By Arthur H. Hall (auth.)
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Note that 31 + 13 = 44 is twice (1 0 + 12) and the error is ± (4 + 5). e. (A- B)+ (a+ b). The minimum difference is (A- a)- (B +b)= (A- B)- (a+ b). 4), giving the absolute error form. 4. 6. 6) = 5 = 25-20. 4. With both these processes we use the numbers approximated to obtain the approximated or most likely answer. This is then modified by using an error which is the sum (never the difference) of the absolute errors. (500 ± 10)- (350 ± 20) + (60 ± 5) = (500- 350 + 60) ± (10 + 20 + 5) = 210±35 The expected answer is 210.
We may predict for values within the range- interpolation; it is not advisable to try and predict for values beyond the range - extrapolation. Calculation of the coefficient of correlation by what is known as the productmoment method is outside our needs at this level. It involves the mean and variances of the two distributions as well as a new item- covariance- which takes the deviations from the means and pairs them as products. For example worked through it can be calculated from the formula covanance .
6. 04, giving the answer correct to two decimal places. (b) Correct the two numbers in (a} to two significant figures and evaluate the product to two significant figures. 47 (c) Accepting (a) as the correct answer and (b) as an approximated answer, what is the relative error? 7. Six numbers are rounded to the nearest I 00. What is the error in (a) their sum, (b) their average? 8. A sack of potatoes weighs I cwt correct to the nearest lb. What are (a) the maximum possible, (b) the minimum possible, weights?