How will I interpret standard deviation in context?

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onesun0000

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I am not sure how I will interpret the standard deviation (contextual interpretation) in this problem. I think standard deviation is large, so the data points may be more spread from the mean. I just don't know how to interpret using the given problem. Next, the effect of adding 50 to the data set may increase the mean and the standard deviation right? The mean and standard deviation are not resistant to adding, changing or removing any data point, especially if the data point is an outlier.

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You have, for purposes of answering the question: 45, 45, 45, 45, 45 from which to calculate the 2a Mean.
You have: 45, 45, 45, 45, 45, 50 from which to calculate the 2b Mean.
What difference does it make?

(50-45)/10 = 0.50 -- The new score is only ½ Standard Deviation away from the mean. Can you suggest what this might do to the old Standard Deviation?

With only five data points, are you SURE your data are sufficiently NORMAL so that the Standard Deviation means ANYTHING?
 
tkhunny said:
You have, for purposes of answering the question: 45, 45, 45, 45, 45 from which to calculate the 2a Mean.
You have: 45, 45, 45, 45, 45, 50 from which to calculate the 2b Mean.
What difference does it make?

(50-45)/10 = 0.50 -- The new score is only ½ Standard Deviation away from the mean. Can you suggest what this might do to the old Standard Deviation?

With only five data points, are you SURE your data are sufficiently NORMAL so that the Standard Deviation means ANYTHING?
Click to expand...

The 2a mean is 45 and 2b mean is about 45.83. There's is just a very slight decrease in mean. This means that the standard deviation and mean will almost not change. There's just gonna be a very small difference between the original and new.

For question 2a, the problem didn't say whether the data set is normally distributed, so I guess it won't mean much of anything. But if I were to interpret it, is it okay to say that the standard deviation suggests that the minutes the five students spent on reviewing are closer/farther from the average minutes. All I can think of is just the variation of the data set.
 
onesun0000 said:
How will I interpret standard deviation in context? …
Click to expand...
Hi onesun. You can google keywords like explain standard deviation with examples, to find a lot of different presentations in context. Hopefully, some of those will click for you.

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Otis said:
Hi onesun. You can google keywords like explain standard deviation with examples, to find a lot of different presentations in context. Hopefully, some of those will click for you.

?
Click to expand...
Well, I searched and all I can say about the problem is that the students' times of review are close to the average of the data. That suggests that the students reviewed at an average of 45 minutes, no outliers, I guess. Can I use the empirical rule to answer this? and Is the data enough to say that the Sd has significance?
 
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