Example Find the mean of the following 50 observations.

19, 19, 20, 20, 20, 19, 20, 18, 21, 19,

20, 20, 19, 19, 20, 19, 21, 19, 19, 21,

18, 20, 18, 18, 17, 20, 20, 22, 20, 20,

20, 20, 20, 21, 20, 17, 23, 18, 17, 21,

20, 21, 20, 20, 20, 18, 21, 19, 20, 19

Solution: We may tabulate the given observations as follows.

The arithmetic mean is

Example Eight coins were tossed together and the number of times they fell on the side of heads was observed. The activity was performed 256 times and the frequency obtained for different values of x, (the number of times it fell on heads) is shown in the following table. Calculate then mean by:

i) Direct method ii) Short-cut method

x :    0    1      2      3     4     5      6       7     8   

f :     1    9     26   59    72    52    29    7     1

Solution:

Index

4.1 Introduction
4.2 Arithmetic Mean
4.3 Properties of Arithmetic Mean
4.4 Median
4.5 Mode
4.6 Empirical relation between mean, median & mode

Chapter 5