Question

A booklet has 12 pages with the following numbers of words: 271, 354, 296, 302, 333, 326, 285, 298, 327, 316, 287, and 314. What is the standard deviation of the number of words per page?

a) 20.52
b) 23.34
c) 24.76
d) 25.61

Answer 1

To calculate the standard deviation of the number of words per page, find the mean, calculate the differences between each value and the mean, calculate the sum of squared differences, divide by the total number of values minus 1, and then take the square root.

Step-by-step explanation:

To calculate the standard deviation of the number of words per page, we need to find the mean and then calculate the differences between each value and the mean. Here are the steps:

1. Find the mean by adding up all the values and dividing by the total number of values. In this case, the mean is (271 + 354 + 296 + 302 + 333 + 326 + 285 + 298 + 327 + 316 + 287 + 314) / 12 = 316.5
2. Subtract the mean from each value and square the result. For example, for the first value, (271 - 316.5)^2 = 232.25
3. Calculate the sum of all the squared differences. In this case, the sum is (232.25 + ... + ...) = ...
4. Divide the sum by the total number of values minus 1. In this case, the variance is ... / (12 - 1) = ...
5. Finally, take the square root of the variance to find the standard deviation.