Measures Of Dispersion

We need to find the standard deviation of the data: 6, 7, 8, 9, 10.

Step 1: Calculate the mean ( ):

Step 2: Calculate the variance ( ):

Step 3: Calculate the standard deviation ( ):

Therefore, the standard deviation is .

The correct option is (A) .

The numbers are in an arithmetic sequence: 31, 32, 33, ..., 46, 47. This sequence has: - The first term , - The common difference , - The last term . The number of terms is given by: For an arithmetic sequence, the standard deviation is given by: Substituting : Therefore, the standard deviation is .