Monday, 25th October 2010
Date : Sunday, 24th Oct 2010 From 8.00AM to 10.00AM
4.1 Measurements of Central Tendency
Consists of
1) Mean
2) Median ( also known as second quartile ) Q2
3) Mode
4) First Quartile (Q1)
5) Third Quartile (Q3)
4.2. The Mean
Mean for ungrouped data
Mean = X1 + X2 + ...+ Xn
--------------------
n
Example
(a) Mean For 53 32 61 27 39 44 49 57
Mean = 53 + 32 + 61 + 27 + 39 + 44 + 49 + 57
-----------------------------------------
8
= 362
------
8
= 45.25
(b) Mean for repeated numbers
Mean = F1X1 + F2X2 + .....FnXn
-----------------------------
F1 + F2 + ... + Fn
Example
Score Number of Participants Fx
0 4 0
1 6 6
2 3 6
3 7 21
4 5 20
25 53
Mean = 53
----- = 2.12
25
(c) Mean For Grouped Data
Example : Calculate The Mean of the Height of the Students
Height Frequency
100 - 104 3
105 - 109 2
110 - 114 4
115 - 119 1
Mean = Sum (Mid-Point X Frequency )
--------------------------------
Total Frequency
Mid-Point = 1/2 (Upper Boundary + Lower Boundary ) or
= 1/2 ( Upper Limit + Lower Limit )
Height Frequency Mid-Point
100 - 104 3 1/2 (100 + 104) = 102
105 - 109 2 1/2 (105 + 109 ) = 107
110 - 114 4 1/2 ( 110 + 114 ) = 112
115 - 119 1 1/2 ( 115 + 119) = 117
------------
10
Mean = (102X3) + (107 X 2 ) + ( 112 x 4) + (117 x 1 )
------------------------------------------------
10
------
10
= 108.5
(c) Mean of combined sets of data
Mean = H1 + H2
-----------
n1 + n2
Or Mean = n1m1 + n2m2
----------------
n1 + n2
Example :
The mean age for 8 children is 11 years old while the mean age for 7 adults is 35 years old. What is the overall age for the 15 persons
Mean = (8) (11) + (7) ( 35 )
--------------------------
15
= 22.2 Years Old
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