Learn Basic Statistics Exam

Introduction to Learn Basic Statistics Exam

Statistics is the formal science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments. Now we will learn the basic statistics exam . (Source: Wikipedia).

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Learn Basic Questions for Statistics Exam


The following are the basic questions and solution for the exam

Question 1:

Find the mean for the following series. 4,8,9,10,12.

Question 2:

What is the mode for the following numerical number series? 3,7,8,10,12,10.

Question 3:

Find out the range of the following series. 10,20,30,12,55.

Question 4:

Calculate the median of the following series.15,13,19,16,30.

Question 5:

Find the mode of the following series. 32,10,12,17,28,39.

Question 6:

Find out the range of the following series. 14,18,24,28,30,33,36.

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Solutions for Statistics Exam


Solution 1:

Average of the given series is known as the mean. Mean is (.4+8+9+10+12)/5. So the solution is 8.6.

Solution 2:

We learn,the duplicate value of the given series is called as the mode. Therefore the mode is value is 10.

Solution 3:

We learn,Subtract the smallest value from the highest value is known as the range. Here the range is 55-10= 45.

Solution 4:

The central value of the given series is known as the median of the series. Before finding the median value we must arrange the series from low to high value. So the arranged values are 13,15,16,19,30.

Therefore solution is 16.

Solution 5:

The basic concept of mode is the duplicate value. The given series there is no repeated value. So the value of mode is null or empty.

Solution 6:

Range is the subtraction of the lowest value from the highest value. Highest values is 36. Least value is 14.The given series range value is 36-14=22.

Learn Unit Vectors

Introduction to learn unit vector:

Physical quantities are divided into two groups, i.e. scalars and vectors. Scalar quantities are those having only magnitude like work done, length, mass etc. Vector quantities are those having magnitude as well as direction like displacement, force, acceleration etc.

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Learn Unit Vectors:


Vectors are symbolically denoted by a line segment with a direction. The length of the line segments gives the magnitude and the direction of the arrow denotes the direction of the vector.

A vector whose magnitude is one unit is called a unit vector, a unit vector is represented with   a letter that names the vector with a cap. The cap in the letter is the indication that it is a vector.

Denoted by â, read as ‘a cap’. Thus, │â│=1.

If│ │ represents the magnitude of a vector, then │â │=1.

The vectors are extensively used in linear algebra. The variable in linear algebra exists in two dimensional x or y axis or y and z axis. The vector not only gives the magnitude of the variable, they also give the direction of the variables.

Vectors are usually defined by the corresponding coordinates. A unit vector in a two dimensional space will have two co-ordinates and a vector in a three dimensional space will have three co-ordinates. A vector with more than one co-ordinate will have the magnitude equal to the square root of the sum of the squares of the co-ordinates.

To find the magnitude of the vectorV (1, 3), we add the squares of the co-ordinates 1 and 3.

This is equal to 10. Now the square root of 10 is greater than 1. ThereforeV (1, 3) is not a unit vector. The basic unit vectors for the three dimensions individually are represented as

X (1, 0, 0), y (0, 1, 0) and z (0, 0, 1)

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Conclusion to Unit Vectors:

Vectors are physical quantities that have a direction and magnitude. Unit vectors have magnitude equal to one unit.  Vectors in two dimensional and three dimensional spaces are represented by the co-ordinate values. Vectors are an important part of linear algebra studies.

Learn Triangles Area

Introduction to learning area of triangles

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted as `Delta ABC`. (Source: From Wikipedia).

Types of triangles

Equilateral triangles (3 equal sides and angles).
Isosceles triangles (Two equal sides and angles)
.Scalene triangles (No equal sides and angles).
Right triangles (Special case - any triangle with right angle).
Here, we are going to learn how to find the areas of triangles.


Learning formulas for finding the area of triangles


Here we are going to learn basic arithmetic formulas to find the area of different types of triangles.

Area of equilateral triangles
The area of an equilateral triangle can be found by using the formula,

A = `sqrt(3)/4` s2 square units, s - side of the triangle

Area of isosceles triangles
The area of an isosceles triangle can be found by using the formula,

A = `1/2` bh square units, b and h are base and height of the triangle respectively.

Area of scalene triangles
The area of a scalene triangle can be found by using the formula,

A = `sqrt(s(s-a)(s-b)(s-c))` square units

s = `(a + b + c)/2`. a, b, and c are the sides of the triangle


Example problems for finding the area of triangles


Here we are going to learn how to find the area of a triangle.

Example 1

Find the area of a triangle whose sides are equal to 16 cm.

Solution

Area of equilateral triangle = `sqrt(3)/4` s2

= `sqrt(3)/4` * 16 * 16

= `sqrt(3)` * 4 * 16

= `64sqrt(3)`

So the area of the given triangle is `64sqrt(3)` square cm.

Example 2

Find the area of a triangle with height 5 cm and base 4 cm.

Solution

Area = `1/2` bh square units

= `1/2` * 4 * 5

= 10

So, the area of the given triangle is 10 square cm.

Example 3

Find the area of a triangle with sides, 2 ft, 5 ft, and 6 ft.

Solution

Area of a scalene triangle = `sqrt(s(s-a)(s-b)(s-c))`

s = `(a + b + c)/2`

s = `(2 + 5 + 6)/2`

= `13/2`

= 6.5

Area = `sqrt(6.5(6.5-2)(6.5-5)(6.5-6))`

= `sqrt((6.5)(3.5)(1.5)(0.5))`

= `sqrt(17.0625)`

= 4.13

So the area of the given triangle is 4.13 square ft.

Ways to Help to Learn Ratios

Introduction to ways to help to learn ratios:
The ratios contain the fractional numbers. The ratio of two numbers a and b in the same units is the fractions a/b, it can be written as a: b., where a represent the antecedent and b represent the consequent. We can represent (a: b)> (c: d) as (a/ b)> (c/ d). The multiplication and division of the terms of the ratio by the same number does not affect the ratio.

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Example problem for learn ratios:

Example 1 to learn ratios:

Divide 350 in the ratio 2:3.

Solution:

The sum of the ratio terms = 2+3=5

For the ratio 2,

First part= 350 x (`2/5` ) =140

For the ratio 3,

Second part= 350 x (`3/5` ) =210

Example 2 to learn ratios:

A mixture has the alcohol and water in the ratio of 4:2. If 5 liters of the water is mixed with the mixture, the ratios can be changed to 4:5. What is the quantity of alcohol in that mixture?

Solution:

Let the quantity of alcohol and water is 4x liters and 2x liters respectively. Then the ratio is,

`(4x)/(2x+5)`= `(4)/(5)`

20x =4(2x+5)

20x= 8x+ 20

28x=20

x=0.71

The quantity of the alcohol =4x 0.71 = 2.8 liters.

Example 3 to learn ratios:

Find the simplified ratio for 49: 324.

Solution:

The given ratio is 49: 324

The above ratio can be written as 72: 182.

The ratio can be simplified as 7: 18.

The ratio 121: 169 can be simplified as 11: 13.

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Practice problem for learn ratios:


A bag consists of 50 p, 25 p and 10 p coins in the ratio of 2: 3: 4, amounting to Rs. 206. What is the number of coins of each type?
Answer: 50 p coins are 192, 25 p coins are 288 and 10 p coins are 384.

Worker A takes 2 hours to do a particular work. Worker B takes 5 hours to do the same work. How long it take both of them A and B, working jointly but independently to do the same work?
Answer: `10/7 ` days

A and B together can complete a piece of work in 6 days. If A alone can finish the same work in 12 days, in how many days can B alone complete that work?
Answer: 12 days

Learn Fractions The Easy Way

Introduction for Learn Fractions the Easy Way:

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator.

Source – Wikipedia.

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Learn Fractions the Easy Way – Addition:


Learn addition of fractions: `1/6 + 1/6` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `1/6+1/6`

= `(1+1)/6`

By simplifying the fractions we get

= `2/6`

= `1/3` is the solution.

Learn addition of fractions: `1/12 + 1/12` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `1/12+1/12`

= `(1+1)/12`

By simplifying the fractions we get

= ` 2/12`

= `1/6 ` is the solution.

Learn addition of fractions: `2/24 + 4/24` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `2/24+4/24`

= `(2+4)/24`

By simplifying the fractions we get

= `6/24`

= `1/4` is the solution.

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Learn Fractions the Easy Way – Subtraction:


Learn subtraction of fractions: `1/6 - 2/6` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `1/6-2/6`

= `(1-2)/6`

By simplifying the fractions we get

= `-1/6` is the solution.

Learn subtraction of fractions: `3/12 - 1/12` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `3/12-1/12`

= `(3-1)/12`

By simplifying the fractions we get

= `2/12`

= `1/6` is the solution.

Learn subtraction of fractions: `2/24 - 4/24` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `2/24-4/24`

= ` (2-4)/24`

By simplifying the fractions we get

= `-2/24`

= `-1/12` is the solution.

Learn Multiplication

Introduction for learn Multiplication:

In math, any two numbers can be manipulated by using operations. Basically, there are four different operators. Subtraction, addition, division and multiplication are the operations carried out. Here multiplication is an operator, which is denoted by (cross) × , (star) * . (dot) •. There are some basic rules for the multiplication of two numbers. In this article, we shall learn about multiplication operation. Also we shall learn to solve problems based on multiplication operation.

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Learn Multiplication Properties:

7 * 5 = 35

Here   7 is the multiplier

5 is the multiplicand

35 is the product.

For example:

3 * 5

Three times 5: 5 + 5 + 5 = 15.

Or five times 3: 3 + 3 + 3 + 3 +3 = 15

Properties of Multiplication:

There are several properties that are used while multiplying the given expressions.

1. Learn Distributive Property:

a * (b + c) = (a * b) + (a * c)

For example:

7 * (5 + 3) = (7 * 5) + (7 * 3)

Solution:

Left Handed Side  = 7 * (5 + 3)

= 7 * 8

= 56

Right Handed Side = (7 * 5) + (7 * 3)

= 35 + 21

= 56

Left Handed Side  = Right Handed Side

Hence the proof.

2. Learn Commutative Property:

a * b = b * a

For example:

7 * 5 = 5 * 7

Solution:

7 * 5 = 35

5 * 7 = 35

Both are same.

So 7 * 5 = 5 * 7

Hence the proof

3. Learn Associative Property:

a * (b * c) = (a * b) * c

For example:

7 * (5 * 3) = (7 * 5) * 3

Solution:

Left handed side:

7 * (5 * 3) = 7 * (15)

= 105

Right Handed side:

(7 * 5) * 3 = 35 * 3

= 105

Both are same.

So, 7 * (5 * 3) = (7 * 5) * 3.

Hence the proof

4. Learn Multiplicative Identity Property:

a * 1 = a

For example:

7 * 1 = 7

5 * 1 = 5

3 * 1 = 3

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Example Problems to learn Multiplication operations:


Example 1:

What is the Multiplication of 8 and 4.

Solution:

We can express the given problem as 8 * 4.

8 times 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32.

Or 4 times 8 = 8 + 8 + 8 + 8 = 32

Therefore the multiplication of 8 and 4 is 32.

Example 2:

What is the Multiplication of 9 and 3.

Solution:

We can express the given problem as 9 * 3.

9 times 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27.

Or 3 times 9 = 9 + 9 + 9 = 27

Therefore the multiplication of 8 and 4 is 27.

Third Grade Math

Third Grade math:

The mathematics is the basic term. The grade 3 math are the included by arithmetic operations, and basic algebra. The grade 3mathematics contains multiplication, division, addition, subtraction, fractions and decimals, basic geometry, roman numbers. The following math based on the grade 3mathematics only.

Third Grade Time Facts:

1 day = 24 hr

1hr     = 60 min;

1 min  = 60 seconds,

1 hr    = 60 x 60 seconds = 3600 seconds

Third Grade multiplication:

The grade 3 multiplication is two parts these are the multiplicand, multiplier.

Third Grade Division:

The grade 3 division is three parts these are the dividend, quotient, divider, and reminder.

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Third Grade Math Examples:


Solve Third grade Math multiplication:

4487 x 4

Step 1:

Find the multiplier and multiplicand.

Multiplier = 4

Multiplicand = 4487

Step 2:

Start with left hand side to multiplicand to multiply by 4.

4487 x 4

1 7 9 4 8

Step 3:

Therefore the answer is 17948.

Third Grade Time Facts Example:

20 min =? Find how many seconds

Solution:

1 mins = 60 seconds

Therefore,

20 mins = 60 seconds x 20 = 1200 seconds

Answer:

20 min = 1200 seconds.

Example for expanding number:

Find the number 789 arrange the digits in a place value chart as shown below

Hundreds Tens Ones

7             8       9

Solution:

From the chart above, we see that:

The value of 7 is 7 x 100      = 700

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 789 is 700 + 80 + 9.

Third Grade Time Facts Example:

1 hr 20 min =? Find how many mins

Solution:

1 hr = 60 mins

Therefore,

1 hr 20 mins = 60 mins + 20 mins = 80 mins

Answer:

1 hr 20 min = 80 mins

Example for expanding number:

Find the number 1589 arrange the digits in a place value chart as shown below

Thousands Hundreds Tens Ones

1              5             8       9

Solution:

From the chart above, we see that:

The value of 1 is 1 x 1000   = 1000

The value of 5 is 5 x 100   = 500

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 1589 is 1000 + 500 + 80 + 9.

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Practice Problems for Third grade math:


Practice Problem 1:

Solve:

9854 x 4

Practice problem 2:

Expand the form 6795

Answer key:

39416
6000 + 700 + 90 + 5