculated the width as

Continuous Frequency Distribution = (large data value – small data value /  Total number of the class )

Width of the class interval.

 

Check this Instantaneous Velocity Formula awesome i recently used to see.

 

Ranking Formula for Cumulative Frequencies:

F = Rd / (N + 1)

Where, Rd = it is the reference value for a certain rank number of P and Q.

N = number.

Consider the data as P and the data can be arranged in a descending order. Then the first and last value for maximum, minimum can be written in them.

F = 1 – Ra / (N – 1)

Where Ra = the rank number of the frequency and has the relation between the Rd, Ra and N.

In the rotational motion, the term related to the frequency is the angular frequency. The angular frequency is same as the angular velocity. As the velocity plays the role in the linear motion, the angular frequency plays the same role in the rotational motion. If a rigid body that means the intermolecular spacing of the body is very less rotates about any axis, then the angular frequency comes into play. Here we discuss about the angular frequency and the factors on which it depends.

 

definition of Angular frequency

The angular frequency is defined as the angle rotated by an object, which is rotating about a fixed axis in the unit time. The angular frequency can be calculated by the frequency also. Angular frequency is equal to the product of two times of the pie and frequency.

The formula for the angular frequency (omega ) = dtheta  /dt

And in the terms of the frequency

[omega]  = 2 × prod  × f, where f is the frequency.

 

The angular frequency is a scalar quantity and the unit of the angular frequency is radian per second. The dimension of the angular frequency is [M0L0T-1]. In the rotational motion the angular frequency is involved in the equation of rotational motion also and the equations of motion in the rotational motion are:

omega = omega0 + alphat

theta = omega0 + ½ alpha t2

[omega]  = [omega] 0 + 2alphatheta

Where,  [omega] is the final angular frequency, [omega] 0 is the initial angular frequency, alpha is the angular acceleration and theta is the angular displacement.

 

Example for angular frequency

A flywheel is rotating at the speed of 420 rpm slows down the speed at the rate of 2 radians per squared second. Find the time to stop the flywheel.

Solution

Here, f0 = 420 rpm = 420 / 60 = 7 rps, alpha = - 2 radian per squared second, f = 0, t = ?

[omega] 0 = 2 prod × 7 = 44 radian per second, w = 0

We use  [omega] = [omega] 0 + alpha t

t = ( [omega] - [omega] 0)/alpha = (0 - 44) / (- 2) = 22 seconds

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