If I take a series of measurements for the length and width of arecatangular boa

Question

If I take a series of measurements for the length and width of arecatangular board and find the mean and the Standard deviation forboth the length and the width. How do I answer thisquestion?

Suppose you were to calculate the area of the rectangle youmeasured in the experiment. How might you estimate the errorof the area measurement? (Remember that you have alreadycalculated the standard deviation for each side.)

The mean for the length is 0.28m
The Standard Deviation for the length is .02582

The mean for the width is .206m
The Standard Deviation for the width is .009661   

Explanation / Answer

    Standard deviation is a way of calculating the spread of yourmeasured values. You can express the measured length as mean length ± standard deviation or 0.28±0.02582 The relative uncertainty in your lengthis standard deviation in length/ mean length = 0.02582 / 0.28 = 0.0922 The measured width as 0.206±0.009661 and the relative uncertainty in width is standard deviation in width / mean width =0.009661 / 0.206 = 0.0469 When you calculate the area, you can express it as A± A where A = mean length * mean width = 0.28 * 0.206 The uncertainty in your area is A which is the error±A calculated as sum of the relative uncertainties in length andwidth = 0.0922 + 0.0469 When you calculate the area, you can express it as A± A where A = mean length * mean width = 0.28 * 0.206 The uncertainty in your area is A which is the error±A calculated as sum of the relative uncertainties in length andwidth = 0.0922 + 0.0469

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