Question

Use the following data set to answer the question. 16,59,40,19,29,60,43,22 Find the sum of the differences squared between the data entries and the mean.

Answer 1

To calculate the sum of the differences squared for a dataset, first find the mean, then subtract the mean from each data entry, square those differences, and finally sum them all together. For the given dataset, the sum of the differences squared is 2104.

Step-by-step explanation:

To find the sum of the differences squared between the data entries and the mean of a dataset, you need to follow these steps:

1. Calculate the mean (average) of the dataset.
2. Subtract the mean from each data point to find the differences.
3. Square each difference.
4. Sum all the squared differences to find the total.

Let's apply this to the provided data set: 16, 59, 40, 19, 29, 60, 43, 22.

1. Mean = (16 + 59 + 40 + 19 + 29 + 60 + 43 + 22) / 8 = 288 / 8 = 36.
2. Differences = (16-36, 59-36, 40-36, 19-36, 29-36, 60-36, 43-36, 22-36) = (-20, 23, 4, -17, -7, 24, 7, -14).
3. Squared differences = (400, 529, 16, 289, 49, 576, 49, 196).
4. The sum of the differences squared = 400 + 529 + 16 + 289 + 49 + 576 + 49 + 196 = 2104.

The sum of the differences squared is 2104.