1.
2.

o The mean may often be confused with the median , mode or range. The mean is the arithmetic average of a set of values, or distribution.
Example: The following table gives the frequency distribution of the number of orders received each day during the past 50 days at the office of a mail-order company. Calculate the mean.
Solution:
Number of order
10 – 12
13 – 15
16 – 18
19 – 21 f
4
12
20
14
n = 50 x
11
14
17
20
Number of order
10 – 12
13 – 15
16 – 18
19 – 21 fx
44
168
340
280
= 832 f
4
12
20
14
n = 50
X is the midpoint of the class. It is adding the class limits and divide by 2.
x =
 n fx 832
=
50
= 16.64

o a median is described as the numerical value separating the higher half of a sample, a population , or a probability distribution ,
Step 1:
Step 2:
Construct the cumulative frequency distribution.
Decide the class that contain the median.
Class Median is the first class with
Median = L m
+ 


 n
- F
2 f m



 i the value of cumulative frequency equal at least n/2.
Step 3: Find the median by using the following formula:
Where: n = the total frequency
F = the cumulative frequency before class median f m
= the frequency of the class median i = the class width
L m
= the lower boundary of the class median

Example: Based on the grouped data below, find the median:
Time to travel to work
1 – 10
11 – 20
21 – 30
31 – 40
41 – 50
Frequency
8
14
12
9
7
Solution:
1 st Step: Construct the cumulative frequency distribution
Time to travel to work
1 – 10
11 – 20
21 – 30
31 – 40
41 – 50
Frequency
8
14
12
9
7
Cumulative
Frequency
8
22
34
43
50 n

50

25
2 2
So, F = 22, f m
= 12, class median is the 3 rd class
L m
= 20.5 and i = 10

Therefore,
Median = L m
 


 n
- F
2 f m



 i
=
12

10
= 24
Thus, 25 persons take less than 24 minutes to travel to work and another 25 persons take more than 24 minutes to travel to work.

Quartiles o a quartile is one of three points that divide a data set into four equal groups, each representing a fourth of the distributed sampled population.
Using the same method of calculation as in the Median, we can get Q
1 and Q
3 equation as follows:
Q
1

L +
1



 n
- F
4 f
Q
1



 i
Q

L +
3 Q
3





3 n
- F
4 f
Q
3




 i
Example: Based on the grouped data below, find the Interquartile Range
Time to travel to work
1 – 10
11 – 20
21 – 30
31 – 40
41 – 50
Frequency
8
14
12
9
7

Solution:
1 st Step: Construct the cumulative frequency distribution
Time to travel to work
Frequency
1 – 10
11 – 20
21 – 30
31 – 40
8
14
12
9
41 – 50 7
2 nd Step: Determine the Q
1 and Q
3
Class Q
1
 n

50

4 4
Class Q
1 is the 2
Therefore, nd class
Cumulative
Frequency
8
22
34
43
50
Q
1

L
Q
1
 


 n
- F
4 f
Q
1



 i

10 5
 

14

10

Class Q
3

3n

4 4

Class Q
3 is the 4
Therefore, th class
Q
3

L
Q
3
 



 n
- F
4 f
Q
3




 i

30 5
9

34 3889
10
Interquartile Range
IQR = Q
3
– Q
1
IQR = Q
3
– Q
1 calculate the IQ
IQR = Q
3
– Q
1
= 34.3889 – 13.7143 = 20.6746

Mode
•Mode is the value that has the highest frequency in a data set.
•For grouped data, class mode (or, modal class) is the class with the highest frequency.
•To find mode for grouped data, use the following formula:
Mode = L mo
+


Δ
1
2

 i
Where: i is the class width

1 is the difference between the frequency of class mode and the frequency of the class after the class mode

2 is the difference between the frequency of class mode and the frequency of the class before the class mode
L mo is the lower boundary of class mode

Example: Based on the grouped data below, find the mode
Time to travel to work Frequency
1 – 10
11 – 20
21 – 30
31 – 40
41 – 50
8
14
12
9
7
Solution:
Based on the table,
L mo
= 10.5, = (14 – 8) = 6,
1

2
= (14 – 12) = 2 and i = 10
Mode = 10 5


6
6

2 
10

.

Population Variance:
Variance for sample data:
 fx 2 
N
  fx

2
N s 2 
 fx 2 
  fx

2 n n

1
Standard Deviation:
Population:
Sample:

2  s 2
 s 2

2 o the variance is used as a measure of how far a set of numbers are spread out from each other.
o Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory . It shows how much variation or " dispersion " there is from the average ( mean , or expected value).

Example: Find the variance and standard deviation for the following data:
No. of order
10 – 12
13 – 15
16 – 18
19 – 21 f
4
12
20
14
Total n = 50
Solution:
No. of order f
10 – 12
13 – 15
16 – 18
19 – 21
4
12
20
14
Total n = 50 x
11
14
17
20 fx
44
168
340
280
832 fx 2
484
2352
5780
5600
14216

s


 fx 2
14216 n


  n

1

832

2
50 fx

2

Standard Deviation, s
 s
2 
7 .
5820

2 .
75
Thus, the standard deviation of the number of orders received at the office of this mail-order company during the past 50 days is 2.75.