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maths question help please

hi, please could I have some help on part b of this question? I thought that one sd away from the mean occupies 33% area, so i estimated the mean to be 164, indicated by the peak and one 33% away was roughly at 178 so the sd would be 14 but this is wrong?
question: https://ibb.co/nsKD0cLS
thanks!

Reply 1

Original post
by anonymous56754
hi, please could I have some help on part b of this question? I thought that one sd away from the mean occupies 33% area, so i estimated the mean to be 164, indicated by the peak and one 33% away was roughly at 178 so the sd would be 14 but this is wrong?
question: https://ibb.co/nsKD0cLS
thanks!

What you say is ok, but the 33% being 178 looks way too large. Why that number?

You could say the (visual) range was ~6 std devs or the point(s) of inflection are 1 std dev from the mean or ...

Reply 2

33% away was roughly at 178 ?? I'm not sure how you reached such conclusion.
33% of 3 standard deviations? it's just one standard deviation
Why do you think about mean that it occupies area?
area is flat, or two-dimensional,
distance, variance, between two values (on the same axis, if there are no units mentioned) is linear, one-dimensional

From graph, you can derive:
mean, ~163.5, I think both 163, and 164 would be correct answers
95% of data points falls between ~145, and ~182,
so 145 is 3 standard deviation lower than mean, and 182 is 3 standard deviation higher than mean,
that gives standard deviation ~(163-145)/3=~6

Reply 3

Original post
by M.W.Shayboski
33% away was roughly at 178 ?? I'm not sure how you reached such conclusion.
33% of 3 standard deviations? it's just one standard deviation
Why do you think about mean that it occupies area?
area is flat, or two-dimensional,
distance, variance, between two values (on the same axis, if there are no units mentioned) is linear, one-dimensional
From graph, you can derive:
mean, ~163.5, I think both 163, and 164 would be correct answers
95% of data points falls between ~145, and ~182,
so 145 is 3 standard deviation lower than mean, and 182 is 3 standard deviation higher than mean,
that gives standard deviation ~(163-145)/3=~6

Pretty much, though the +/-3 std dev corresponds to ~99.7% of the data and +/-2 std dev corresponds to ~95%. Going down those routes, just get max-min (range) and divide by 6 or 4.
(edited 10 months ago)

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