4 The given 3 unit by 12 unit rectangle in the
standard (x, y) coordinate plane was obtained by
applying a sequence of transformations to the
1 unit by 4 unit rectangle. One of the
transformations was a dilation centered at the
origin.
12
3
0
Which of the following sequences could have
been applied?
Dilation with a scale factor of 3 centered
at the origin followed by a rotation about
the origin
Dilation with a scale factor of 12 centered
at the origin followed by a rotation about
the origin
Dilation with a scale factor of 3 centered
at the origin followed by a reflection
across the y-axis
Dilation with a scale factor of 12 centered
at the origin followed by a translation of
4 units to the right
Dilation with a scale factor of 3 centered
at the origin ollowed by a translation of
16 units to the right

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