Automobiles traveling on a road with a posted speed limit of 65 miles per hour are...
Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following is a frequency distribution of speeds. Speed (miles per hour) Frequency 45 up to 55 50 55 up to 65 325 65 up to 75 275 75 up to 85 25 The standard deviation of this distribution is the closest to ____. 5.35 6.81 9.54 10.25
Homework Answers
Solution:
| Group | Midpoint X | Frequency f | f*x | x^2 | f*(x^2) |
| 45 to 55 | 50 | 50 | 2500 | 2500 | 125000 |
| 55 to 65 | 60 | 325 | 19500 | 3600 | 1170000 |
| 65 to 75 | 70 | 275 | 19250 | 4900 | 1347500 |
| 75 to 85 | 80 | 25 | 2000 | 6400 | 160000 |
| SUM | 675 | 43250 | 17400 | 2802500 |
= 
= 43250/675 = 64.0740740741
Variance = 
= [2802500/675] - [64.07407407412]
= 46.3648834019
Variance = 46.3648834019
Standard deviation = 
= 
= 6.81
Answer : 6.81
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