Imagine your boss makes the following claim: \"I\'ve tested all 75 of our new cl

Question

Imagine your boss makes the following claim: "I've tested all 75 of our new clients, and, on average, they score 7 on the suicide risk scale. Given that the cutoff for extreme risk is 10, and our average is 3 points below that, I don't think we should focus on suicide prevention efforts." Script a response to your boss in which you explain why you need to know the standard deviation in addition to the mean in order to make a well-informed decision. Provide examples to make your explanation clear.

Explanation / Answer

The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. Standard Deviation introduces two important things, The Normal Curve (shown below) and the 68/95/99.7 Rule. We'll return to the rule soon. ... Standard deviation is considered the most useful index of variability. It is a single number that tells us the variability, or spread, of a distribution (group of scores). In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and threestandard

So, if average score is 7 and cut off point is 10

So, if standard deviation of the scores is let's say 4

68.27% of the People wil have the scores between 7 - 4 = 3 and 7 + 4 = 11 thus exposing some people with extreme risk more often than not and more people in moderate risk.

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