The document provides formulas for calculating measures of variation such as variance, standard deviation, and quartile deviation. It includes an example using data on class intervals and frequencies to calculate the mean, median, mode, variance, standard deviation, first quartile, third quartile, and quartile deviation.

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

6. MEAN= Σfi Xi = 1270 = 25.4
n 50
MEDIAN= L1+ (n/2-cf)c = 20.5+ 50/2 -10 (5) = 24.67
f 18
MODE= L1+ (d1)c = 20.5+ _8_ (5)= 23.36
d1+d2 8+6
2-(Σfixi)2 = 50(33770)-(1270) 2
n(n-1) 50(49)
VARIANCE= nΣfixi
= 1688500-1612900
2450
= 75600 = 30.86
2450

7. S= ퟑퟎ. ퟖퟔ
QUARTILE DEVIATION
Q1= L1+ (n/4 –cf)c = 20.5 + (50/4 – 10)5
f 18
= 20.5 + 0.69= 21.19
Q3= L1+(3n/4 –cf)c = 25.5 + (3/4 (50) – 28) 5
f 12
= 25.5 + 3. 96 = 29. 46
Q= Q3-Q1 = 29. 46- 21. 19 = 4. 135
2 2