Question

Find the standard deviation of 122, 133, 147, 116, 147, and 140. If necessary, round your answer to the nearest tenth.

a) 11.4
b) 12.2
c) 13.7
d) 14.5

Answer 1

To find the standard deviation, calculate the mean, subtract each value from the mean, square the differences, find the sum of the squared differences, divide by (n-1), and take the square root of the result.

Step-by-step explanation:

The standard deviation of the given data set can be found using the following steps:

1. Find the mean of the data set by adding up all the numbers and dividing by the total number of values. In this case, the mean is (122+133+147+116+147+140)/6 = 130.8.
2. Find the difference between each value and the mean, and square each difference. For example, (122-130.8)^2 = 73.44.
3. Find the sum of all the squared differences. In this case, the sum is 73.44 + 7.84 + 288.24 + 207.36 + 288.24 + 0 = 865.12.
4. Divide the sum of squared differences by (n-1), where n is the total number of values. In this case, divide 865.12 by (6-1) = 5 to get 173.024.
5. Finally, take the square root of the result obtained in the previous step. The square root of 173.024 is approximately 13.1.

Therefore, the standard deviation of the given data set is approximately 13.1.