Introduction of solving variables in statistics
Statistics deals with the collection and analysis of numerical data. Statistics is specifically useful in drawing general conclusions about a set of data from a sample of the data. We can say Statistics as descriptive statistics and analytical Statistics, Since it is describing the data and drawing conclusions from the data. Statistics can solves problems related to standard deviation, variance, mean, median, binomial coefficient,standard error parameter, sample size, variability coefficient and populations. Understanding What are Variables? is always challenging for me but thanks to all math help websites to help me out.
Formulae
Formulas for solving variables in statistics:
For solving mean m = `(sum_(k=1)^nxx_(k))/n`
median is the number in the middle
For solving variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)`
For solving standard deviation s =`sqrt(v)`
By solving the above formulas we get the result of the variables. Is this topic what is a rational number hard for you? Watch out for my coming posts.
Examples of Solving Variables in Statistics:
Now let us see some examples of solving variables in statistics.
How to find Mean?
Consider the series : 15, 18, 22, 20
Here n = 4
The sum : `sum_(k=1)^nx_(k)` =15+18+22+20
By substituting K=1 to 4 we get sum as 75
Mean m = `(sum_(k=1)^nxx_(k))/n` = `75/4`
The Mean or Average is 18.75
How to find Median?
Here take the variable median
Here we have to take the series in order and there are two case available
Case 1:
Numbers in the series is odd
9, 3, 44, 17, 15
Line up your numbers(smallest to largest): 3, 9, 15, 17, 44
The number in the middle is 15
Median is 15
Case 2:
Numbers in the series is even
8, 3, 44, 17, 12, 6
Line up your numbers: 3, 6, 8, 12, 17, 44
Having 2 middles numbers
Add 8 and 12 and then divide by 2: 8+12 = 20 ÷ 2 = 10
The Median is 10.
How to find Variance?
Here take a variable variance
44,50,38,96,42,47,40,39,46,50
`(44+50+38+96+42+47+40+39+46+50)/10`
Mean m = 49.2
Variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)` `= 2600.4/(10-1)`
The variance is 289
How to find Standard deviation?
Here take a variable standard deviation
The square root of variance is standard deviation =`sqrt(289)`
The standard deviation is 17
Statistics deals with the collection and analysis of numerical data. Statistics is specifically useful in drawing general conclusions about a set of data from a sample of the data. We can say Statistics as descriptive statistics and analytical Statistics, Since it is describing the data and drawing conclusions from the data. Statistics can solves problems related to standard deviation, variance, mean, median, binomial coefficient,standard error parameter, sample size, variability coefficient and populations. Understanding What are Variables? is always challenging for me but thanks to all math help websites to help me out.
Formulae
Formulas for solving variables in statistics:
For solving mean m = `(sum_(k=1)^nxx_(k))/n`
median is the number in the middle
For solving variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)`
For solving standard deviation s =`sqrt(v)`
By solving the above formulas we get the result of the variables. Is this topic what is a rational number hard for you? Watch out for my coming posts.
Examples of Solving Variables in Statistics:
Now let us see some examples of solving variables in statistics.
How to find Mean?
Consider the series : 15, 18, 22, 20
Here n = 4
The sum : `sum_(k=1)^nx_(k)` =15+18+22+20
By substituting K=1 to 4 we get sum as 75
Mean m = `(sum_(k=1)^nxx_(k))/n` = `75/4`
The Mean or Average is 18.75
How to find Median?
Here take the variable median
Here we have to take the series in order and there are two case available
Case 1:
Numbers in the series is odd
9, 3, 44, 17, 15
Line up your numbers(smallest to largest): 3, 9, 15, 17, 44
The number in the middle is 15
Median is 15
Case 2:
Numbers in the series is even
8, 3, 44, 17, 12, 6
Line up your numbers: 3, 6, 8, 12, 17, 44
Having 2 middles numbers
Add 8 and 12 and then divide by 2: 8+12 = 20 ÷ 2 = 10
The Median is 10.
How to find Variance?
Here take a variable variance
44,50,38,96,42,47,40,39,46,50
`(44+50+38+96+42+47+40+39+46+50)/10`
Mean m = 49.2
Variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)` `= 2600.4/(10-1)`
The variance is 289
How to find Standard deviation?
Here take a variable standard deviation
The square root of variance is standard deviation =`sqrt(289)`
The standard deviation is 17
