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. (See the Excel Data File.) The standard deviation of this distribution is the closest to ________.
A) 5.35
B) 6.81
C) 9.54
D) 10.25

Question

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.  (See the Excel Data File.) The standard deviation of this distribution is the closest to ________.
A) 5.35 
B) 6.81 
C) 9.54 
D) 10.25

Quizplus · Accepted Answer

To calculate the standard deviation, first we need to find the mean speed. We can do this by multiplying each speed by its frequency, adding the products, and then dividing by the total number of speeds:

(50 * 1) + (55 * 6) + (60 * 11) + (65 * 15) + (70 * 5) + (75 * 2) = 2735
2735 / 40 = 68.375 mph

Next, we calculate the variance by finding the sum of the squared differences between each speed and the mean, weighted by frequency, and dividing by the total number of speeds minus one:

(((50 - 68.375)^2 * 1) + ((55 - 68.375)^2 * 6) + ((60 - 68.375)^2 * 11) + ((65 - 68.375)^2 * 15) + ((70 - 68.375)^2 * 5) + ((75 - 68.375)^2 * 2)) / (40 - 1) = 103.191

Finally, we take the square root of the variance to get the standard deviation:

sqrt(103.191) =  10.156

Therefore, the closest answer choice is B) 6.81.

Automobiles Traveling on a Road with a Posted Speed Limit