Question

P4 us Background) Counts N (Counts minus Background) CountsN (Counts minu 1. 1589 2. 1602 3. 196 6. 19i9 506. 1559.6 15496 443.6 1593 8. 636 9. İ601 10. 1619 1623.6 1558.6 5. 1596

Answer 1

N_avg = sigma^10_i N_i/n n = 10 = 1576.6 + 1589.69 + 1548.6 + - - - + 1606.6/10 N_avg = 1555 sigma = squareroot sigma^n_i = 1 (N_i - N_avg)^2/(n - 1) = squareroot (1576.6 - 1555)^2 + (1589.6 - 1555)^2 + - - - -+ (1606.6 - 1555)^2/9 sigma = 45.46 Now (N_avg)^1/2 = (1555)^1/2 = 39.43 % difference = 45.46 - 39.43/45.46 times 100 = 13.25 % sigma is more accurate than (N_avg)^1/2 sigma_mean = sigma/squareroot n = 45.46/squareroot 10 = 14.37 For only five data points N_avg = 1576.6 + 1589.6 + 1443.6 + 1548.6 + 1583.6/5 N_avg = 1548.4 sigma = (1576.6 - 1548.4)^2 + (1589.6 - 1548.4)^2 + (1548.6 - 1548.4)^2 + (1443.6 - 1548.4)^2 + (1583.6 - 1548.4)^2/4 sigma = 60.65 sigma_mean = 60.65/squareroot 5 sigma_mean = 27.12 see that sigma_mean changes appreciably when you increase the number of trial.