# Calculating Mean / Variance - S1Watch

#1
I have to estimate the mean and variance from a histogram, with no data values or boundaries given.

I'm given 2 histograms to look at:
one has a x axis range from 0 to 70 , with every 10 increments. The other is from 0 to 90 .

Couple of questions,
1) How would you know which set has the greater variance / mean just by looking at it ?
2) How would you estimate the mean / variance from one of the histogram given ?

+rep on offer , just not sure how to do this and would appreciate help
0
7 years ago
#2
(Original post by Tulian)
I have to estimate the mean and variance from a histogram, with no data values or boundaries given.

I'm given 2 histograms to look at:
one has a x axis range from 0 to 70 , with every 10 increments. The other is from 0 to 90 .

Couple of questions,
1) How would you know which set has the greater variance / mean just by looking at it ?
2) How would you estimate the mean / variance from one of the histogram given ?

+rep on offer , just not sure how to do this and would appreciate help
1) The one with the largest mean would be the one where roughly the 'middle' of the bars is at a higher x value, and the larger bars are generally at higher x values. From what you've said, it's likely that the one on the 0-90 scale would have a larger mean, but this depends where abouts the bars are positioned on this scale.

Varience is a measure of spread - the more spread out the data is the larger the varience. So if you had lots of bars of similar-ish height covering a large range of x values then that would have a larger varience. If the bars make a sort of spike within a small range of x values then that would have a smaller varience.

2) To estimate the mean, look at roughly where the middle of the clump of bars is, or where the tallest bar is.

Estimating the variance is harder to do by eye. One way of getting a rough estimate is to look at the bars and ask yourself - how far from the mean are the data values on average? This will give you an estimate of the standard deviation. Square this number to get the variance.
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