I have 20 Score values:
1, 3, 4, 6, 10, 14, 16, 19, 23, 32, 34, 38, 43, 48, 53, 59, 63, 69, 74, 85.
So, I calculate the Standard Deviation using:
$$ \sigma = \sqrt{\frac{\sum(x-\bar x)^2}n} $$
.. which is 25.4 and mean is 34.7.
Now, from 68-95-99.7% rule:
- How many values and what are the values in one standard deviation?
- How many values and what are the values in the second standard deviation?
How do I calculate all that?
Best Answer
The 68-95-99.7% rule can only be validly applied to a normal distribution. Your data are from a finite sample, so the rule does not apply.
You don't need the rule though. You can just count. "Within one standard deviation of the mean" means within the interval $[\bar{x} - \sigma, \bar{x} + \sigma] = [34.7 - 25.4, 34.7 + 25.4] = [9.3, 60.1]$. How many and which values are between 9.3 and 60.1?
You can then apply the same principle to find the values within two standard deviations of the mean. I'll let you figure those out since this is clearly a homework problem and we're not here to give you homework answers.