6.1. The Mean http://www.ck12.org
From the calculations, you can say that the team scored a mean of 4 goals per game.
Example 2: The following numbers represent the number of days that 12 students bought lunch in the school
cafeteria over the past two months. What is the mean number of times that each student bought lunch at the cafeteria
during the past two months?
22 , 23 , 23 , 23 , 24 , 24 , 25 , 25 , 26 , 26 , 29 , 30
Solution:The mean is^22 +^23 +^23 +^23 +^24 +^2412 +^25 +^25 +^26 +^26 +^29 +^30
The mean is^30012
The mean is 25
Each student bought lunch an average of 25 times over the past two months.
If we letxrepresent the data numbers andnrepresent the number of numbers, we can write a formula that can be
used to calculate the mean ̄xof the data. The symbol∑means ’the sum of’ and can be used when we write a formula
for calculating the mean.
x ̄=
∑x 1 +x 2 +x 3 +...+xn
nIf we are given a large number of values and if some of them appear more than once, the data is often presented in
a frequency table. This table will consist of two columns. One column will contain the data and the second column
will indicate the how often the data appears. Although the data given in the above problem is not large, some of the
values do appear more than once. Let’s set up a table of values and their respective frequencies as follows:
TABLE6.2:
Number of Lunches Bought Number of Students
22 1
23 3
24 2
25 2
26 2
29 1
30 1Now, the mean can be calculated by multiplying each value by its frequency, adding these results, and then dividing
by the total number of values (the sum of the frequencies). The formula that was written before can now be written
to accommodate the values that appeared more than once.
x ̄=
∑x 1 f 1 +x 2 f 2 +x 3 f 3 +...+xnfn
f 1 +f 2 +f 3 +...+fn