1.52 First, let's calculate the standard deviation. So first, let's calculate the mean: M = (135+71+69+80+158+152+161+96+122+118+87+85)/12 M = 1334/12 = 111.1666667 Now the mean of the squares from the mean. So: (135-111.1666667)^2 = 23.83333333^2 = 568.0277778 (71-111.1666667)^2 = -40.16666667^2 = 1613.361111 (69-111.1666667)^2 = -42.16666667^2 = 1778.027778 (80-111.1666667)^2 = -31.16666667^2 = 971.3611111 (158-111.1666667)^2 = 46.83333333^2 = 2193.361111 (152-111.1666667)^2 = 40.83333333^2 = 1667.361111 (161-111.1666667)^2 = 49.83333333^2 = 2483.361111 (96-111.1666667)^2 = -15.16666667^2 = 230.0277778 (122-111.1666667)^2 = 10.83333333^2 = 117.3611111 (118-111.1666667)^2 = 6.833333333^2 = 46.69444444 (87-111.1666667)^2 = -24.16666667^2 = 584.0277778 (85-111.1666667)^2 = -26.16666667^2 = 684.6944444 And their mean: (568.0277778+1613.361111+1778.027778+971.3611111+2193.361111+1667 .361111+2483.361111+230.0277778+117.3611111+46.69444444+584.027777 8+684.6944444)/12 = 12937.66667/12 = 1078.138889 And finally, the square root: SDEV = sqrt(1078.138889) SDEV = 32.83502534 So the mean is 111.1666667 and the standard deviation is 32.83502534. Let's determine how far from the mean the lowest and highest values are: Low 69 = 69 - 111.1666667 = -42.16666667 High 161 = 161 - 111.1666667 = 49.83333333 The high value is further away from the mean than the low value. The number of standard deviations from the mean si: 49.83333333 / 32.83502534 = 1.517688286 Rounding to 3 figures gives an answer of 1.52
