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)

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%.

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For rest parts we need two variables.

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