Day 9: Descriptive Statistics

Hello frndz,

today we will learn about Descriptive Statistics..

:- Average: The average of n number is defined as the sum of the n numbers divided by n.
For eg. the average of 6,4,7,10 and 4 is (6+4+7+10+4)/5 = 31/5 = 6.2


;- Median: To calculate the median of n numbers, first order the numbers from least to greatest; if n is odd, the median is the middle number.

For eg. the median of 6,4,7,10,4

step 1: first order it form least to greatest - 4,4,6,7,10
step 2: find the middle number i.e. 6

So median is 6

whereas, if n is even, the median is the average of the two middle numbers.
For eg. the median of 4,6,6,8,9,12 = (6+8)/2 = 7

(Note: if n is odd, median is (n+1)/2; else the average of n/2 and n/2 + 1)



:- It is not always true that half of the data in a series is less than median and half of the data is more than the median.
For eg. 3,5,7,7,7,7,7,7,8,9,9,9,9,10,10
Here the median is 7, but only 2/15 of the data is less than the median.



:- Mode; The mode of a list of numbers is the number that occurs most frequently in the list.
For eg. mode of 1,3,6,4,3,5 is 3 (occurs twice)

(Note: A list of numbers may have more than one mode.)


:- Range: Range is defined as the greatest value minus the least value.
For eg. the range of 11,10,5,13,21 is
21-5 = 16


:- Standard deviation: To calculate standard deviation;

step 1: find the arithmetic mean (average)
step 2: find the difference between the mean and each of the n numbers
step 3: square each of the differences
step 4: find the average of the squared differences
step 5: take the non negative square root of this average

For eg. standard deviation of 0,7,8,10,10

step 1: average = 7
step 2: differences = -7,0,1,3,3
step 3: square of differences = 49,0,1,9,9
step 4: average of step 3 = 68/5 = 13.6
step 5: square root of step 4 = 3.7

So S.D = 3.7

(Note: the more data are spread away from the mean, the greater the standard deviation and same as vice-versa).




Okie guys, keep practice on!! catch u soon.....


Er. Ankur Garg
garg.ankur6@gmail.com

Day 8: Powers and Roots of Numbers

Hello frndz,

Sorry, I was bit busy from last two days so was unable to take session... Today we will learn about Powers and Roots of Numbers.



:- When we multiplied a number k, n times then it looks like this: k*k*k*k*......n times
Lets pick a value of n i.e. 2 then k*k = k^2
Same as k*k*k*....n times can be expressed as k^n (called it 'nth power of k')



:- Tips: Squaring a number greater than 1 results in larger number. for eg.
2^3 = 2*2*2 = 8
and 8 >2
Squaring a number between 0 and 1 results in smaller number. for eg.
(1/2)^3 = (1/2)*(1/2)*(1/2) = 1/8
and 1/8 < 1/2



:- Square root of  a number greater than 1 results in smaller number. for eg.
  (4)^1/2 = 2
and 2 < 4
Square root of  a number between 0 and 1 results in larger number. for eg.
(1/4)^1/2 = 1/2
and 1/2 > 1/4



:- The square root of a negative number is not a real number; known as imaginary number.
For eg. (-4)^1/2 = Imaginary number.


:- The square root of every positive number has two results; one is positive and one is negative.
For eg. Square root of 9 = 3 and -3


:- Like Square root, Squaring a number of 1/3 known as cube root.


Okie guys, keep practice on!!! will be back soon....





Er. Ankur Garg
garg.ankur6@gmail.com

Day 7: Percents

hello frndz,

first of all, happy Dhusera to all!!! Today we will learn about percent and its uses....

:- A percent is a number out of 100. For eg. 20% means 20 out of 100.
20% = 20/100 = 0.2



:- To find a certain percent of a number for less than 50%, first calculate 10% by putting decimal after unit digit then calculate accordingly. For greater than more than 50%, first calculate 50% by doing half the number and then calculate remaining one...
For eg. To find 20% of 90;
First calculate 10% and 10% of 90 is 9 (remove unit digit 0).
Now, 20 % is twice of 10% i.e. twice of 9 = 2*9 = 18;

To find 80% of 90;
First calculate 50% i.e. 45 (half of 90)
Now, calculate remaining 30% i.e. thrice of 10% = 3*9 = 27
So 80% of 90 = 45 + 27 = 72

To find 3% of 90;
First calculate 1% by putting decimal after last two digits i.e. 0.90
now, 3% of 90 is thrice of 1% = 3*0.9 = 2.7


:- Percents greater than 100% known as numbers greater than 1.
for eg. 300% means 3 times, 200% means 2 times and 250% means 2.5 times etc....
250% of 80 = 2.5 * 80 = 200

:- Percents less than 1%: The percent 0.5% is half of 1%. For eg. 0.5% of 12 is the half of 1 % of 12 i.e.
1/2 * 0.12 = 0.06;

:- Percent change: For eg. if price of an item increased from $24 to $30, then price increased by $6 on the base price of $24 So percent increase is '$6 is what percent of $24?'

(Short method: half of $24 is $12 that is 50% of $24 and $6 is half of $12, again 50% of $12 So $6 is one forth of $24 i.e. 25% of $24).

So percent increase from $24 to $30 is 25%

Now reverse the question; If price of an item decreased from $30 to $24, then price decreased by $6 on the base price of $30 So percent decrease is '$6 is what percent of $30?'

(Short method: 10% of $30 = 3 and $6 is twice of $3 So $6 is 20% of $30).

So percent decrease from $30 to $24 is 20%

(Note: Percent increase from 24 to 30 is not equal to Percent decrease from 30 to 24).


:- If the cost of a certain house in 1983 was 300% of its cost in 1970, by what percent did the cost increase?
Let assume the cost of a house in 1970 was 100 then cost in 1983 was 300 So increase by 200 on base price of 100 i.e. 200%


Okie guys, Keep practice on !!!

Some good books for GMAT Quant prep:

1. Quant Official guide 12th Edition
2. Kaplan Matrial
3. Nova GMAT
etc..............


Er. Ankur Garg
garg.ankur6@gmail.com
www.nascentedutech.com

Day 6: Ratio and Proportion

Hello frnz,

Happy Navmi!!! today we will learn about Ratio and Proportion....

:- The ratio of number a to b is known as a/b (if b is not equal to 0).
For eg. Ratio of 2 to 3 is 2/3.


:- 2/3 can be written as 2 to 3 or 2:3. ratio of 4 to 6 is 4/6 and reduced form is 2/3.
So Ratio of 4 to 6 = Ratio of 2 to 3.


:- In ratio, ordered is important means ratio of 2 to 3 is not equivalent to ratio of 3 to 2.

:- Proportion: A proportion is a statement that two ratios are equal.
For eg. 2/3 = 4/6

:- Suppose in given four values of proportion, One is unknown Let's
2/3 = n/6, to solve it, we will cross multiply and get the value of n.

i.e. 2*6 = n*3 (Cross Multiplication)
12 = 3n So n = 4;





Okie guys, Keep practice On.....


Er. Ankur Garg
garg.ankur6@gmail.com


www.nascentedutech.com

Day 5: Real Numbers

hello frndz,

today we will learn about real numbers and some of their properties.

:- Number Line: A number line has a center with value 0. Left side, it has negative numbers and Right side, it has positive numbers.

:- All numbers reside on number line are known as Real numbers. All real numbers except zero are either positive or negative.

:- If you say, A number n is between 1 and 4 then you will write 1<n<4 and if n is 'between 1 and 4, inclusive' then 1<=n<=4

:- Absolute value: the distance between a number and zero on the number line is called Absolute value.
For eg. 3 and -3 are either side of 0 but has same absolute value (i.e. 3).

(Easier definition: A distance that you have to travel from zero to reach at that number means to reach at both number 3 and -3, you have to travel 3 units from zero.)
Absolute value is a distance and distance can not be negative so absolute value always be positive.
Modulus value = absolute value
So |3| = 3 always;


:- Properties of real numbers: Let's take x,y and z as real numbers.

1. x + y = y + x and x*y = y*x
2. (x + y) + z = x + (y + z) and (xy)z = x(yz)
3. xy + xz = x (y + z)
4. If x and y are both positive, then x + y and xy are positive.
5. If x and y are both negative, then x + y is negative and xy is positive.
6. If x is positive and y is negative, then xy is negative.
7. If xy = 0, then x = 0 or y = 0.
8. |x + y| <= |x| + |y| (check it for all four condition i.e. x and y positive, x and y negative  and either is positive).


Okie guys, Keep practice on!!! Hope you are doing well.....



Er. Ankur Garg
garg.ankur6@gmail.com 

Day 4: Decimals

Hello frndz,

Howz ur sunday... Have you enjoyed it!!!!!!!!!
Today we will learn about decimals and operation on decimals.

:-  7654.321, by which name, each digit known as?

In 7654.321, 1 known as Thousandth Digit (*1/1000)
In 7654.321, 2 known as Hundredth Digit (*1/100)
In 7654.321, 3 known as tenth Digit (*1/10)
In 7654.321, 4 known as Unit Digit  (*1) 
In 7654.321, 5 known as Ten Digit (*10)
In 7654.321, 6 known as Hundred Digit (*100)
In 7654.321, 7 known as Thousand Digit (*1000)

So 7654.321 can be rewrite as

7*1000 + 6*100 + 5*10 + 4 + 3*1/10 + 2*1/100 + 1*1/1000



:- Addition and Subtraction of Decimals:

To add 17.5612 and 635.27, first lined them. First number (17.5612) has 4 digits after decimals and second number (635.27) has 2 digits after decimals. Insert 2 zeros after second number.
So Now add, 17.5612 and 635.2700.
Add them as we simply do.....

To subtract 635.27 and 17.5612, first lined them. First number (635.27) has 2 digits after decimals and second number (17.5612) has 4 digits after decimals. Insert 2 zeros after first number.
So Now subtract, 635.2700 and 17.5612.
Subtract them as we simply do.....             



:- Multiplication of decimals:

To multiply decimals, first remove decimals from both numbers and multiply them as usual. In result, insert decimal at the place of total number of decimal place included by both number from right...

Confused!!!!!!!!! Don't worry
For eg. 2.09 * 1.3

Step 1: remove decimals. then 209 * 13 that gives us 2717

Step 2: Count the total number of decimals place in both numbers (2.09 has 2 decimal place from right and 1.3 has 1 decimal place from right So total number of decimal place is 2+1 = 3).

Step3: Put decimal after same number of place from right that gives us 2.717
So 2.09 * 1.3 = 2.717

Got it!!!!!



:- Division of decimals:


To divide decimals, first remove decimals from both numbers and divide them as usual. In result, insert decimal at the place of remaining number of decimal place included by both number from right...

Again Confused!!!!!!!!! Don't worry
For eg. 698.12 / 12.4

Step 1: remove decimals. then 69812 / 124 that gives us 563

Step 2: Count the remaining number of decimals place in both numbers (2.09 has 2 decimal place from right and 1.3 has 1 decimal place from right So remaining number of decimal place is 2-1 = 1).

Step3: Put decimal after same number of place from right that gives us 56.3
So 698.12 / 12.4 = 56.3

Got it!!!!!

   
Okies frndz, Hope you enjoyed this class also. Keep practice and we will come back with Real numbers in Next Class. Byee....


Er. Ankur Garg
garg.ankur6@gmail.com

Day 3: Fractions

Hello frndz,

Today we will learn about Fractions.

Any number in the form of a/b is a fractional number, where a is numerator and b is denominator.
Remember one thing, denominator can not be 0.

Two fractions are said to be equivalent if they represents the same number in their reduced form.
For eg. 8/36 and 14/63

To convert these in reduced form, divide each number by their HCF (Highest Common Factor). Let start with 8/36. HCF of 8/36 is 4 (8 = 2*2*2 and 36 = 2*2*3*3 SO in these number, 2*2 is common so HCF is 2*2 = 4).

Divide 8/36 by 4 (both numerator and denominator separably) So result is 2/9.
Same happen with 14/63 and result is 2/9.

Both represent the same number 2/9 so both are equivalent.


:- Addition and Subtraction: To add or subtract two fractional number, take the LCM of denominator. and Add or subtract numerator.
For eg  . 3/5 + 4/5
Denominators are 5 and 5 so LCM is 5.
So (3+4)/5 = 7/5

Again, 3/5 - 4/7
Denominators are 5 and 7 so LCM is 35. Now, 5 is 7 multiple of 35 and 7 is 5 multiple of 35.
So (3*7 - 4*5)/35 = 1/35


:- Multiplication and division of fractions:

1. To multiply two fractions, simply multiply both numerators and denominators.
For eg. 2/3 * 4/7
(2*4)/(3*7) = 8/21

2. To divide two fractions, find the reciprocal (a/b becomes b/a) of second fraction and multiply it with first one.
For eg. (2/3)/(4/7)
2/3 * 7/4 = 14/12
reduced form = 7/6


:- Mixed fractions: A number that consists of a whole number and a fraction is Mixed fraction.
For eg. 7(2/3)

To convert Mixed fraction into simple fraction, First find numerator by Multiply whole number with denominator and add it with numerator.
then find denominator that will be same.

For eg. 7(2/3) = (7*3 + 2)/3 = 23/3


Ok frndz, I hope you enjoyed this class. For any query, please post me a comment.
Next day, we will learn about Decimals.

Byee....


Er. Ankur Garg
garg.ankur6@gmail.com