Page 32 - Basic Statistics

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b. Interquartile range :

Q1 lies in ((n +1) / 4)th observation.
with (n+1)/4 = ( 10 +1)/ 4 = 2.75

So that Q1 = X2 + 0.75 ( X3 - X2 )

Q1 = 7 + 0.75 ( 8-7) = 7.75

Q3 lies in (3(n+1)/4)th observation

with 3(n+1)/4 = 3 ( 10 +1)/ 4 = 8.25

So that Q3 = X8 + 0.25 ( X9 - X8 )

Q3 = 37 + 0.25 ( 40-37) = 37.75

Interquartile range Q3 – Q1 = 37.75 – 7.75 = 30

Range of data after trimmed 25% down and 25% up is 30.

c. Variance :

To calculate the variance, first performed the following preliminary
count :

X = 4 + 7 + . . . + 48 = 230
 i

2
 X = 16 + 49 + 64 + 81 + 484 + 676 + 841 + 1369 + 1600 + 2304
i
= 7484

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