Question

In: Statistics and Probability

The file “RadioShack” contains the number of RadioShack stores located in each of the 50 U.S....

The file “RadioShack” contains the number of RadioShack stores located in each of the 50 U.S. states and the District of Columbia, as of December

31, 2013. 65 20 76 53 565 82 68 18 12 309 127 24 28 197 122 68 56 75 81 33 99 115 155 81 47 97 28 33 40 36 156 41 342 139 9 203 59 70 232 20 69 22 88 408 41 16 144 111 36 101 19

a. Find mean, Variance, and  Standard deviation
b. What percentage of the 50 states have RadioShack stores within +/1 standard deviations? Round to a whole numb

c. Compute the covariance (round to whole number)

d.Compute the coefficient of correlation (round to 2 decimal places with a leading zero; e.g., 0.50)

Solutions

Expert Solution

(a)

Following table shows the calculations:

X (X-mean)^2
65 1274.918436
20 6513.458436
76 610.386436
53 2275.862436
565 215568.9184
82 349.914436
68 1069.682436
18 6840.282436
12 7868.754436
309 43386.39044
127 691.374436
24 5883.810436
28 5286.162436
197 9272.534436
122 453.434436
68 1069.682436
56 1998.626436
75 660.798436
81 388.326436
33 4584.102436
99 2.910436
115 204.318436
155 2947.838436
81 388.326436
47 2884.334436
97 13.734436
28 5286.162436
33 4584.102436
40 3685.218436
36 4186.866436
156 3057.426436
41 3564.806436
342 58222.79444
139 1466.430436
9 8409.990436
203 10464.06244
59 1739.390436
70 942.858436
232 17238.11444
20 6513.458436
69 1005.270436
22 6194.634436
88 161.442436
408 94429.60244
41 3564.806436
16 7175.106436
144 1874.370436
111 105.966436
36 4186.866436
101 0.086436
19 6675.870436
Total 5136 577224.5882

(b)

The interval corresponding to 1 SD of mean is

Out of 51 data values, 5 are not in the above interval and 46 are in above interval so required percentage is

46 /51 = 0.902

Hence, the required percentage is 90%.

-----------------

For rest parts we need two variables.


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