Solve Elementary Statistics Problems

Introduction of elementary statistics problem:

Data is a word in a plural form of the Latin word datum. Every part of our lives utilizes data in one form or the other. This extraction of significant information is study in a branch of mathematics called statistics. A step additionally by studying certain numerical representatives of the ungrouped data, also called measures of central tendency, namely, mean, median, mode and also range are under the elementary statistics only.

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About Elementary statistics


Elementary statistics is deals with the basic static calculations of data’s for finding the mean values etc... The word ‘statistics’ appears to have been taken from the Latin word ‘status’ meaning ‘a state (related to a political)’... Statistics deals with collection, organization, analysis, and Interpretation of data. ‘Statistics’ has held different meanings in different contexts, so that the calculation process is based on the meaning and data. Elementary statistics problems are mainly deals with the mean, median, mode, and range.

Example for elementary statistics problems


Let us see about the basic elementary stastistics problem below,
Example for Mean: what is the mean of 3, 8 and 5?
Add the numbers: 6 + 8 + 4 = 16
divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
so the Mean is 6
Example for Median: Find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.
Special Case: If there are two middle numbers (as happens when there are an even amount of numbers) then average those two numbers.
Find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.
Example for Mode: The number, which appears mostly, repeated in a set of numbers. In Set {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Example for Range: is nothing but the difference between the lower and higher values.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.
Range can also mean all the output values of a function.

Patterns in Elementary Algebra

Introduction of Patterns in algebra:

Numeric patterns in algebra are patterns made from numbers.

The numbers can be in a list. Any math operation (addition, subtraction, multiplication, or division) can be used to make the pattern.

Many of the patterns in algebra you see will use addition. The same number will be added to each number in the list to make the next number in the list.

Example

2,5,8,11,14,17…

The pattern in algebra is to add 3 every time. The next number is 20, then 23.

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Example for patterns in algebra:


Example 1:

2,4,6,8,10,12,…

Solution:

The rule here is counting by 2 using even number, so next term are 14 and 16.

Example 2:

1,3,5,6,9,11,13,15,…

Solution:

If you guessed that the rule is counting by 2 using odd numbers, you are correct.

Example 3:

1,1,2,3,5,8,13,21,34,55,…

Solution:

Look carefully and think!!!

If you concluded that the answer to this pattern in algebra is that you need to add number together to get the next number in line, you are correct.

1+1=2,2+1=3,3+2=5,5+3=8,…

This is a famous pattern in algebra or sequence known as the Fibonacci sequence.

Example 4:

A store gives a door prize to its third customer and to every fifth customer after that. Which of the following customers will get a door prize?

The 62nd

The 71st

The 79th

The 98th

Solution:

Whenever you see a problem like this one, do not just stare at it hoping to see the pattern in algebra. Start working out the problem on paper, and after a few steps, you should be able to see the pattern in algebra. If the third customer gets a prize, as does every fifty customer who follows, the list of customer who will get prizes should be numbers.

3,8,13,18,23,28,33,…

Therefore, every number that ends in a 3 or an 8 will get a prize. Of the choices listed, only D ends with 3 or an 8, so it must be the answer.

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Practices problem for patterns in algebra:


Problem 1:

Which of the following best describes the pattern in algebra of these numbers?

5/2,3,7/2,4.

Answer:          Each number is one-half more than the number before it.

Problem 2:

Consider the pattern in algebra of numbers given.

Row 1:                  2

Row 2:                  4                6

Row 3:                  8               10                    12

Row 4:                  14             16                    18                    20

What will be the sum of the number is Row 7?

Answer: 350

Linear Elementary Algebra

Introduction to linear elementary algebra:

A linear elementary algebra  equation is constructed by constants and one or more variables by using only the arithmetic operations like, addition, subtraction, multiplication and division.

The linear equations are most often used in linear elementary algebra.

A general form with two variables x and y is

y= mx +c

Where, m and b values are constants.


Example problem for linear elementary algebra 1


Example problem for linear elementary algebra 1 is given below:

Find four different solutions of the linear equation x + 2y = 6.

Solution:

x = 2, y = 2 is a solution because for x = 2, y=2

x + 2y = 6, 2 + 2(2) = 6, 2+4=6, 6=6.

Now, let us choose x = 0. With this value of x, the specified equation reduces to 2y = 6, which has the unique solution y = 3.

So x = 0, y = 3 is also a solution of x + 2y = 6.

Similarly, plug y = 0, the given equation reduces to x = 6.

So, x = 6, y = 0 is a solution of x + 2y = 6 as well.

Finally, let us take y = 1.

The given equation now reduces to x + 2 = 6, whose solution is given by x = 4. Then, (4, 1) is also a solution of the given equation so four of the infinitely many solutions of the given linear equation are:

(2, 2), (0, 3), (6, 0) and (4, 1).

Example problem for linear elementary algebra 2:


Example problem for linear elementary algebra 2 is given below:

The price of 2 pencils and 3 erasers is Rs 9 and the price of 4 pencils and 6 erasers is Rs 18. Find the price of each pencil and each eraser.

Solution:

The pair of linear equations formed was:

2x + 3y = 9 ……………..… (1)

4x + 6y = 18 …………….... (2)

We first write the value of x in terms of y from the equation

2x + 3y =9, to get x = (9-3y)/2 ………………. (3)

Now we plug this value of x in Equation (2),

4(9-3y)/2+ 6y = 18

18 – 6y + 6y = 18

18 = 18

This statement is true for all values of y.

However, there is no specific value for y as a solution.

Therefore, we cannot get a specific value of x.

Therefore, Equations (1) and (2) have infinitely lots of solutions.

Here an exact cost of a pencil and an eraser  can't be found, because there are many common solutions, to the given situation.

Elementary Geometry Definitions

Introduction to learning elementary geometry definitions:

Learning elementary geometry definitions,

In learning elementary geometry definitions, the word geometry can be defined as the system of concepts, in which a few ideas were initialized to derive the big ones. It is said to be Deductive systems. Geometry tells you the deduction concepts and consequence logic's, which can be applied throughout your life time. By learning this article, you can learn about the elementary definitions of geometry. I like to share this Find the Volume of a Cube with you all through my article.


Learning Elementary Definitions of Geometry:

Let we see elementary definitions of geometry,

Point: A Point can be defined as the basic object of geometry. A point has no dimensions, denote position.

Line: A line is connection of many points. The line having one dimension, i.e., length.

Concurrent lines: By learning geometry, if three lines are said to be a concurrent lines, then the three lines should pass through common point.

Intersecting Lines: If two lines are not parallel, then they will intersect each other at a common point.

Collinear points: Collinear Points are the points, which lie on the same line.

Plane: By learning, a Plane is an infinite set of points combined to form a flat surface.

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Learning Elementary Shapes and their Definitions in Geometry :


Let we see elementary shapes of geometry and their definitions,

Square: A Square can be defined as a regular quadrilateral. All the four sides of the square are equal.

Rectangle: A Rectangle is a four sided geometrical figure. The opposite sides of a rectangle are equal.

Triangle: In geometry, triangle is one of the basic shapes. It consists of three sides. It belongs to polygon family.

Circle: A circle is a geometric figure, formed by a locus of points equidistant from a common point.

Midpoint: A midpoint is point, which separates a line segment from both the end points.

Ray: A line having one fixed end point and an infinite extension on other end.

Angles: An angle can be formed by two rays having common end point.

Right angle: If an angle is 90°, it is said to be  right angle.

Obtuse angle: If an angle is more than 90° but less than 180°, it is said to be an obtuse angle.

Straight angle: If an angle is 180°, it is said to be straight angle.

By learning the geometry, many elementary shapes are found and their definitions are known.

Elementary Linear Algebra 8th Solution Kolman

Introduction of elementary linear algebra 8th solution kolman:

Algebra is a part of mathematics, which deals with the study of operations and relations. Algebra also includes the equations and polynomials. Algebra also performs topologies, number theory, addition, equation solving, etc can be done. Algebra derived from Arabic language al-jabr. Algebra consists of simultaneous equation, partial fractions, factorization, rational expressions, square root, etc. Let us see about elementary linear algebra koulman.  For example,

5+3 = 3+5 is same as a+b = b+a.

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Examples for elementary linear algebra 8th solution kolman:


Problem 1 for elementary linear algebra 8th solution Kolman:

Find the value of the expressions 3x+7, if x=5.

Solution for elementary linear algebra 8th solution Kolman:

sub, x=5 in the given expression 3x+7

3x+7 = 3(5) +7

=15 + 7

= 22

Therefore the value of expression 3x + 7 is 22.

Problem 2 for elementary linear algebra 8th solution Kolman:

Solve 7x-5 =79

Solution for elementary linear algebra 8th solution Kolman:

7x-5 = 79

7x = 79 +5 from rule(2)

7x = 84

x= 84 *1/7 from rule(3)

x = 84 / 7

x = 12

Value of x is 12.

Problem 3 for elementary linear algebra 8th solution Kolman:

The perimeter (p) of a rectangle is twice the sum of its length (l) and breath(b).

1. Frame a formula to find the perimeter

2. Find b when p=34 and l=10cm

Solution for elementary linear algebra 8th solution Kolman:

From the given statement

Perimeter = 2[length +breadth]

I.e p=2[l+b]

p=2[l+b]

2[l+b] = p

l+b = ½ *p

b = (p/ 2)-l

then sub, p=34 and l=10 in above step,

b = (34/2)-10

=17-10 =7

b = 7cm

Practice Problems for Elementary Linear Algebra 8th Solution Koulman:


Q 1.  6x + 40 = 94.Find x?

Answer: x = 9

Q 2.  Solve 2x+7y = 11, -3x+5y=-1

Answer: x=2,y=1

Q 3.  Solve for x 3x + 10 = 8x + 5

Answer: x = 1

Elementary Statistics Homework

Introduction to elementary statistics homework:

Our world is flattering more and more information oriented. Every part of our lives utilizes data in one form or the other. So, it becomes necessary for us to know how to extract meaningful information from such data. This taking out of meaningful information had studied in a branch of mathematics called Statistics.


elementary statistics homework Problems of find median:


Statistics example:

The points scored by a Tennis team in a series of matches are as

Follows:

20, 5, 10, 30, 18, 8, 17, 11, 14, 27, 51, 13, 11, 10, 21, 31

Find the median of the points scored by the team.

Statistics solution:

To arrange the given points in ascending order, we get

5, 8, 10, 10, 11, 11, 13, 14, 17, 18, 20, 21, 27, 30, 31, 51

There are 16 terms. Therefore, there are two middle terms.

That is, (16/2)th term and ((16/2)+1)th term. Therefore, these are the 8th and 9th terms.

Hence, the median is the average values of the 8th and 9th terms.

Median (14+17)/2=15.5

Therefore, the medial point scored by the Tennis team is 15.5.

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elementary statistics homework Problems of find mode:


Statistics example 1:

Find the mode of the following numbers (out of 10) obtained by 20 peoples:

4, 6, 5, 8, 3, 2, 7, 7, 6, 5, 4, 8, 10, 10, 3, 4, 7, 6, 8, 8

Statistics solution:

We arrange this data in the following form:

2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 10, 10

Here 8 occur most frequently, i.e., four times. Therefore, the mode is 8.

Statistics example 2:

A team in a series of 10 matches given below scored the number of goals:

2, 5, 4, 3, 0, 1, 5, 5, 4, 5

Find the mode of these scores.

Statistics solution:

We arrange this data in the following form:

0, 1, 2, 3, 4, 4, 5, 5, 5, 5

Here 5 occur most frequently, i.e., four times. Therefore, the mode is 5.

These are some of the homework problem on elementary statistics.

Elementary Algebra

Introduction to elementary Algebra

In elementary level the childrens would reading the lessons and solve their  algebra math problems with help of  simple arithmetic functions like addition,subtraction,division and multiplications and these can be denoted by (+ ,`xx` ,`-` ,÷ ).This elementary level of reading the algebra is the growing stage for the childrens in their  education field.Let we see about the problem based on elementary algebra. I like to share this help with algebra 2 problems with you all through my article.



Elementary Algebra solved problems

Problem 1:

Solve the given problem 20x - 6 = 12
Solution:

Step 1: Given that 20x - 6 =12

Step 2: Here we are going to add the 6 on both the sides

Step 3: 20x  - 6 + 6  = 12+ 6

Step 4 : 20x =18

Step 5: X = `18/20`

X = 0.9

So the solution foe x  is  0.9

Problem 2:

Calculate and simplify the given problem
6d2 + 48da

Solution:

Step 1: 6d2 + 48d

Step 2: We will take the 8a as common from 6d2 and 48d

Step 3: Then the expression become as,

6d (d + 8)

The answer: 6d2 + 48d = 6a (a + 8)

Problem 3:

solve  ` (3/2)` + `(6/2)`

Solution:

Step 1: Take LCM as 2
Step 2: = ` (3/2)` + `(6/2)`

Step 3:  Add the above terms.
= `(12+6) / 2`
= `18/2`

The answer is = `18/2`


One more solved problemsElementary Algebra


Problem 4:

Calculate and find the  system of equation 8x + 10y = 12, y = 2
Solution:

Given that:

Step 1: 8x + 10y = 12, y = 2

In the problem the y value is mentioned as 2 ,So apply the y value in 8x + 10y = 12

Step 2: 8x + 10y = 12

Step 3: 8x + 10(2) = 12

Step 4: 8x + 20 = 12

x =1

We get a variables as x =1 and y = 2.

So the answer is x =1 and y = 2.

The above solved problems done in basic elementary algebra for the childrens used in elementary. Please express your views of this topic How to Rationalize the Denominator by commenting on blog.


Practice problems in Elementary Algebra


Problem 1:

Solve the given problem 30x - 8 = 12
Answer:  X = 0.66

Problem 2:

Calculate and simplify the given problem
5d2 + 45da

Answer: 5a (a + 9)

Problem 3:

solve  ` (6/2)` + `(5/2)`

Answer:  = `22/2`