Introduction to Empirical formula Statistics:
The science of making effective use of numerical data values related to groups of individuals or experiments is called Statistics. Empirical Statistics denotes the information gained by means of observation, experience, or experiment. Empirical Statistics fully depends on the evidence or consequences that are observable by the senses.It refers to the use of working hypothesis that are tested using observation or experiment.
Formula for Finding Empirical Statistics:
The Formula to find the Empirical Statistics is listed as below
Formula for Mean (or) Expected value:
μ = E[x] = np
Formula for Standard deviation:
σ =`sqrt(npq)`
Formula for Variance:
E[x^2] = σ^2 = npq
Example Problems for Solving Empirical Formula Statistics:
Example 1:
A coin is flipped for 68 times. Determine the mean, variance and standard deviation with the help of Binomial distributions.
Solution:
Let coin flipped for 68 times. So n =68.
If we flip a coin means, possibility of getting head is p =`(1)/(2)`
Probability of achieving tails is represented by q.
q = 1 – p [p + q = 1]
q = 1 –`(1)/(2)`
q =.`(1)/(2)`
Mean:
μ = E[x] = np
=` 68(1/2)`
μ = E[x] =34
Variance:
E[x2] = σ^2 = npq
=`68(1/2)(1/2)`
E[x2] = σ^2 = 17
Standard deviation:
σ =`sqrt(npq)`
σ = `sqrt(68*(1/2)*(1/2))`
= `sqrt(17)`
σ = 4.12
Example2:
A coin is tossed for 48 times. Find the mean of tails, variance and the standard deviation with the help of Binomial distribution. Please express your views of this topic horizontal asymptotes by commenting on blog.
Solution:
Let coin tossed for 48 times. So n = 48.
If we toss a coin means, probability of getting tail is p = `(1)/(2)`
Probability of getting head is represented by q.
q = 1 – p [p + q = 1]
q = 1 –`(1)/(2)`
q = `(1)/(2)`
Mean:
μ = E[x] = np
= `48(1/2)`
μ = E[x] = 24
Variance:
E[x2] = σ^2 = npq
= `48(1/2)(1/2)`
= 48
E[x2] = σ^2 =12
Standard deviation:
σ =`sqrt(npq)`
σ = `sqrt(48*(1/2)*(1/2))`
=` sqrt(12)`
σ = 3.46
The science of making effective use of numerical data values related to groups of individuals or experiments is called Statistics. Empirical Statistics denotes the information gained by means of observation, experience, or experiment. Empirical Statistics fully depends on the evidence or consequences that are observable by the senses.It refers to the use of working hypothesis that are tested using observation or experiment.
Formula for Finding Empirical Statistics:
The Formula to find the Empirical Statistics is listed as below
Formula for Mean (or) Expected value:
μ = E[x] = np
Formula for Standard deviation:
σ =`sqrt(npq)`
Formula for Variance:
E[x^2] = σ^2 = npq
Example Problems for Solving Empirical Formula Statistics:
Example 1:
A coin is flipped for 68 times. Determine the mean, variance and standard deviation with the help of Binomial distributions.
Solution:
Let coin flipped for 68 times. So n =68.
If we flip a coin means, possibility of getting head is p =`(1)/(2)`
Probability of achieving tails is represented by q.
q = 1 – p [p + q = 1]
q = 1 –`(1)/(2)`
q =.`(1)/(2)`
Mean:
μ = E[x] = np
=` 68(1/2)`
μ = E[x] =34
Variance:
E[x2] = σ^2 = npq
=`68(1/2)(1/2)`
E[x2] = σ^2 = 17
Standard deviation:
σ =`sqrt(npq)`
σ = `sqrt(68*(1/2)*(1/2))`
= `sqrt(17)`
σ = 4.12
Example2:
A coin is tossed for 48 times. Find the mean of tails, variance and the standard deviation with the help of Binomial distribution. Please express your views of this topic horizontal asymptotes by commenting on blog.
Solution:
Let coin tossed for 48 times. So n = 48.
If we toss a coin means, probability of getting tail is p = `(1)/(2)`
Probability of getting head is represented by q.
q = 1 – p [p + q = 1]
q = 1 –`(1)/(2)`
q = `(1)/(2)`
Mean:
μ = E[x] = np
= `48(1/2)`
μ = E[x] = 24
Variance:
E[x2] = σ^2 = npq
= `48(1/2)(1/2)`
= 48
E[x2] = σ^2 =12
Standard deviation:
σ =`sqrt(npq)`
σ = `sqrt(48*(1/2)*(1/2))`
=` sqrt(12)`
σ = 3.46
No comments:
Post a Comment