Learn Basics B4 being a Master :::…

Lets begin the LESSON 01…

what do you mean by chance ?

chance is an event of an alternative occuring for a given incident.

Am i correct. This is what i think of the chance….

oh i forgot what the heck is an event..?

I think that you should answer this question by yourself  because if  i do answer this simple question too this blog is not gonna be about PS but about common sense….

OK then now let cut the babies work and get into bussiness…

consider the figure 1

figure 1

what is the chance of selecting a color?

there are 4 colors available therefore the chance of selecting a color is 0.25. That is if any one who is going to select a color can choose “a” color from the group of four. one out of four.

lets try another example try figure 2

figure 2

what is the chance of selecting a color ?                        — Answer by your own.

what is the chance of selecting a empty circle ?        — Answer by your own.

what is the chance of filling all empty circles with a single color at a time ?       –Answer by your own.

can you answer the above three questions…. ahaa goto next lesson…. Advance comrade..

if you cannot don’t bother just do the figure 1 again…..

Try & try one day you can fly…

Welcome SLIIT 2nd year students

Yo guys i start this blog hoping that you could get some help from my knowledge for your studies. One thing i’m soo sure is that I’m not perfect and i do have my draw backs.  But i have figured out that most of the 2nd year students who do Probability & Statistics (PS)  find it so hard to understand the concepts behind the scene. But if you get hold of the basic concepts of  PS is more easy than riding a bicycle as they say…….

So any one who need some kinda help in PS i hope this could be an advantage to their studies……………..

Before the learning i’m gonna set out some terms. Do not make this as the “only” help to PS but just an alternative!!!!!!!

And to know the extent of how much you have grapsed from this answer the Q’s in the Q’s category…. and if you really want to,  submit your answers to me. This part i know most of you will avoid cause i know if  i was in this position i would also neglect to submit the answers. But i must  atleast ask you to do so….

LETS START PS…………

target the sun you may end up in mercury or if you are willing you could end up in …………………..

2.) Measures of dispersion…

Now you know what are measures of location. You should learn what are measures of dispersion. They measure how the data are dispersed through out. Always you should remember that what theses measures do?. What do they do ?

They measure the dispersion.

what the heck does that mean right!!

Ok check out the following examples then you’ll now what is data dispersion…

2   4   5   3    6    2    3    4    5    2     3    4      6    8   9     21     34

if you closely examin these observations you’ll find out that there are outliers.

these two out liers make an huge damage to measurements like range and mean. So we need to find out what is the extent that these data are dispersed from each other;

Ok inorder to do so i’ll first calculate the mean

u = 7.12~

then i’ll take the difference of each value with the mean

2 – 7.21 = -5.21

2 – 7.21 = -5.21

2 – 7.21 = -5.21

3 – 7.21 = -4.21

3 – 7.21 = -4.21

3 – 7.21 = -4.21

4 – 7.21 = -3.21

4 – 7.21 = -3.21

4 – 7.21 = -3.21

5 – 7.21 = -2.21

5 – 7.21 = -2.21

6 – 7.21 = -1.21

6 – 7.21 = -1.21

8 – 7.21 = 0.79

9 – 7.21 = 1.79

21 – 7.21 = 13.79

34 – 7.21 = 26.79

Ok now i’ll squar the values inorder to let go the minus mark which is in front of several values….

27.1441  ,27.1441  ,27.1441  ,17.7241  ,17.7241  ,17.7241  ,10.3041  ,10.3041  ,10.3041  ,4.8841  ,4.8841  ,1.4641  ,1.4641  ,0.6241  , 3.2041  ,190.1641  ,717.7041

now add these up

you get 1089.9097

now divide this by 16  (Don’t worry about this, i got 16 by substracting 1 from 17. one of my friends told me some would face a problem from where the hell did 16 come from. Its just (n-1) sample size minus one… (- Thanx manju))

you’ll get 68.12

So  you ge the varience of the data set

if you get the squareroot of this you’ll find the value called standard deviation..

ok heres what i did       ———–>>

if the last (n-1) was (n) then its σ²

as I said before there are two concepts in statistics which is population and sample, This (S) is for the sample and 

σ is for the population.

if you take the square root of varience you get the standard deviation….

NoW i WoUld LiKe tO MakE a SugGesTiOn

do lots of questions from standard deviation untill you are not afraid of the question…..

Here I would like to show you what does this value mean. Take the standard deviation of the values.

S.D = 8.25

You can see that the S.D is much higher than the “mean” this mean that the data set has a skewness to the right, that is the values are shifted away fromthe mean…

now Do you get the meaning of DisPerSiOn

(1.2.2)The quantiles…

The quantiles…

There are three types,

Quartile.

Deciles.

Percentiles.

These are really simple concepts but you need to have the basic concepts about the quantiles then it is real easy to tackle really hard questions.

Ok I’m gonna draw you simple figures that you’ll get the meaning of these quantiles.

..Quartiles..

..Deciles..

..Percentiles..

Therefore X_m = Q₂ = D₅₀ = P₅₀

Quartiles..

Q₁ first quartile :- Q₁ covers 25% of the total observations,

Q₂ second quartile :- Q₂ covers 50% of the total observations,

Q₃ second quartile :- Q₃ covers 75% of the total observations,

Deciles…

This could be also defined as above, but you could follow the pattern and try your own.

Percentiles…

This could be also defined as above, but you could follow the pattern and try your own.

(1.3) Arithmetic Mean

Arithmetic Mean…

mean we denote in two different ways.

Miu

X – “Bar”

Remember these two symbols have two different means in advance statistics. But in this era our statistics are not that advance so i’ll not go into discussion about it. But remeber this these two have different meanings, when it come to, be ready to accept that they are different.

1.3.1) Mean for raw data

Its simple, all you have to is take the sum of all the observations and divide it with the number of observations.

here is a simple fomular for it….

miu_equation

xbar_equation

Both are the same……..

pick your choice……………..

But Remeber this is the basic definition for the mean SO WHAT EVER YOU PICK STICK WITH IT.

1.3.1) Mean for frequency distribution…

ok i’m gonna describe you how to get this in a different manner….

How did you get the mean for raw data….

sum of total divide by total number.

Anyone who visit first tell me how to get the total from a frequency distribution ?

and if you can tell me how to get the total number of observation without using ‘N’ or ‘n’

then i’ll get you the answer….

<<<<<<<<<<<<<Waiting for the Answers>>>>>>>>>>>>>>>>>>>

1.3.3)Mean for a grouped frequency distribution…

Here we do the same as we did in frequency distributions.

for this we need to find the “class mid point”,

For what?

that is the main purpose of “class mid-point” or sometimes known as “class mark”

Then you only have to replace the X Value with the X` or the mid-point of each class.

—————————————————————————————————————————————————

#!/Note/

if [ you do not know the mid point ]

then

read below….

class mid point or the class mark is used for representing the class by a single value. Its easy, we donot have an exact value when we deal with classes right, to overcome that we say we take this class mid point which will be calculated by adding class boundaries and dividing by 2 which will be denoted by ” X` “.

fi

—————————————————————————————————————————————————

all the equations will be posted after i get my answer………..

(1.2.1) The Median

1.2.1) The Median

The median is the middle of the data set. Therefore before selecting the median it is necessary to re-arrange the data set in an ascending order of the magnitude.

1.2.1.1) Median for set of raw data.

Lets get this by an simple example.

Ex. 2 9 7 5 3 4 5 4 7 3 1

We should re-arrange the data set in an ascending order.

1 2 3 3 4 4 5 5 7 7 9

Therefore the number in the middle is “4”

Definition Median:

The median is the middle value of an ordered set of data.

This ordered set could be either in ascending order or descending order.

There are two cases; where the data set does exactly have a middle value, and when it does not.

This is also recognized by the number of data elements in the data set. When the number of elements is odd and even. We normally denote median by

“X_m”

Thus we can get two different equations to derive the median.

When the number of elements are odd :-

When the number of elements are even :-

You can always get the median value by following the above 2 equations.

1.2.1.2) Median for a frequency distribution

I’ll get an example I used before

Number of students	30	45	78	69	48	25	5
GPA	1	1.5	2	2.5	3	3.5	4
Cumulative frequency	30	75	153	222	270	295	300

Total number of students =300

Sample size is even, therefore the median should be

X_m = [X₍₁₅₀₎+X₍₁₅₁₎]/2

X_m = 2

1.2.1.3) Median for a grouped frequency distribution

Here we encounter a problem. We should get the value before the summarization of the data.

For that purpose we use the method called interpolation. There is another method to do this estimation it is called extrapolation. In our guiding book it has used the extrapolation mechanism. So I’ll show how to use extrapolation.

I’m taking the example from our book.

Measurements	Cumulative frequency	Relative cumulative frequency
0.0 – 1.0	3	0.075
1.0 – 2.0	7	0.175
2.0 – 3.0	11	0.275
3.0 – 4.0	18	0.450
4.0 – 5.0	24	0.600
5.0 – 6.0	29	0.725
6.0 – 7.0	34	0.850
7.0 – 8.0	35	0.875
8.0 – 9.0	37	0.925
9.0 – 10.0	40	1.000

How did I arrive at the relative cumulative frequency…..

What it means is that the weight of each cumulative frequency value with respect to the total value.

So to get the relative frequency, get each value and divide it with the total value

3/40 = 0.075

——————————————————————————————————————–

#!/Note

if [ you do not understand what is going on in the later part of this chapter ]

then

please read the “percentiles” page.

fi

———————————————————————————————————————

P₅₀ = 4.0 + (1/0.600-0.450)*0.05 = 4.33`7;

Here I looked at the 50^th percentile. It should be on the range from 0.450 to 0.600.

I know the exact value for 0.450 that is 4

What I need to estimate is for the other 0.05

Also I know that from 0.450 to 0.600 represent 1

Then comes simple mathematics.

If 0.450 to 0.600 represent 1 what is for 0.05

That is 1 —> 0.600 – 0.450 = 0.15

For 0.05 —-> (1/0.15) * 0.05 = 1/3;

Ok now you know how to get the median lets move into next chapter………

(1.1)The Mode

The Mode

Definition :

The mode is the value of a variable which occurs most frequently.

1.1.1)Mode for raw data…..

Ex.

17 5 7 6 5 5 8 9 2 5 3 4

By using the “tally method”

Distinct observations	Tally marks	frequency
2	I	1
3	I	1
4	I	1
5	IIII	4
6	I	1
7	I	1
8	I	1
9	I	1
17	I	1

Modal frequency = 4

Therefore the Mode = 5

There is a single mode. So this scenario is called as “unimodal”

Ah there you find a question ….

Is there a scenario when more modes available?

Yeah!!!! In that case its called “Bimodal”

Ok now you got it right answer me this???

Distinct observations	Tally marks	Frequency
2	IIII	4
3	IIII	4
4	IIII	4

What is the mode ? …………………….. I will answer this question when the 1^st viewer answer this correctly or incorrectly.

1.1.2) Mode for a frequency distribution

Number of students	30	45	78	69	48	35	5
GPA	1	1.5	2	2.5	3	3.5	4

I guess that you guys can distinguish the variable from its frequency….

Variable GPA other is frequency.

The trick is to find the modal frequency which is easy = 78

Therefore the mode is 2

1.1.3)Mode for a grouped frequency distribution

There are ways to calculate the exact mode for the grouped frequency distribution. To our course of study we do not have that much advance basic statistics. So to give you guys a brief idea I’ll tell you how to locate the “MODAL CLASS”

Guess the trick ……………….

Find the highest frequency,

Get the class…………… Vola !!!!!! you got the “modal class”.

Definition modal class:

The modal class which is the class corresponding to the highest frequency.

Basic Statistics . .. …

I’m following our guiding book.  So i would skip some parts that are soo easy, like the part of derawing stem & leaf diagrams, histograms, I want you guys to learn about what a “population” is and a “sample” is. I’m saying this cause in future when you guys come to Hpothesis testing and its concepts you guys will not understand anything if you do not know the concepts behind the scene, like population/ sample.

There are two major categories of measurements that we take in statistics.

1.) measures of location

2.) measures of dispersion

know these you’ll have no problem with standard deviation and variation.

1). Measures of location

There are three main measuring instruments to do location measuring.

1.1) Mode

• 1.1.1) Mode for raw data
• 1.1.2)Mode for a frequency distribution
• 1.1.3)Mode for a grouped frequency distribution

1.2)Median

• 1.2.1) The median

1.2.1.1) The median for raw data
1.2.1.2)The median for a frequency distribution
1.2.1.3)The median for a grouped frequency distribution

• 1.2.2) The quantiles

1.2.2.1) Quartiles

1.2.2.2)Deciles

1.2.2.3)Percentiles

1.3)Arithmetic Mean

• 1.3.1) Mean for raw data
• 1.3.2)Mean for a frequncy distribution
• 1.3.3)Mean for a grouped frequncy distribution

More Basics (think about permutations and combinations)

Lesson 02…

Consider the figure 03.

figure 3

1.) what is the chance of filling the empty circles with some color at a time ?     — Try the answer.

2.) what is the chance of filling the first circle with color green ?    — Try answer.

Answering …..

1.)

there are four ways to fill the first empty circle.

there are four empty circles. so there are 4*4*4*4 times arrangements.

So to select a one occurrence is 1/256

so the chance of selecting an arrangement of colors is 1/256;

2.)     Try to follow the same logic as above . i don’t like to provide every answer. But i would provide the logic inorder to derive the answer.

here are some helping figures…