Statistical Mean

In Mathematics in the branch of Statistics, the expression for the mathematical mean of a statistical distribution is the mathematical average of all the terms in the data. To calculate this, we add up the values of the terms given and divide the sum by the number of terms in the data. This expression is also called the
Arithmetic Mean.


While solving word problems, we come across problems like, Scott drove from Bloomington to Chicago driving at 6 different speeds on the same freeway; 63mph, 72mph,42mph, 53mph, 67mph, 59mph. how do we calculate the Mean driving speed? It is very simple, we know that Arithmetic Mean is the regular average, so we just add up the different speeds and divide the sum by the number of different speeds given. Let us see the steps involved,
 The Mean driving speed = total sum of driving speeds /total number of speeds
Total sum of driving speeds = 63+72+56+68+59+48 =366
Total number of different speeds = 6
So, Mean driving speed = 366/6 = 61mph


Definition of Mean Or Definition Mean
To define mean, let us first learn about average in mathematics. Given a data of values, the average would be the total sum of the values divided by the total number of values given in the data. This in statistics is called the Mean or Arithmetic Mean. So, Definition of Mean is the average of the values given in a data.
Mean Formula
The Arithmetic Mean is the regular average of the values given in a data.
So, Mean Formula = Total sum of the values/Total number of values

Example: A student took 8 tests in a subject in one marking period. What is the mean test score?
                88, 75, 82, 90, 86, 78, 94, 87
Solution:  Number of tests = 8
  Sum of the marks =88+75+82+90+86+78+94+87= 680
   Mean = sum of the marks/number of tests
= 680/8 = 85

Sample Mean Formula
The sample mean in statistics, branch of Mathematics is the sum of all observed outcomes from the sample divided by the total number of events (Arithmetic Average). It is denoted by the symbol x with a (bar) above it. The Sample Mean formula is as follows:
X (bar) = (1/n) (x1+x2+x3………xn)

Example: At a car rental shop data was collected on the number of rentals on each of 10 consecutive Saturdays.  50, 44, 96, 38, 39, 40,50,46,47,42. Find the Sample Mean of the rentals.
Solution:   n = 10
Sigma(rentals) = 50+44+96+38+39+40+50+46+47+42=492
X(bar) =sigma(rentals)/n
            = 492/10
            = 49.2 is the Sample mean