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.