Statistics And Probability
Statistics analysis depends on the characteristics of the particular probability distributions, and the two topics are often studied together to some extent. However, probability theory contain much that is of mostly mathematical interest and not directly relevant to statistics. Probability theory is the branch of the mathematics concerned with analysis of random phenomena. The central objects of the probability theory are random variables, stochastic processes, and events mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion (Source. Wikipedia).
Statistics is the 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.
Various probability distributions are not a particular distribution, except are in detail a relations of distributions. This is suitable to the distribution have one or extra shape parameters.Shape parameters allow a distribution to get on a multiplicity of shapes, depending on the value of the shape parameter. These distributions are mainly valuable in modeling applications because they are flexible sufficient to model a variety of data sets.
In this article we are going to solve some problems for understanding statistics and probability.
Statistics Example problems - understanding statistics and Probability:
Here we are going to see some example problems for understanding statistics.
Example 1:
The marks obtained by 10 students in the class test out of 100 marks are 62, 49, 71, 75, 33, 41, 100, 88, 50, and 31. Calculate mean
Solution:
mean = X = x / n =[ 62+ 49+ 71+ 75+ 33+ 41+ 100+ 88+ 50 +31] / 10
= 600/10 = 60
The mean is 60
Example 2:
Establish the median for the following listing of values8, 5 4, 7, 2, and 9
Solution:
Find the Median of: 8, 5 4, 7, 2, and 9(Even amount of numbers)
Line up your numbers: 2, 5 4, 6, 7, and (smallest to largest)
Add the 2 middles numbers and divide by 2:
= (4 + 6) / 2
= 10 / 2
= 5
The Median is 5.
Example 3:
Establish the median for the following listing of values 8, 8, 8, 9, 9, 9, 11 and 12
Solution:
Find the Median of: 8, 8, 8, 9, 9, 9, 11 and 12(Even amount of numbers)
Line up your numbers: 8, 8, 8, 9, 9, 9, 10 and 12(smallest to largest)
Add the 2 middles numbers and divide by 2:
= (9 + 9) / 2
= 18 / 2
= 9
The Median is 9
Probability Example problem - understanding statistics and probability:
Here we are going to see an example problem for understanding probability.
Example 1
Two coins are tossed simultaneously, what is probability of the getting
(i) Exactly one head (ii) at least one head (iii) almost one head.
Solution:
The sample space is S = {HH, HT, TH, TT}, n(S) = 4
Let A be the event of getting one head, B be the event of getting at least one head and C be the event of getting almost one head.
"' A = {HT, TH}, n(A) = 2
B = {HT, TH, HH}, n(B) = 3
C = {HT, TH, TT}, n(C) = 3
(i) P(A) =n(A) / n(S) =2/4 =1/ 2
(ii) P(B) =n(B) / n(S) = 3 / 4
(iii) P(C) =n(C) / n(S) = 3 / 4
Statistics is the 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.
Various probability distributions are not a particular distribution, except are in detail a relations of distributions. This is suitable to the distribution have one or extra shape parameters.Shape parameters allow a distribution to get on a multiplicity of shapes, depending on the value of the shape parameter. These distributions are mainly valuable in modeling applications because they are flexible sufficient to model a variety of data sets.
In this article we are going to solve some problems for understanding statistics and probability.
Statistics Example problems - understanding statistics and Probability:
Here we are going to see some example problems for understanding statistics.
Example 1:
The marks obtained by 10 students in the class test out of 100 marks are 62, 49, 71, 75, 33, 41, 100, 88, 50, and 31. Calculate mean
Solution:
mean = X = x / n =[ 62+ 49+ 71+ 75+ 33+ 41+ 100+ 88+ 50 +31] / 10
= 600/10 = 60
The mean is 60
Example 2:
Establish the median for the following listing of values8, 5 4, 7, 2, and 9
Solution:
Find the Median of: 8, 5 4, 7, 2, and 9(Even amount of numbers)
Line up your numbers: 2, 5 4, 6, 7, and (smallest to largest)
Add the 2 middles numbers and divide by 2:
= (4 + 6) / 2
= 10 / 2
= 5
The Median is 5.
Example 3:
Establish the median for the following listing of values 8, 8, 8, 9, 9, 9, 11 and 12
Solution:
Find the Median of: 8, 8, 8, 9, 9, 9, 11 and 12(Even amount of numbers)
Line up your numbers: 8, 8, 8, 9, 9, 9, 10 and 12(smallest to largest)
Add the 2 middles numbers and divide by 2:
= (9 + 9) / 2
= 18 / 2
= 9
The Median is 9
Probability Example problem - understanding statistics and probability:
Here we are going to see an example problem for understanding probability.
Example 1
Two coins are tossed simultaneously, what is probability of the getting
(i) Exactly one head (ii) at least one head (iii) almost one head.
Solution:
The sample space is S = {HH, HT, TH, TT}, n(S) = 4
Let A be the event of getting one head, B be the event of getting at least one head and C be the event of getting almost one head.
"' A = {HT, TH}, n(A) = 2
B = {HT, TH, HH}, n(B) = 3
C = {HT, TH, TT}, n(C) = 3
(i) P(A) =n(A) / n(S) =2/4 =1/ 2
(ii) P(B) =n(B) / n(S) = 3 / 4
(iii) P(C) =n(C) / n(S) = 3 / 4
