Question

The weights (to the nearest pound) of some boxes to be shipped are found to be:. Weight 65 68 69 70 71 72 90 95 frequency 1 2 5 8 7 3 2 2 Their mean weight is 72.97 pounds. What is the standard deviation of these weights? The standard deviation, to the nearest tenth, is a0.

Answer 1

A is the weight
B is the frequency
C is weight times frequency
D is mean minus weight
E is D raised to the 2nd power ; variance
F is E times frequency ; total variance

A B C D E F
65 1 65 7.97 63.47 63.47
68 2 136 4.97 24.70 49.40
69 5 345 3.97 15.76 78.80
70 8 560 2.97 8.82 70.57
71 7 497 1.97 3.88 27.17
72 3 216 0.97 0.94 2.82
90 2 180 17.03 290.02 580.04
95 2 190 22.03 485.32 970.64
30 2,189 1,842.91

2,189 / 30 = 72.97 mean
1,842.91 / 30 = 61.43 variance
√61.43 = 7.8377 or 7.84 standard deviation.