Statistical Data

Quantitative : Discrete, Continuous

Referred to as numeric,  Quantitative data have two types: Discrete and Continuos. Continuous are measurement and discrete are counts, as a general rule.

A count that can't be made precise more is discrete data. It involves integers typically. It is a discrete data which is the number of children (or pets, or adults), for instance, the reason is whole are counting by yourself, entities indvisible: 1.3 pets or 2.5 kids, you can't have it.

On the other hand, continuos data, to finer and finer levels it could reduce and could be divided. For examlple, at progressively more precise - beyond, milimiters, centimeters and meters - so height are continuos data.

Qualitative 

Qualitative data is characterizes or approximates by data but properties, attributes, characteristics, etc are not measured,  of phenomenon or a thin. Whereas quantitative data defines is where qualitative data describes.

Measures of dispersion

Standard Deviation

Within a set of data, a measure of the spread of scores are the standard deviation defines.

Formulas for the standard deviation

Sample standard deviation formula is:

where,

= sample mean
n = number of scores in sample.
s = sample standard deviation
= sum of...

Measures of central tendency

Mean:
                      -- The mean is found when the numbers of data entries dividing and adding up all of the given data. It is also known as the average.
                Example:
                             - the grades were as follows,  the class of grade 110 math had a mathematics test recently:
 
                                       78
                                       66
                                       82                                  464 / 6 = 77.3
                                       89
                                       75                        Hence, the mean average of the class is 77.3.
                                    + 74
                                      464
     Median:
                      -- The middle number is the median.  First you arrange the numbers in order from lowest. Firstly, from the lowest, in order you arrange the numbers
                to highest, by crossing off the numbers until you reach the
                middle then you find the middle number.
              Example:
                               - to find the median, use the above data:
                                                66  74  75  78  82  89\
                            - There is no middle number, as you can see we have two numbers  What should we do?
                    find the average and we take the two middle numbers , ( or mean ).  It is simple;
                                                             75 + 78 = 153
                                                              153 / 2 = 76.5
                             Hence,  76.5 is the middle number.
 
         Mode:
                        -- this is the number that most often occurs.
                 Example:
                                 - the following data below, find the mode:
 
                                    78  56  68  92  84  76  74  56  68  66  78  72  66
                                    65  53  61  62  78  84  61  90  87  77  62  88  81
                                                   78 is the Mode.

Sets and Venn Diagram

At the left shows overlap of two sets A and B of the Venn diagram. U is the universal set.  In the center region labeled where the circles overlap is where the values that belong to both set A and set B are located. "Intersection" of the two sets is the region are called.

 

Videos of Shading regions Venn Diagrams

(Can only be played at google chrome)

Geometric Progression

Geometric Progression, Series & Sums

Introduction

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,

where	r	common ratio
	a1	first term
	a2	second term
	a3	third term
	an-1	the term before the n th term
	an	the n th term

The geometric sequence is sometimes called the geometric progression or GP, for short.
For example, the sequence 1, 3, 9, 27, 81 is a geometric sequence. Note that after the first term, the next term is obtained by multiplying the preceding element by 3.
The geometric sequence has its sequence formation:
To find the nth term of a geometric sequence we use the formula:

where	r	common ratio
	a1	first term
	an-1	the term before the n th term
	n	number of terms

Arithmetic Progression

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.
For example, the sequence 1, 2, 3, 4, ... is an arithmetic progression with common difference 1.
Second example: the sequence 3, 5, 7, 9, 11,... is an arithmetic progression
with common difference 2.
Third example: the sequence 20, 10, 0, -10, -20, -30, ... is an arithmetic progression
with common difference -10.

Notation

We denote by d the common difference.
By a_n we denote the n-th term of an arithmetic progression.
By S_n we denote the sum of the first n elements of an arithmetic series.
Arithmetic series means the sum of the elements of an arithmetic progression.

Properties

a₁ + a_n = a₂ + a_n-1 = ... = a_k + a_n-k+1

and

a_n = ½(a_n-1 + a_n+1)

Sample: let 1, 11, 21, 31, 41, 51... be an arithmetic progression.
51 + 1 = 41 + 11 = 31 + 21
and
11 = (21 + 1)/2
21 = (31 + 11)/2...

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If the initial term of an arithmetic progression is a₁ and the common difference of successive members is d, then the n-th term of the sequence is given by

a_n = a₁ + (n - 1)d, n = 1, 2, ...

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The sum S of the first n numbers of an arithmetic progression is given by the formula:

S = ½(a₁ + a_n)n

where a₁ is the first term and a_n the last one. or

S = ½(2a₁ + d(n-1))n

Number Pattern

(can only be played in google chrome)

Pattern or a certain sequence that are followed by a list of numbers.


For Example:  tarts at 1 and jumps 3 every time... 1, 4, 7, 10, 13, 16,

Another Example: doubles each time ...  2, 4, 8, 16, 32