What is absolute value?

What is absolute value?
Absolute value of number is defined asthe difference between it and zero and is denoted by symbol of |x| or sometime we can use abs(x). Absolute valueismost commonly used by mathematicians and scientists as a tool which is used to separate magnitude and direction when only magnitude matters. Absolute value is positive. The absolute value of a real number is the difference between that real number and zero

If x is the real number then the absolute value for real number |x| = x, when it is positive. |x| = -X, when x is not positive. The absolute value is the distance of x from 0.
The equation for absolute value is,
K = |x-b| ------------- (1)
If x-b is positive
Then k = x - b
X = b + k   ------------- (2)
If x-b is negative
-k = x - b
X = b – k ---------------- (3)
Finding the absolute values.
Example: | x-5 | = 7
From equations 2 and 3 the absolute values are
| x-5 | = 7 | x-5| = -7
X = 7 + 5 x = -7 + 5
X = 12 x = -2
So the absolute values are {12, -2}

Definition for absolute value

The absolute value of a number measures its distance to the origin/zero on the real number line. From above the figure x is 5 units away from the zero. The absolute value is always positive, so it can change the sign of the negative number in to positive number. But the absolute value of zero has no sign, since it is equal to its absolute value.

Absolute value equations:
Isolate the absolute value expression to solve absolute value equations. The expression is called as k. Then write both the equations in which the expression provided within the absolute value symbol is one of the two expressions.  Write the first equation k should be equal to the expression inside the absolute value symbol, and then write the other equation should be equal to –k. Then we get the set of solution obtaining the solution for the equations.

Example: | 2x+12 | = 4x
| x – b | = k
From above equation 2 and 3
| x – b | = k | x – b | = - k
2x + 12 = 4x 2x + 12 = -4x
X = 6 x = -2
So the solution of equation is {-2, 6}

Absolute value in algebra
Absolute value is defined as; it is functions which measure the size of the element as a field or integral domine (D).
|x| = 0
|x| = 0 if and only if x =0
|xy| = |x||y|
|x+y| = |x| + |y|

Example: |1|  = 1
  |-1| = 1

Statistical Mean

In Mathematics in the branch of Statistics, the expression for the mathematical mean of a statistical distribution is the mathematical average of all the terms in the data. To calculate this, we add up the values of the terms given and divide the sum by the number of terms in the data. This expression is also called the
Arithmetic Mean.


While solving word problems, we come across problems like, Scott drove from Bloomington to Chicago driving at 6 different speeds on the same freeway; 63mph, 72mph,42mph, 53mph, 67mph, 59mph. how do we calculate the Mean driving speed? It is very simple, we know that Arithmetic Mean is the regular average, so we just add up the different speeds and divide the sum by the number of different speeds given. Let us see the steps involved,
 The Mean driving speed = total sum of driving speeds /total number of speeds
Total sum of driving speeds = 63+72+56+68+59+48 =366
Total number of different speeds = 6
So, Mean driving speed = 366/6 = 61mph


Definition of Mean Or Definition Mean
To define mean, let us first learn about average in mathematics. Given a data of values, the average would be the total sum of the values divided by the total number of values given in the data. This in statistics is called the Mean or Arithmetic Mean. So, Definition of Mean is the average of the values given in a data.
Mean Formula
The Arithmetic Mean is the regular average of the values given in a data.
So, Mean Formula = Total sum of the values/Total number of values

Example: A student took 8 tests in a subject in one marking period. What is the mean test score?
                88, 75, 82, 90, 86, 78, 94, 87
Solution:  Number of tests = 8
  Sum of the marks =88+75+82+90+86+78+94+87= 680
   Mean = sum of the marks/number of tests
= 680/8 = 85

Sample Mean Formula
The sample mean in statistics, branch of Mathematics is the sum of all observed outcomes from the sample divided by the total number of events (Arithmetic Average). It is denoted by the symbol x with a (bar) above it. The Sample Mean formula is as follows:
X (bar) = (1/n) (x1+x2+x3………xn)

Example: At a car rental shop data was collected on the number of rentals on each of 10 consecutive Saturdays.  50, 44, 96, 38, 39, 40,50,46,47,42. Find the Sample Mean of the rentals.
Solution:   n = 10
Sigma(rentals) = 50+44+96+38+39+40+50+46+47+42=492
X(bar) =sigma(rentals)/n
            = 492/10
            = 49.2 is the Sample mean

Decimal Numbers

Decimals:
The Number system that we follow is called base 10 number system. In this system, we have numbers between 0 and 9, which defines every other number.  Fractional part of a number can be expressed as decimals.
What is a decimal?
Decimal is way of representing a fraction without numerator and denominator. The period or decimal point signifies that the number following it is fractional part. Decimal number can be either greater than or lesser than one. In case of decimal numbers, which are less than one, the leading number is zero.
Example:
39/10 = 3.9 [Decimal number greater than one]
79/100 = 0.79 [Decimal number less than one]
Decimal Place value:
In numbers, position of a number decides its value.
For example in counting number 345, the 3 represents three hundreds, 4 represents four tens and 5 represents 5 units. Similarly, in decimal numbers also, we have place value
Naming decimals:
One tenths = 1/10
One hundredths = 1/100
In 0.7, there are seven tenths.
In 0.79, there are seventy nine hundredths
In 0.798, there are seven hundred and ninety eight thousandths.
Decimal to fraction:
Let us learn how to convert a decimal into fraction.
Step 1: Find the number digits after the decimal point
Step 2: Write the number without the decimal point in the numerator
Step 3: in denominator write 1, followed by as many zeros as the number of digits after the decimal point in the given number
Example: Convert 0.347 into a fraction
Step 1: Number of digits after the decimal point is 3
Step 2: Numerator = 347
Step 3: Denominator = 1000
Hence, the fraction is 347/1000
Decimal to percent:
Let us learn how to convert a decimal number into a percentage.
To convert decimal to percent, multiply the decimal number by 100 and add % sign.
In other words, shift the decimal point to the right and add % sign.
Example: Convert 0.95 into percentage.
0.95 x 100 = 95%
Convert 0.895 into percentage.
0.895 x 100 = 89.5%
Rounding decimals:
Reducing the number of digits without any appreciable change in its value is called Rounding off.  You need to know how many digits you would like to have after the decimal point to round off.
It involves two steps.
Step 1: Decide the number of digits that want to keep in a decimal number.
Step 2: Increase by 1 if the next digit is greater than or equal to 5.
Step 3: Leave it, as it is if the next digit is less than 5.
Example:
Round off 0.789 to nearest hundredths.
0.789 is rounded off to 0.79, as the next digit 9 is greater than 5.
Round off 0.5674 to nearest thousandths.
0.5674 is rounded off to 0.567, as the next digit 4 is less than 5.

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.

Do post your comments.

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.

If you are interested to learn English Tenses, you can click on given link.

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.