Miles/ Hour Frequency
50 - 54 2
55 - 59 4
60 - 64 5
65 - 69 10
70 - 74 9
75 - 79 5
what is the mean? Variance? Standard Deviation?
2006-09-28 08:48:27 · 2 answers · asked by KISMET 2 in Science & Mathematics ➔ Engineering
The mean is (the sum of the value of each sample times the number of occurrances of that value) / (total number of occurrances). In your problem, this would be (50*54.2+55*59.4+..+75*79.5) divided by (54.2+59.4+...+79.5).
The variance is the sum of the squares of each sample's value minus the mean. If the mean calculated above is M, then the variance is
(50-M)^2*50+(55-M)^2*59.3+
...+(75-M)^2*79.5
The standard deviation is the square root of the variance divided by the number of samples less 1. If the variance computed above is V, then Std Dev = sqrt[V/(54.2+59.2+...+79.5)-1]
2006-09-28 09:22:22 · answer #1 · answered by gp4rts 7 · 1⤊ 0⤋
52.5 * 2 = 105
57.5 * 4 = 230
62.5 * 5 = 312.5
67.5 * 10 = 675
72.5 * 9 = 652.5
77.5 * 5 = 387.5
105 + 230 + 312.5 + 675 + 652.5 + 387.5 = 2362.5
2 + 4 + 5 + 10 + 9 + 5 = 35
Mean = 2362.5 / 35 = 67.5 exactly
(67.5 - 52.5)^2 * 2 = 450
(67.5 - 57.5)^2 * 4 = 400
(67.5 - 62.5)^2 * 5 = 125
(67.5 - 72.5)^2 * 9 = 225
(67.5 - 77.5)^2 * 5 = 500
450 + 400 + 125 + 225 + 500 = 1700
Variance = 1700 / 34 = 50.0 exactly
Standard deviation = sqrt(variance) = 7.07
Variance corrected for class width = 50.0 - 5^2 / 12 = 47.917
Standard deviation = 6.92
2006-09-28 09:37:47 · answer #2 · answered by Anonymous · 1⤊ 0⤋