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## Arithmetic mean and standard deviation

This topic has 3 member replies
vaibhav.iit2002 Master | Next Rank: 500 Posts
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#### Arithmetic mean and standard deviation

Mon Oct 12, 2009 9:50 am
Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
10.5, 11, 11.5, 12, 12.5

sanjana Master | Next Rank: 500 Posts
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Tue Oct 13, 2009 3:06 am
Mean is 13.5
SD = 1.5
2sd = 2* 1.5 = 3

We need to find the value exactly 2 sd less than the mean so we need to find 13.5-3
If we had to find the value exactly 2 sd greater than the mean we would do 13.5+3

In general :

Points k Sd above the mean : x+k*SD
points k sd below the mean : x-k*SD

papgust Community Manager
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Mon Oct 12, 2009 10:06 pm
maihuna wrote:
10.5, one SD away means +/- SD so 2 less means: 13.5-3
Can you help me understand how you get -3 in the calculation?

maihuna Legendary Member
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Mon Oct 12, 2009 9:55 am
vaibhav.iit2002 wrote:
Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
10.5, 11, 11.5, 12, 12.5
10.5, one SD away means +/- SD so 2 less means: 13.5-3

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