S1 - variance and standard deviation help! Watch

Music With Rocks
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I can't figure out how to answer a question like this or how you go about it. Any help appreciated.

In a certain district, the mean annual rainfall is 80cm with standard deviation 4cm.
1) One year it was 90cm. Was this an exceptional year?
2) The next year had a total of 78cm. Was that exceptional?
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Music With Rocks
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That is the way the question is phrased so I guess I have to use judgement there, so the SD is 4 but from that how do I work out the probability of 90 happening?
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SarcasticMel
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(Original post by Music With Rocks)
I can't figure out how to answer a question like this or how you go about it. Any help appreciated.

In a certain district, the mean annual rainfall is 80cm with standard deviation 4cm.
1) One year it was 90cm. Was this an exceptional year?
2) The next year had a total of 78cm. Was that exceptional?
Draw a picture. Always helps. Even if it's just to sort information or make it understandable all at once.
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Music With Rocks
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(Original post by SarcasticMel)
Draw a picture. Always helps. Even if it's just to sort information or make it understandable all at once.
I know this sounds stupid but I really have no idea where to start, I am not sure what I could draw.
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SarcasticMel
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(Original post by Music With Rocks)
I know this sounds stupid but I really have no idea where to start, I am not sure what I could draw.
Draw the distribution. Then mark in the mean and map out one or two standard deviations. So here it's 80 for the mean and 84 and 88 for 1 and 2 sd. So 90 is more than 2 sd's away from the mean - that's pretty far, no? Whereas 78 is only half a sd away, that's close.
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Langyboi10
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(Original post by Music With Rocks)
I can't figure out how to answer a question like this or how you go about it. Any help appreciated.

In a certain district, the mean annual rainfall is 80cm with standard deviation 4cm.
1) One year it was 90cm. Was this an exceptional year?
2) The next year had a total of 78cm. Was that exceptional?
For a roughly symmetrical distribution, 95% of the data lies within 4 standard deviations of the mean (in your case 95% of the data will lie between 72-88 as the mean is 80 and SD=4).
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Music With Rocks
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(Original post by SarcasticMel)
Draw the distribution. Then mark in the mean and map out one or two standard deviations. So here it's 80 for the mean and 84 and 88 for 1 and 2 sd. So 90 is more than 2 sd's away from the mean - that's pretty far, no? Whereas 78 is only half a sd away, that's close.
Ah okay I understand now, thank you very much I was completely clueless beforehand.
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Music With Rocks
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(Original post by Langyboi10)
For a roughly symmetrical distribution, 95% of the data lies within 4 standard deviations of the mean (in your case 95% of the data will lie between 72-88 as the mean is 80 and SD=4).
I did not know this, thank you this has helped a lot!
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