1.  ∑-denotes addition of a set of values
 X-the variable used to represent the
individual data values
 N-the number of values in a population
 n-the number of values in a sample

2.  Population
--complete collection of all elements to be
studied
 Sample
--subcollection of members selected from
a population

3. Population Sample Weighted
1
N
i
i
x
N
 


1
i
i
n
x
x
n


 1
1
iWi
i
i
i
k
x
x
k
w






4.  =lower case Greek mu
=denotes all values of the population
 =pronounced as x- bar
=denotes all the data values from a
sample of larger population

x

5. PopulationSample
 If N is odd
 If N is even
 If n is odd
 If n is even
1
( )2
N
x 

( 1)2 2
1
[ ]
2
N N
x x  
( 1)2 2
1
[ ]
2
n n
x x x  
1
( )2
n
x x 


6.  Observations: Number of hours spent by
the students in studying 2
3
3
3
6
2
3
2
4
2.5

7. 10
1
1 2 3 4. .... 10
10
30.5
10
3.05
xi
x
n
x x x x x

    





8. ( 1)2 2
1
[ ]
2
1 10 10
[ ( 1)]
2 2 2
1
( 5 6)
2
1
(3 3)
2
3
n n
x x x
x x
x x
 
  
 
 



9.  3
 -- the highest frequency

11. Observations=60
87, 85, 79, 75, 81, 88, 92, 86, 77, 72, 75, 77, 81, 80, 77,
73, 69, 71, 76, 79, 83, 81, 78, 75, 68, 67, 71, 73, 78, 75,
84, 81, 79, 82, 87, 89, 85, 81, 79, 77, 81, 78, 74, 76, 82,
85, 86, 81, 72, 69, 65, 71, 73, 78, 81, 77, 74, 77, 72, 68
μ = (87+85+ 79 +….+72+68)/60
= 4751/60
= 79.183

12. We now find the median of the population of temperature readings
87, 85, 79, 75, 81, 88, 92, 86, 77, 72, 75, 77, 81, 80, 77,
73, 69, 71, 76, 79, 83, 81, 78, 75, 68, 67, 71, 73, 78, 75,
84, 81, 79, 82, 87, 89, 85, 81, 79, 77, 81, 78, 74, 76, 82,
85, 86, 81, 72, 69, 65, 71, 73, 78, 81, 77, 74, 77, 72, 68
Arrange these 60 measurements in ascending order
65, 67, 68, 68, 69, 69, 71, 71, 71, 72, 72, 72, 73, 73, 73, 74, 74, 75,
75, 75, 75, 76, 76, 77, 77, 77, 77, 77, 77, 78, 78, 78, 78, 79, 79, 79,
79, 80, 81, 81, 81, 81, 81, 81, 81, 81, 82, 82, 83, 84, 85, 85, 85, 86,
86, 87, 87, 88, 89, 92
Since N/2 = 30 and both the 30th and 31st values in the list are the same,
we obtain median = 78

13. One further parameter of a population that may give some indication of
central tendency of the data is the mode
Define: mode = most frequently occurring value in the
population
From the previous data we see:
65, 67, 68, 68, 69, 69, 71, 71, 71, 72, 72, 72, 73, 73, 73, 74,
74, 75, 75, 75, 75, 76, 76, 77, 77, 77, 77, 77, 77, 78, 78, 78,
78, 79, 79, 79, 79, 80, 81, 81, 81, 81, 81, 81, 81, 81, 82, 82,
83, 84, 85, 85, 85, 86, 86, 87, 87, 88, 89, 92
That the value 81 occurs 8 times mode = 81
Note! If two different values were to occur most frequently, the distribution
would be bimodal. A distribution may be multi-modal.

14. Grade
99
92
90
91
88
85
82
Units
3
2
6
1
4
3
3

15. 1
1
iWi
i
i
i
k
x
x
k
w





99(3) 92(2) 90(6) 91(6) 88(4) 85(3) 82(3)
3 2 6 1 4 3 3
89.32GPA
     

     
