You have learned in previous topics that the data collected is in form of raw data. If the data is very large the user cannot get much information from it. For this reason, the data are grouped together to give us relevant information.

Sometimes we are interested in describing the data arithmetically so that we can draw certain conclusions from it, that is, the user may want to get certain numbers to represent certain features of data. These are called Arithmetical Descriptors of data or Measures of Location or Central Tendency. These measures are the mean, median, and mode obtained from the data.

Mean

A mean is a measure of central tendency and is the same as the arithmetic average. Recall batting averages, goal averages, rainfall, etc.

FOR RAW DATA MEAN =

MEAN OF n NUMBERS =

Example : 10

The heights of 5 boys in a group are 152cm, 170cm, 156cm, 164cm, and 158cm. Find the mean height.

Solution:

Sum of observations

        =152 + 170 + 156 + 164 + 158

        = 800cm

Number of observations = 5

Mean =

        = 800/5

        = 160cm.

The Mean height is 160cm.

Example : 11

Find the mean of the following numbers.

25, 27, 19, 29, 21, 23, 25, 30, 28, 20

Solution:

Sum of Numbers      = 25 + 27 + 19 + 29 + 21 + 23 + 25 + 30 + 28 + 20

                                = 247

Number of Addends = 10.

Mean =

= 247/10

= 24.7

The mean of the given numbers is 24.7.

Try this problem

Find the mean of 11, 13, 17, 19, 23

Answer: To find mean of

11, 13, 17, 19, 23

n = number of observations = 5

Mean =

Mean = 16.6.