Definition of mean difference:
Mean difference is defined as the measure of the difference between the given data set and mean value.For finding the mean difference first have to find the mean,
Formula for finding the mean,
`barx = (sumx) / n`
Using the mean value mean difference have to be found Formula for mean difference is,
`x-barx`
Definition of Standard Deviation:
Standard Deviation is the determination of describing the variability and spread of the Data set in the given total values in data set. It is used to take the measurement for the average of numbers in the given Data set. Standard Deviation given by the square root for the summation of the total squared mean difference and it is divided by the total number of values minus one.
Formula for standard deviation,
S =` sqrt(((sum(x - barx))) / (n-1))`
Steps for calculating mean difference and standard deviation:
Get the mean for the given n numbers in the given data set.
Get mean difference of each given numbers in the Data set from the mean.
Take Square for all each deviations. It is called as the squared mean deviation.
Calculate the summation for standard mean deviations.
Now apply the Standard Deviation formula for finding the Standard deviation form the mean.
Mean difference standard Deviation - Example Problems:
Mean difference standard Deviation - Problem1:
Calculate the mean difference and standard deviation in the following data set.56, 52, 54, 57, 58.
Solution:
Mean:
Formula For finding the mean.
`barx = (sum x) / n`
` barx = (56+ 52+ 54+ 57+ 58) / 5`
`barx = 277 / 5`
`barx = 55.4`
Mean difference is given below
x `(x - barx)`
56 56 - 55.4 = 0.6
52 52 - 55.4 = -3.4
54 54 - 55.4 = -1.4
57 57 - 55.4 = 1.6
58 58 - 55.4 = 2.6
Standard Deviation: Standard Deviation is given by,
S =` sqrt(((sum(x - barx))) / (n-1))`
S = `sqrt(((0.6)^2+(-3.4)^2+(-1.4)^2+(1.6)^2+(2.6)^2 )/ (5-1))`
S = `sqrt(23.2 / 4)`
S = `sqrt(5.8)`
S = 2.40831892
Mean difference standard Deviation - Problem 2:
Calculate the mean difference and standard Deviation for the given data set. 23, 25, 24, 26.
Mean:
Formula For finding the mean.
`barx = (sum x) / n`
` barx = (23+ 25+ 24+ 26) /4`
`barx = 98 / 4`
`barx = 24.5`
Mean difference is given below
x `(x-barx)`
23 23 - 24.5 = 0.5
25 25 - 24.5 = - 0.5
24 24 - 24.5 = 1.5
26 26 - 24.5 = - 1.5
Standard Deviation: Standard Deviation is given by,
S =` sqrt(((sum(x - barx))) / (n-1))`
S = `sqrt(((0.5)^2+(-0.5)^2+(1.5)^2+(-1.5)^2)/ (4-1))`
S = `sqrt(5 /3)`
S = `sqrt(1.66666667)`
S = 1.29099445
No comments:
Post a Comment