Measures of Central Tendency for Grouped Data
 Mean
a. Long Method
x
b. Short Method or Assumed Mean Method
 fx
n
x  x0 
 fd
i
n
where f = frequency
x = class mark
n = number of samples
x0 = assumed mean
d = class deviation
i = class size
 Median
a. Median from below
  cf  
%
x  LB  
 i
 f 
n
2
b. Median from above
 n  cf  
%
x  UB   2
 i
 f 
where LB = lower boundary of the median class
UB = upper boundary of the median class
cf< = sum of the frequencies below the median class
cf> = sum of the frequencies above the median class
 Mode
 d1 
x̂  LB  
 i
 d1  d2 
where LB = lower boundary of the modal class
d1 = difference between the frequencies of the modal class and the lower class
d2 = difference between the frequencies of the modal class and the higher class
Problems
Find the mean, median and mode of the following frequency distribution.
1.
Class Interval
7–9
10 – 12
13 – 15
16 – 18
19 – 21
f
2
10
12
9
7
n=