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Lesson Posted on 01 Feb Tuition/BSc Tuition/Basic Statistics and Probability

Corelation, Scatter Plot, Outlier, Co-Variance & Regression

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

i. Scatter plot: Graphical representation of relation between two or more variables. ii. Covariance: between two random variables is statistical measure of the degree to which two variables move together. Covariance captures how one variable is different form its mean as other variable is different from... read more

i. Scatter plot: Graphical representation of relation between two or more variables.

ii. Covariance: between two random variables is statistical measure of the degree to which two variables move together. Covariance captures how one variable is different form its mean as other variable is different from its mean.

- Positive Covariance indicates that variable tend to move together.

- Negative Covariance indicates that variables tend to move in opposite directions.

iii. Corelation simply tells us strength of relationship between independent & dependent variable. It measures the degree of extent of relation between two variables:

a. Corelation Coefficient: Measure of Strength of relationship between or among variable:

- r=1: Perfect positive relationship.
- 0<r
- r=0: No relationship.
- -1<r
- r=-1: Perfect negative relationship.

Degree of Corelation can be determined by looking at scatter plots:

- If relation is upward: Positive relation
- If relation is Downward: Negative Relation

iv. Outlier: is an extreme value of variable, may be, quite large or small.

v. Regression is analysis of relation between one variable & some other variables assuming a linear relation also referred as least square regression.

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Comments Answered on 09 Mar Tuition/BSc Tuition/Atomic and Molecular Physics

How does Mercury and Venus doesn't have natural satellites?

Sahil Sharda

Personalized self defence and yoga classes

Moons or natural satellites are either created during the creation of the planet/solar system, or are captured. Mercury doesn't have a gravitational pull powerful enough to hold anything else in orbit around itself. That's why it doesn't even have an atmosphere. And proximity to the Sun ensures that... read more

Moons or natural satellites are either created during the creation of the planet/solar system, or are captured.

Mercury doesn't have a gravitational pull powerful enough to hold anything else in orbit around itself. That's why it doesn't even have an atmosphere. And proximity to the Sun ensures that any object coming within Mercury's vicinity is sucked into the Sun directly. So capture is out of the question. Even if Mercury did have a small satellite, the Sun's pull would disturb the orbit of the satellite, causing it to fall into the planet.

While Venus has a greater gravitational pull, it still faces the same problem. It's simply too close to the sun to hold on to another body. However, in the past, Venus might have had a moon that spiraled into the planet after collision with another body that might or might not have caused the planet to flip along its axis.

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Answers 1 Comments Answered on 30 Jan Tuition/BSc Tuition

Sanjeev Kumar

Tutor

Electronics is an interesting subject. First opt self study method and starts from basics. If you are not able to understand electronics subject properly, then you can contact a tutor. A teacher is equivalent to studying at least five books.

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Lesson Posted on 11 Jan Tuition/BTech Tuition/Engineering Mathematics (M1) Tuition/BTech Tuition/Advanced Mathematics (M2) Tuition/BSc Tuition/BSc Mathematics

Probability: Random Variable, Discrete Probability Distribution And Expectation

Sreedevi S.

Current Profession - Assistant Professor in Mathematics, University, Punjab Total Experience - 14 years Part...

An experiment whose outcome cannot be predicted is called random experiment. The set of all outcomes of a random experiment is called a sample space and is denoted by S. A sample Space is discrete if it has finitely many or a count ably infinite number of elements. A sample space is continuous it contains... read more

An experiment whose outcome cannot be predicted is called random experiment. The set of all outcomes of a random experiment is called a sample space and is denoted by S. A sample Space is discrete if it has finitely many or a count ably infinite number of elements. A sample space is continuous it contains uncountable number of elements. Any subset of a sample space is called event. is called an impossible event and whole space is called a sure event.

i. Random variable: A real valued function, defined over the sample space of a random experiment is called the random variable associated to that random experiment. That is the values of a random variable correspond to the outcomes of a random experiment.

Example: In the case of tossing three coins, the outcomes can be described as getting ‘0’ head, 2 heads and 3 heads. Let us consider a variable ‘X’ which takes values 0, 1, 2, 3. The value of X correspond to the outcomes 0 Head, 1 Head, 2 Heads and 3 Heads. Then X can be considered to be a random variable associated to the Random experiment of tossing three coins.

ii. Discrete and Continuous Random Variables: A random variable may be discrete or continuous. A random variable is said to be discrete if it assumes only specified values in an interval. When X takes values 1, 2, 3, 4, 5, 6 it is a discrete variable.

iii. A random variable is said to be continuous if it can assume any value in a given interval. When X takes any value in a given interval (a, b), it is a continuous variable in that interval.

iv. Distribution (Probability distribution) (Probability function) (Density function): Let ‘X’ be a random variable assuming values x_{1}, x_{2}, x_{3}….. Let ‘x’ stand for any one of x_{1}, x_{2}, x_{3 }…… Then probability that the random variable ‘X’ takes the value x is defined as probability function of ‘X’ and is denoted by f(x) or P(x). Therefore P(x) = P(X = x) where X is the random variable and ‘x’ stands for values of X, is the probability function of x.

When X takes values x_{1}, x_{2} … we have the corresponding probabilities P(x_{1}), P(x_{2})…such that P(x_{1}) + P(x_{2}) +………..= 1

i.e. ∑ P(x) = 1 and all P(x) >0

Example: In tossing two coins the random variable representing the number of heads takes the values x = 0, 1, 2…….

P (no head) = 1/4 Therefore P(x=0) = 1/4

P (one head) = 2/4 Therefore P(x=1) = 2/4

P (two heads) = 1/4 Therefore P(x=2) = 1/4

v. Properties of Discrete Probability Distribution:

Let P(x) be the probability density function, then,

P(x) > 0 for all values of x

- ∑ P(x) = 1

vi. Expectation of X (Expected value of X): Let the random variable X assume that the values of x_{1}, x_{2 … }with corresponding probabilities P(x_{1}), P(x_{2})… Then the expected value of the random variable X denoted by E (x) is given by the formula.

E(x) = x_{1} p (x_{1}) + x_{2} p (x_{2}) + ……….. I.e. E(x) = ∑ x p (x)

Example: When a die is thrown, the random variable X (number on the die takes the values 1, 2, 3, 4 ,5, 6 with corresponding probabilities 1/6, 1/6, 1/6, 1/6, 1/6, 1/6. Then

E(x) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 21/6

Variance of X: Variance of a random variable X, whose expectation denoted by E (x), is defined as

V (x) = E (x^{2}) – [E(x)]^{ 2}

^{ }

vii. Discrete Distribution function: Let X is a random variable and ‘x’ be any value of it. Then P[X < x] denoted by F (x) is called distribution function.

viii. Properties of distribution function:

- F (x) is a non decreasing function
- F (x) > 0
- F (∞) = 1.

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Comments Lesson Posted on 11 Jan Tuition/BSc Tuition/Basic Statistics and Probability

Range, Quartile Deviation, Mean Deviation & Standard Deviation

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

1. Range: Difference between Smallest & Largest value, R = L-S Higher Vaqlue of Range implies Higher Dispersion & Vice-versa. 2. Quartile Deviation: i. The quartile deviation is a slightly better measure of absolute dispersion than the range, but it ignores the observations on the tails. ii.... read more

1. Range:

Difference between Smallest & Largest value,

R = L-S

Higher Vaqlue of Range implies Higher Dispersion & Vice-versa.

2. Quartile Deviation:

i. The quartile deviation is a slightly better measure of absolute dispersion than the range, but it ignores the observations on the tails.

ii. If we take difference samples from a population and calculate their quartile deviations, their values are quite likely to be sufficiently different.

Quartile Deviation= (Third Quartile-First Quartile)=Q3-Q1/2

3. Mean & Standard Deviation:

i. Two measures which are based on deviation of values from average is called mean deviation.

ii. Since Average is central Value .Some Deviations are +ve & Some are -ve.

iii. If these are added sum will not reveal anything.

iv. In fact Sum of deviations from arithmetic mean is always Zero, mean deviation tries to overcome this problem by ignoring the signs of deviation.

v. It Considers all deviation positive:

Mean Deviation = Modulus (Observation-Arithmetice Mean)/No of Observations

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Comments Lesson Posted on 11 Jan Tuition/BSc Tuition/Basic Statistics and Probability

Raj Kumar

I am Six Sigma Black belt certified. I am 2011 pass out in B.tech from NIT Srinagar. I am an experienced,...

1. Discrete Data: Data is a count that can't be made more precise. Typically it involves integers. For instance, the number of children (or adults, or pets) in your family is discrete data, because you are counting whole, indivisible entities: you can't have 2.5 kids, or 1.3 pets. 2. Attribute &... read more

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Lesson Posted on 11 Jan Tuition/BSc Tuition/Basic Statistics and Probability

Editing Of Primary & Secondary Data

Raj Kumar

The main objective of editing is to detect possible errors and irregularities. While editing primary data the following considerations need attention: 1. The data should be complete. 2. The data should be consistent, 3. The data should be accurate, and 4. The data should be homogeneous. 1. Editing... read more

The main objective of editing is to detect possible errors and irregularities.

While editing primary data the following considerations need attention:

1. The data should be complete.

2. The data should be consistent,

3. The data should be accurate, and

4. The data should be homogeneous.

1. Editing for completeness: The editior should see that each schedule and questionnaire is complete in all respects, i.e., answer to each and every question has been furnished. If some questions have not been answered and those questions are of vital importance the informants should be contacted again either personally or through correspondence. It may happen that in spite of best efforts a few questions remain unanswered. In such questions, the editor should mark ‘No answer ’ in the space provided for answers and if the questions are of vital importance then the schedule or questionnaire should be dropped.

2. Editing for consistency: While editing the data for consistency, the editor should see that the answers to questions are not contradictory in nature. If there are mutually contradictory answers, he should try to obtain the correct answers either by referring back the questionnaire or by contacting, wherever possible, the informant in person. For example, if amongst others, reply to the questions: (a) Are you married? (b) Mention the number of children you have, and the are respectively ‘no’ and to ‘three’, then there is a contradiction and it should be clarified.

3. Editing for accuracy: The reliability of conclusions depends basically on the correctness of information. If the information supplied is wrong, conclusions can never be valid. It is, therefore, necessary for the investigators to see that the information is accurate in all respects. However, this is one of the most difficult tasks of the investigators. If the inaccuracy is due to arithmetic errors, it can be easily detected and corrected. But if the cause of inaccuracy is faulty information supplied, it may be difficult to verify it, e.g., information relating to income, age, etc.

4. Editing for uniformity: By homogeneity we mean the condition in which all the questions have been understood in the same sense. The investigators must check all the questions for uniform interpretation. For example, as to the question of income, if some informants have given monthly income, others annual income and still others weekly income or even daily income, no comparison can be made. Similarly, if some persons have given the basic income whereas others the total income, no comparison is possible. The investigators should check up that the information supplied by the various people is homogeneous and uniform

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Comments Lesson Posted on 03 Jan Tuition/BSc Tuition/Basic Statistics and Probability

Understanding Qualitative, Quantitative, Attribute, Discrete And Continuous Data Types

Raj Kumar

Quantitative data deals with numbers and things you can measure objectively: i. Dimensions such as height, width, and length. ii. Temperature and humidity. iii. Prices. iv. Area and volume. Qualitative data deals with characteristics and descriptors that can't be easily measured, but can be observed... read more

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Comments Lesson Posted on 03 Jan Tuition/BSc Tuition/Basic Statistics and Probability

Raj Kumar

Control charts are simple but very powerful tools that can help you determine whether a process is in control (meaning it has only random, normal variation) or out of control (meaning it shows unusual variation, probably due to a "special cause"). Continuous data usually involve measurements, and often... read more

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Asked on 03 Jan Tuition/BSc Tuition/BSc Physics

How winter affects the speed of sound?

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