Step 1) Work out the Mean (the simple average of the numbers)
#m_n = (35 + 36 + 36 + 38 + 41 + 42 + 45 + 48)/8#
#m_n = 321/8#
#m_n = 40.125#
Step 2) Then for each number: subtract the Mean and square the result
#(35 - 40.125)^2 = 26.265625#
#(36 - 40.125)^2 = 17.015625#
#(36 - 40.125)^2 = 17.015625#
#(38 - 40.125)^2 = 4.515625#
#(41 - 40.125)^2 = 0.765625#
#(42 - 40.125)^2 = 3.515625#
#(45 - 40.125)^2 = 23.765625#
#(48 - 40.125)^2 = 62.015625#
Step 3) Then work out the mean of those squared differences.
#m_s = (26.265625 + 17.015625 + 17.015625 + 4.515625 + 0.765625 + 3.515625 + 23.765625 + 62.015625)/8#
#m_s = 154.878/8#
#m_s = 19.35975#
Step 4) Take the square root of that and we are done!
#s = sqrt(19.35975)#
#s = 4.399971590817377#
#s = 4.4# rounded to the nearest tenth
