Question

Hallux abducto valgus (call it HAV) is a deformation of the big toe that often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here are the data. 29 23 15 31 15 28 25 17 28 35 21 18 38 22 49 25 16 23 26 31 27 16 23 26 28 21 29 25 22 39 27 22 31 11 16 22 21 26 what is the standard deviation?

Answer 1

Solution: The formula for calculating Standard deviation is given below:

Standard deviation $=\sqrt{\frac{\sum (x_{i}-\bar{x})^{2}}{n-1}}$

Where $x_{i}$ is the angle if ith patient

$\bar{x}=\frac{\sum x_{i}}{n}$ is mean angle of 38 patients

   is number of patients

Now lets calculate the mean angle of 38 patients

$\bar{x}=\frac{\sum x_{i}}{n}$

Angle (x) 23 31 28 17 28 35 21 18 38 49 16 23 26 31 27 16 23 26 28 21 3 39 27 31 16 21 26

i = 947-24.921 38

Now lets find the Standard deviation of the given data:

Angle 16.63781163 3.690443213 9842728532 36.95360111 9842728532 9.479916898 0.006232687 62.74307479 9.479916898 101.5851801 15.37465374 47.90096953 171.0588643 8.532548476 579.7957064 0.006232687 79.58518006 3.690443213 1.164127424 36.95360111 4.322022161 79.58518006 3.690443213 1.164127424 9.479916898 15.37465374 16.63781163 0.006232687 8.532548476 198.216759 4.322022161 8.532548476 36.95360111 193.7957064 7958518006 8.532548476 15.37465374 1.164127424 Е(х-К)2-2066.763 29 23 15 31 28 25 17 28 35 18 38 49 25 16 23 26 31 27 16 23 26 28 21 29 25 39 27 31 16 21 26

Therefore standard deviation is

2066.763-7.4739 Standard deviation 37-7.4739