First we find the average (mean) of the data set:

(52 + 61 + 31 + 44 + 47 + 45 + 25 + 48 + 47)/9 = 400/9

Take each value in the data set and subtract the mean from, square it and add up all the values to get the sum of squares, divide by the number of numbers in the data set minus one:

((52 - 400/9)^2 + (61 - 400/9)^2 + (31 - 400/9)^2 + (44 - 400/9)^2 + (47 - 400/9)^2 + (45 - 400/9)^2 + (25 - 400/9)^2 + (48 - 400/9)^2 + (47 - 400/9)^2 )/(9 - 1) = 114.527778

Take the square root to get the sample standard deviation, s:

s = √114.527778

s = 10.72