Measures of Central Tendency

Central Tendency is one of the main topics of statistics. There are three measures of statistics central tendency. The three measures of central tendency are mentioned bellow:

• Mean
• Median
• Mode

There are again three different types of mean: arithmetic mean, geometric mean and harmonic mean.

Next time i will help you with inference statistics. Till then understand this concept better. For more help you can connect with an online tutor and get your required help. Not just statistics, but you can get help from a trig tutor for trigonometry concepts.

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Units of time

Let us learn about Units of time

• Milliseconds, Minutes, Nanoseconds, Picoseconds
• Seconds, Weeks, Attoseconds, Centiseconds, Centuries
• Deciseconds, Days, Microsecond, Hours
• Leap year, Year, Yoctoseconds
• Millennia, Femtoseconds

Time is very precious especially to students. Time has been referred as the continuum in which events occur in succession from the past to the present and on to the future

In our next blog we shall learn about density altitude calculator I hope the above explanation was useful.Keep reading and leave your comments.

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easy general knowledge questions

Let us try to find answers for easy general knowledge questions

1) what is 55-17?

2) What number is 75% of 4?

3) A triangle with 2 equal sides is what kind of triangle?

4) Is this true, all Real Numbers belong to Complex Numbers?

5) The product of 2 fractions is 5. If 1 of them is the mixed number 61/5, what is the other number?

In our next blog we shall learn about properties of covalent compounds I hope the above explanation was useful.Keep reading and leave your comments.

composite number chart

Let us learn about composite number chart

A composite number has factors in addition to 1 and itself. All numbers which end in 5 are divisible by 5. Hence all numbers which end with 5 & are greater than 5 are composite numbers.

A number is known as "composite" if it can be divided evenly into 2 or more parts. In other words, it is a positive integer which is divisible by numbers other than 1 & itself. The smallest composite number is four. The 1st few composite numbers are as follows: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21...... A composite number is "an integer that is exactly divisible by at least 1 positive integer other than both itself and 1. All numbers are divisible by both one & itself. That is, a number which has more than 2 divisors other than 1 & the number itself is known a composite number.

In our next blog we shall learn about cost of sales formula I hope the above explanation was useful.Keep reading and leave your comments.

quantitative variables

Let us learn about quantitative variables

Measure the variable by a number is known as quantitative variable. The numeric values are known as variable. Quantitative variables are always ordered values, interval sequence & ratio scales.

Distributions of quantitative variables are represented by dot plots, histogram, box plots & scatter plots. Quantitative variables are always discrete & continuous variables.

In our next blog we shall learn about properties of alkali metals I hope the above explanation was useful.Keep reading and leave your comments.

integration by partial fractions

Let us learn about integration by partial fractions

If the integrand is in the form of an algebraic fraction & the integral cannot be evaluated by simple methods, the fraction requires to be expressed in partial fractions before integration takes place.

We decompose fractions into partial fractions like this due it makes certain integrals much easier to do, & it is applied in the Laplace transform, which we meet later.

Evaluate ∫ (x² + 1) / (x² -5x + 6) dx.

The integration by partial fractions is not a proper rational function on dividing

(x² + 1) by (x² - 5x + 6), we get

(x² + 1) / (x² - 5x + 6) =1 + (5x - 5) / (x² -5x + 6) =1 + (5x -5) / (x - 2) (x - 3)

Now, let (5x - 5) / ( x - 2)(x - 3) = A / ( x -2) + B / ( x -3)

=> (5x - 5) / (x - 2) (x -3) = A(x -3) + B(x -2) / (x -2) (x -3)

Placing x =2 on both sides of (i), we get A = -5

Placing x =3 on both sides of (i), we get B =10

( x² + 1) / (x² - 5x +6) =1 - 5 / (x -2) + 10 / (x -3)

=> ∫ (x² + 1) / (x² -5x + 6)dx = ∫ dx - 5 ∫ dx / (x - 2) + 10 ∫ dx / (x -3)

= x -5 log | x -2 | + 10 log | x -3 | + C

In our next blog we shall learn about extraction of aluminium I hope the above explanation was useful.Keep reading and leave your comments.

equation of ellipse

Let us learn about equation of ellipse

Equation of ellipse in standard form

[ x²/a² ] + [ y²/b² ] = 1

Let x'ox & yoy' be the co-ordinate axes.

Let F(c, o) and f'(- c, o) be 2 given fixed points .

Let us consider the locus of a point which moves in such a way that the sum of its distances from F & F' remains constant say equal to 2a where a > c.

Let P(x, y) be any point on the locus.

Then
PF + PF' = 2a

=> √[(x - c)² + y²] + √[(x + c)² + y²] = 2a
√[(x + c)² + y²] = 2a - √[(x-c)² + y²]

On squaring both sides,

we get
[(x + c)² + y²] = 4a² + (x - c)² + y² - 4a√[(x - c)² + y²]
[(x + c) ² - (x - c) ²] - 4a² = - 4a √[(x - c)² + y²]
4 x c – 4a² = - 4a √[(x - c)² + y²]
√[(x - c)² + y²] = a – (c/a) x

Again squaring on both sides ,

we get
(x - c)² + y² = a² + [c²x²/a²] - 2cx
x² - [c²x²/a²] + y² = a² - c²
x² [1 – (c²/a²)] + y² = a² - c²
[x²(a² - c²)] / a² +y² = a² - c²

Dividing by (a² - c²)

we get
(x²/a²) + (y²/(a²- c²)) = 1
(x²/a²) + (y²/b²) = 1 , where b² = a² - c²

Thus (x²/a²) + (y²/b²) = 1 is the required equation of an ellipse in standard form

In our next blog we shall learn about relative molecular mass I hope the above explanation was useful.Keep reading and leave your comments.