Question

Using this data set, identify the four measures of center (using formulas or definitions) and estimate the standard deviation (using the range rule of thumb). You must show your work. Describe the effects of the measures of center and the standard deviation on the shape of the distribution.

-please show work so I can learn how to use the range rule of thumb to estimate the standard deviation, thank you.

HADLEN

17.0

16.5

16.5

16.0

16.0

16.0

15.5

15.5

15.5

15.5

15.5

15.0

14.5

14.5

14.5

14.0

14.0

13.5

13.5

13.5

13.5

13.5

13.5

13.5

13.0

13.0

13.0

13.0

13.0

13.0

13.0

13.0

12.5

12.5

12.5

12.5

12.0

11.5

11.5

11.5

11.5

11.5

11.0

11.0

11.0

10.0

10.0

10.0

10.0

10.0

9.5

9.0

9.0

9.0

Answer 1

Solution-;

mean=sum of values /total values

=699.5/54

= 12.9537

median is middle value after sorting

9.0 9.0 9.0 9.5 10.0 10.0 10.0 10.0 10.0 11.0 11.0
11.0 11.5 11.5 11.5 11.5 11.5 12.0 12.5 12.5 12.5 12.5
13.0 13.0 13.0 13.0 13.0 13.0 13.0 13.0 13.5 13.5 13.5
13.5 13.5 13.5 13.5 14.0 14.0 14.5 14.5 14.5 15.0 15.5
15.5 15.5 15.5 15.5 16.0 16.0 16.0 16.5 16.5 17.0

27 it item is 13

28t h item is 13

meidan=13+13/2=13

mode is most repeating value

13 repeats 8 times in data

mode=13

Range=max-min

=17-9

=8

Range rule of thumb to find standard deviation is

Range=max-min/4

=(17-9)/4

=8/4

=2

standard deviation=2

using range rule of thumb