Question

The numbers of passengers on 9 airline flights were 22, 33, 21, 28, 22, 31, 44, 50, and 19. The standard deviation of these 9 numbers is approximately equal to 10.22. (a) Find the mean, median, mode, range, and interquartile range of the 9 numbers. (b) If each flight had had 3 times as many passengers, what would have been the mean, median, mode, range, interquartile range, and standard deviation of the 9 numbers? (c) If each flight had had 2 fewer passengers, what would have been the interquartile range and standard deviation of the 9 numbers?

Answer 1

from given data:

S.No		X	|X-x̄|	(X-x̄)2
1		19.000	11.00000	121.00000
2		21.000	9.00000	81.00000
3		22.000	8.00000	64.00000
4		22.000	8.00000	64.00000
5		28.000	2.00000	4.00000
6		31.000	1.00000	1.00000
7		33.000	3.00000	9.00000
8		44.000	14.00000	196.00000
9		50.000	20.00000	400.00000
Σx		270	Σ(X-x̄)2=	940.0000
x̄=Σx/n		30.0000	s2=Σ(x-x̄)2/(n-1)=	117.5000

a)

mean =30

median =middle value =28

mode =22

range =max-min =50-19 = 31

interquartile =quartile 3-quartile 1 =33-22 =11

b)

mean =3*30 =90

median=28*3 =84

mode =66

range=31*3 =93

interquartile range =11*3 =33

c)

interquartile range and standard deviation would remain same

interquartile range = 11

standard deviation =10.22