1. FORMULA FOR MEASURES OF VARIATION:
S2= nΣfixi
2-(Σfixi)2
n(n-1)
where:
fi= the frequency of class interval i.
xi= the midpoint of class interval i.
Σfixi= the sum of the products of the
frequency and midpoint of the class
interval i.
2. THE QUARTILE DEVIATION:
The quartile deviation is used when the
median is used as an average; when the
data depart noticeably from the normal. It is
used for ordinal data.
The quartile deviation, Q, is frequently
called the semi-interquartile range. It is half
of the distance between two quartile points,
Q1, and Q3.
3. FORMULA FOR QUARTILE DEVIATION:
Q= Q3-Q1
2
Q1= L1+ (n/4 –cf)c
f
Q3= L1+(3n/4 –cf)c
f
4. EXAMPLE:
Given the following data,
Class interval f
36- 40 2
31- 35 8
26- 30 12
21- 25 18
16- 20 10
5. Complete the table and find the mean, median, mode, variance,
sd, Q1, Q2, and Q.
Class
interval
f Class
boundaries
Midpoint
(x)
u fu fu2 fixi fx2 cf
36- 40 2 35.5- 40.5 38 2 4 8 76 2888 50
31- 35 8 30.5- 35.5 33 1 8 8 264 8712 48
26- 30 12 25.5- 30.5 28 0 0 0 336 9408 40
21- 25 18 20.5- 25.5 23 -1 -18 18 414 9522 28
16- 20 10 15.5- 20.5 18 -2 -20 4 180 3240 10
