Page 35 - Basic Statistics

30

f c
Q1 = L q 1 + f q 1 1 . W
q
1

 2 - 5 . 6 
Q1 = 5 +  5 .  = 5 + 4.5 = 9.5
 5 

Q3 lies in the (3n/4)th observation, where 3n /4 = 3(26)/4 = 19.5 . In the

column of cumulative frequencies, the 19.5th observation contained in the class

‘ 15 - < 20 ’. thus,

f c
Q3 = L q 3 + f q 3 3 . W q 3



Q3 =15 +  19 - 5 . 15  5 .  = 15 +  4.5  5 = 18.75

 6   6 

Interquartile range = Q3 – Q1 = 18.75 – 9.5 = 9.25

Variance :

p    p  2 


2
 f i ( X i ) −   f i X i  n / 


i= 1   i  = 1  

2
S =
n − 1
6631 . 25 - ((372.5) 2 / 26 )
=
26 − 1
= 51.7789

Standard deviation:

The standard deviation for the grouped data is the square root of the

variance for the grouped data, ie S = 51 . 7789 = 7.1958

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