The table shows the distribution of the diameters of the heads of rivets manufac
ID: 3174575 • Letter: T
Question
The table shows the distribution of the diameters of the heads of rivets manufactured by a company. Compute the mean and variance of the diameter.
Diameter (inches) Frequency 0.7247-0.7249 0.7250-0.7252 0.7253-0.7255 0.7256-0.7258 15 0.7259-0.7261 0.7262-0.7264 68 0.7265-0.7267 49 0.7268-0.7270 25 0.7271-0.7273 12 0.7280-0.7282 TOTAL 250 u-2685289582 1464211 4-5 e-925814703692 h-455566677778 C-222222222222 n-777777777777-L (000000000000-A e700 369258147 t-455556667778 222222222222 m-777777777777 la 000000000000Explanation / Answer
f x fx d = x - x-bar d^2 fd^2 2 0.7248 1.4496 -0.0016164 0.0000026 0.0000052 6 0.7251 4.3506 -0.0013164 0.0000017 0.0000104 8 0.7254 5.8032 -0.0010164 0.0000010 0.0000083 15 0.7257 10.8855 -0.0007164 0.0000005 0.0000077 42 0.726 30.492 -0.0004164 0.0000002 0.0000073 68 0.7263 49.3884 -0.0001164 0.0000000 0.0000009 49 0.7266 35.6034 0.0001836 0.0000000 0.0000017 25 0.7269 18.1725 0.0004836 0.0000002 0.0000058 18 0.7272 13.0896 0.0007836 0.0000006 0.0000111 12 0.7275 8.73 0.0010836 0.0000012 0.0000141 4 0.7278 2.9112 0.0013836 0.0000019 0.0000077 1 0.7281 0.7281 0.0016836 0.0000028 0.0000028 = 250 181.6041 0.0000129 0.0000829 Mean, x-bar = fx / f = 0.7264164 Variance, S^2 (Population) = fd^2 / f = 0.00000033 Variance, s^2 (Sample) = fd^2 / (f - 1) = 0.00000033 SD, S (Population) = (Population variance) = 0.00057593 SD, s (Sample) = (Sample variance) = 0.00057708
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