Difference of Two Means

Mean is defined as the average for the total number of values given in the data set. It is the sum made between the given data set and it is divided it by the total number of values given in the data set. Tis is called as the mean for the given data set. This can also be called as arithametic mean or sample mean. The difference between two mean is nothing but the taking difference for the two sets of data (mu_1 , mu_2 ) and calculating the difference for that mean.

Difference of two mean  = mu_1 - mu_2

Where as

mu_1 is the mean value for the first set of data.
mu_2 is the mean value for the second set of data.

Mean is calculated by the way,
mu = (Sum of all the values given) / (Total Number of values)


Steps for calculating the difference of two means:

Get the two sets of data for calculating the mean.
Measure the sum for the first set of data and divide it by the total number of data's given. This is the mean for the first data set
Measure the sum for the second set of data and divide it by the total number of data's given. This is the mean for the second data set.
Now measure the difference of the two means from the mean calculated.



Difference of two means - Example Problems:

Difference of two means - Problem 1:

Find the difference of two means from the given two data set. 2, 3, 4, 5, 6, 7 and 1, 2, 3, 4, 5, 6

Solution:

Mean for the first set of the data given

mu_1 = (2+3+4+5+6+7) / 6

= 27 / 6

=  4.5

Mean for the second set of the data given

mu_2 = (1+2+3+4+5+6) / 6

=  21 / 6

mu_2    = 3.5

Difference of the two means is given by

Difference of two mean = mu_1 - mu_2

= 4.5 - 3.5

Difference of two mean = 1

Difference of two means - Problem 2:

Find the difference of two means from the given two data set. 24, 23, 24, 25, 26, 27 and 11, 13, 13, 14, 15, 16

Solution:

Mean for the first set of the data given

mu_1 = (24+23+24+25+26+27) / 6

= 149 / 6

=  24.8333333

Mean for the second set of the data given

mu_2 = (11+13+13+14+15+16) / 6

=  82 / 6

mu_2    = 13.6666667

Algebra is widely used in day to day activities watch out for my forthcoming posts on icse syllabus and cbse books. I am sure they will be helpful.

Difference of the two means is given by

Difference of two mean = mu_1 - mu_2

= 24.8333333 - 13.6666667

Difference of two mean  = 11.1666666