The dot plots below show rainfall totals in the Highlands and Lowlands areas of a certain region
Highlands
oto
tooo
öt
tooo
t

+0000
+0000
sto
to
too
too
2 4
TILL
8 10 12 14 16 18 20 22 24 26 28 30 32
Rainfall (mm)
Lowlands
. . . . .
10 12 14 16 18 20 22 24 26 28 30 32
2 4
6
8
Rainfall (mm)

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above