Find CV

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Dreary

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A little tricky but worth the effort:

A bell-shaped symmetrical distribution has a mean of 10 with 16% of the obseravtions below 0. Calculate the CV?
 
Those going with short cuts, try it now..

If 20% of the values fall below 4, find the CV! Hint: Z of 0.845 =0.80
 
if 16% are below 0, and the distribution is bell-shaped symetrical, 16% to the left of 0 is when to the right of 0 are 84, that is equivalent to 1 standard deviation around mean, that must mean standard deviation is 10. CV=1
 
map1 Wrote:
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> if 16% are below 0, and the distribution is
> bell-shaped symetrical, 16% to the left of 0 is
> when to the right of 0 are 84, that is equivalent
> to 1 standard deviation around mean, that must
> mean standard deviation is 10. CV=1


not getting it , where does 10 come from ?
sorry quant is my achilles heel
 
10 is the mean, the distance from 10 to 0 is 10. 16% to the left of 0, with the distribution shape bell symetrical, knowing that 68% of all observations will be in 1 STDV around the mean, means that from the mean to 0 you have only 1 distribution. It helps if you draw the distribution. This is how it must be that the STDV is 10.
 
For second question answer should be 0.714
 
if 16 fall below 0, which is 10 away from 10, then 16% fall above 20. that leaves 68% of observations falling between 0 and 20. we know that 68% of all observations fall within 1 sd of the mean so sd = 1

cv = 1/10 = .1
 
If there's 16% below 0, then there should be 16% above 20 (by symmetry). That leaves 68% in between, which is 1 SD, which is 20?
 
from 0 to 20 you have 2 standard deviations, one to the left, the other to the right of 10.
 
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