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# 7) - Ex Take k=2(1(1/2^2 = ¾= 0.75 = 75 in(sample mean –...

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Statistics 5e 4/07/08 Properties of Standard Deviation: Tells us how far away a value is from the mean For bell-shaped distribution we have the Empirical Rule . 1. 1 – SD Rule: 68% of the data values falls within the interval (Sample Mean-s, Sample Mean+s) 2. 2 – SD Rule: 95% of the data values will fal within the interview (Sample Mean – 2s, Sample Mean +2s) 3. 3 – SD Rule: 99.7% of the data values will fall within the interval (Sample Mean – 3s, Sample Mean +3s) If a histogram is not symmetric – Chebyshev’s Rule : At least (1-1/k^2) of the data values fall within the interval (Sample Mean- ks, Sample Mean+ks)
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Unformatted text preview: Ex: Take k=2 (1-(1/2^2)) = ¾= 0.75 = 75% in (sample mean – 2s, sample mean +2s) Using the Empirical Rule: • If something is around 1 SD from the average then it’s not surprising • If something is around 2 SDs from the average then this is fairly unusual • If something is around 3 SDs from the average then this is unusual • If something is around 4 SDs from the average then this is extreme Z score = (observed value – mean) / SD • Tells us how far away a value is from the SD • How many SDs a value is from the mean...
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