Discrete and continuous random variables

Today we are going to discuss about the variables in statistics that are defined in two types as random variables and continuous variables and these discrete variables or continuous variable are further divided in discrete random variables and continuous random variables .So in this blog we are mainly focusing on the discrete random variables and continuous random variables. Also see What is a Dependent Variable?
Discrete random variables are categorize as the persons, Objects or events that are define according to the kind of quality their characteristics .It is also define as a random variable that have the finite number of values .It can be explained by an example as if you flip a coin six times then how many chances of occurrence of tail then answer of this question is define through the discrete random variable.
If we talk about the continuous random variable then it is define as the random variable that have the infinite number of values Or a continuous random variable is define as a variable that have the infinite number of possibilities of occurrence of possible numerical values that are usually the measurement of an object .
It will also be explained through the example as speed of a car (miles per hour) first time drive by your house then it will be defined through the variable that have the infinite number of values as a car can going on 23 mile per hour or 67 mile per hour or 34 .0065 mile per hour etc .So the variable that is speed can take infinite number of values for define speed. For more see this
Or if we talk about any experiment that is related to the testing for time taken by that task then for a defined sample space S if there is a random variable x then x (s) represents the height of the person that is less than 5 and greater than 1 then the value for the variable is define as 1 < x (s) < 5 so for that random variable there is infinite number of values so x is define as the continuous random variable

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Standard distributions

Standard Distributions is defined as a value, which is greater than mean of whole distribution in the given data set and we use following formula for evaluation of Standard Distribution, for more information try this
 Standard Distribution = (X – μ) / σ,
Here ‘X’ refers to score value, which is produce by normal distribution, ‘μ’ is the mean value of the original normal distribution and ‘σ’ is the standard deviation of original normal distribution.
This standard distribution of group value sometimes called as a z score distribution like we have a group of students and they all give a math test. Also you can try Z Score Table Normal Distribution
One person get 70 score in that math test with a mean of 50 and standard deviation of 10, then question arises that what is standard distribution of these group of students. So, for standard distribution or z distribution, we use above formula –
Standard Distribution = (X – μ) / σ
= > S = (70 – 50) / 10,
= > S = 20 / 10,
= > S = 2,
So, standard or z distribution of this group of class is 2 and this standard distribution score suggest that there are 2 standard deviation, whose value are greater than mean value of original distribution. Z distribution or standard distributions are called as a normal distribution, if value of original distribution is normal.
Therefore for calculation of standard distribution, we use following steps–
Step 1: First we calculate original score means value of X, like value of X is equals to 60.
Step 2: After evaluation of original score, now we calculate mean of original distribution mean value of μ.
Step 3: After first 2 steps, now calculate standard deviation of original distribution mean value of σ.
Step 4: after first 3 steps, now we apply following formula–
Standard Distribution = (X – μ) / σ,
This formula produces the value of standard distribution.


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Mean

In this blog we are going to discuss about the Mean that is a part of statistics .Sometimes in Statistics Mean is explained by doing the average of the numbers that are given in the data set. If we denote the average as an expression is define as the sum of all the numbers that are divided by the total number of data in data set. If there is number in data set are a₁ , a₂ , a₃ , a₄ then
The average of these number = (a₁ + a₂ + a₃ + a₄) / 4 .
According to CBSE board syllabus basically there are three types of mean that are defined as follows:
(I) arithmetic mean
(II) Geometric mean and
(II) Harmonic mean
Arithmetic mean is one of the type of mean that is normally is called as the average.
We can define it by an example as if there is a range of data in the data set as 40, 20, 35, 27, 13 then the arithmetic mean or average of the data of the data set is define as
Average = (40 + 20 + 35 + 27 +13) / 5 = 155 / 5 = 31.
In other type of mean , geometric mean is define the average of numbers not just by adding that data but also multiplying these numbers .These types of mean (for more on mean visit here) are define in calculation of growth rates , birth rates etc .
It is define through the expression as geometric mean g = (∏ⁿ _i=0 g _i) ^{1 / n}.
We can define it by an example as if number in the data set then g = (2 .3.4 .5) ^{1 / 4} = (120)^{1/ 4.}
We use the harmonic mean when we want to define some relation in the units of a set of numbers.


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Mean

Statistics is the very important branch of mathematics. In statistics we deal with some kind of measures of central tendency such as mean, median and mode. In this blog we are going to discuss the mean of CBSE 10th syllabus. The mean in statistics is the very important and most commonly used central tendency measure. We can calculate the mean for both types of data that are ungrouped and grouped data. Mean of Ungrouped data,
Mean = sum of the observations / number of observations,
-Find the mean of (I) First 10 natural numbers (ii) first 10 whole numbers?
Solution : - (I) first 10 natural number are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
x' = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10
x' = 55 / 10 = 5.5.
(ii) First 10 whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
x' = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 / 10,
x' = 45 / 10 = 4.5.
-Mean of grouped data (without class interval)
Mean for direct method = sum of the values of all observations / number of observations, (visit for more information on mean)
or Ƹ f _i x _I / Ƹ f _I,
Mean for step deviation = x' = a + Æ¸ f _i (x_{1 –} a) / Ƹ f _i = a + Ƹ f _i d _I / Ƹ f _i.
-Mean of grouped data (with class interval),
Mean for direct method = upper class limit + lower class limit / 2,
Mean for step deviation = x' = a + Æ¸ f _i (x_{1 –} a / h) * h / Ƹ f _i = a + h (Ƹ f _i u _I / Ƹ f _I)
By applying the above formula we can also calculate the mean.


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