Page 34 - Basic Statistics

29

The formula for calculating the variance of the data grouped is

p   p  2 



 f i ( X i ) −   f i X i  n / 
2


i= 1  i  = 1  


2
S =
n − 1

The standard deviation for the grouped data is the square root of the
2
variance for the grouped data, ie S = S

Worked Example 2.6 :

Calculate the interquartile range, variance, and standard deviation for

the grouped data in Table 2. 2.

Table 2.2 The grouped data

Frequencies Midpoint Cumulative
2
Classes ( fi ) ( xi ) fi. xi fi . (xi) Frequencies
( Fi )

0 - < 5 2 2,5 5 12,50 2

5 - < 10 5 7,5 37,5 281,25 7
10 - < 15 8 12,5 100,0 1250,00 15

15 - < 20 6 17,5 105,0 1837,50 21

20 - < 25 4 22,5 90,0 2025,00 25
25 - < 45 1 35,0 35,0 1225,00 26

Total n = 26 372,5 6631,25

Worked solution :

Q1 lies in the (n/4)th observation, where n / 4 = 26/4 = 6.5 . In the

column of cumulative frequencies, the 6.5th observation contained in the class

“ 5 - <10 “. thus,

~~* CHAPTER 2 NUMERICAL MEASURES TO SUMMARIZE DATA *~~