Question

The weight (gms) of 31 books picked from a consignment are as follows : 106, 107, 76, 82, 106, 107, 175, 93, 187, 95, 123, 125, 111, 92, 86, 70, 127, 68, 130, 129, 139, 119,115, 128, 100, 186, 84,99, 113, 204, 111 Test whether this sample may be treated as random.

Answer 1

There are a lot of ways to test that. Here I use The Runs Test. Here the number of runs equals 17 and the p-values equals 0.309. So there is little or no real evidences against randomness, thus the sample may be treated as random.
To learn more about extbf The Runs Test visit, for instance, https://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm