The table below shows the number of arrests in thousands, for the years from 2005 to 2014 in a
Particular country. Find the mean and sample standard deviation for the number of arrests. Include
Units.
A)mean: 559,000 arrests; standard deviation: 51,509 arrests
B)mean: 571,500 arrests; standard deviation: 49,796 arrests
C)mean: 571,500 arrests; standard deviation: 47,240 arrests
D)mean: 559,000 arrests; standard deviation: 48,866 arrests

Question

The table below shows the number of arrests in thousands, for the years from 2005 to 2014 in a
Particular country. Find the mean and sample standard deviation for the number of arrests. Include
Units. 
A)mean: 559,000 arrests; standard deviation: 51,509 arrests 
B)mean: 571,500 arrests; standard deviation: 49,796 arrests 
C)mean: 571,500 arrests; standard deviation: 47,240 arrests 
D)mean: 559,000 arrests; standard deviation: 48,866 arrests

Quizplus · Accepted Answer

To find the mean, we sum up all the values and divide by the total number of values:
(480 + 508 + 522 + 529 + 537 + 545 + 549 + 555 + 558 + 562) / 10 = 5,715
So the mean is 571,500 arrests. 
To find the sample standard deviation, we need to calculate the variance first:
1. Find the mean: 571,500
2. Find the differences from the mean for each value:
-91,500, -63,500, -49,500, -42,500, -34,500, -26,500, -22,500, -16,500, -13,500, -9,500
3. Square the differences:
8,382,250,000; 4,032,250,000; 2,452,500,000; 1,806,250,000; 1,190,250,000; 702,250,000; 506,250,000; 272,250,000; 182,250,000; 90,250,000
4. Sum the squared differences: 18,914,500,000
5. Divide the sum by n-1 (which in this case is 9 since we have a sample): 18,914,500,000 / 9 = 2,101,611,111
This is the variance. To find the sample standard deviation, we take the square root of the variance:
sqrt(2,101,611,111) = 49,796 arrests
So the answer is B, with a mean of 571,500 arrests and a sample standard deviation of 49,796 arrests. To find the mean, we add up all the numbers and divide by the sample size:
(484 + 479 + 501 + 510 + 535 + 570 + 590 + 588 + 572 + 574) / 10 = 571.5 thousand arrests
To find the sample standard deviation, we first need to find the variance:
1. Find the mean
2. For each number, subtract the mean and square the result
3. Add up all the squared differences
4. Divide the sum by n - 1
(484 - 571.5)^2 = 75476.25
(479 - 571.5)^2 = 85712.25
(501 - 571.5)^2 = 49506.25
(510 - 571.5)^2 = 37556.25
(535 - 571.5)^2 = 13322.25
(570 - 571.5)^2 = 2.25
(590 - 571.5)^2 = 341.25
(588 - 571.5)^2 = 273.25
(572 - 571.5)^2 = 0.25
(574 - 571.5)^2 = 6.25
Total = 262266.5
Divide by n - 1 = 9
262266.5 / 9 = 29140.72
Take the square root of the variance to get the standard deviation:
√29140.72 = 170.86
Therefore, the answer is B.

The Table Below Shows the Number of Arrests in Thousands