For the given set of observations, the calculator will find their standard deviation (either sample or population), with steps shown.
Solution The sample standard deviation of data is given by the formula s = ∑ i = 1 n ( x i − μ ) 2 n − 1 s = \sqrt{\frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1}} s = n − 1 ∑ i = 1 n ( x i − μ ) 2 n n n x i , i = 1.. n ‾ x_i, i=\overline{1..n} x i , i = 1.. n μ \mu μ
Actually, it is the square root of variance .
The mean of the data is μ = 327 35 \mu = \frac{327}{35} μ = 35 327 mean calculator ).
Since we have n n n n = 7 n = 7 n = 7
The sum of ( x i − μ ) 2 \left(x_{i} - \mu\right)^{2} ( x i − μ ) 2 ( 1 − 327 35 ) 2 + ( 37 − 327 35 ) 2 + ( 9 − 327 35 ) 2 + ( 0 − 327 35 ) 2 + ( − 3 5 − 327 35 ) 2 + ( 9 − 327 35 ) 2 + ( 10 − 327 35 ) 2 = 178734 175 . \left(1 - \frac{327}{35}\right)^{2} + \left(37 - \frac{327}{35}\right)^{2} + \left(9 - \frac{327}{35}\right)^{2} + \left(0 - \frac{327}{35}\right)^{2} + \left(- \frac{3}{5} - \frac{327}{35}\right)^{2} + \left(9 - \frac{327}{35}\right)^{2} + \left(10 - \frac{327}{35}\right)^{2} = \frac{178734}{175}. ( 1 − 35 327 ) 2 + ( 37 − 35 327 ) 2 + ( 9 − 35 327 ) 2 + ( 0 − 35 327 ) 2 + ( − 5 3 − 35 327 ) 2 + ( 9 − 35 327 ) 2 + ( 10 − 35 327 ) 2 = 175 178734 .
Thus, ∑ i = 1 n ( x i − μ ) 2 n − 1 = 178734 175 6 = 29789 175 \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{\frac{178734}{175}}{6} = \frac{29789}{175} n − 1 ∑ i = 1 n ( x i − μ ) 2 = 6 175 178734 = 175 29789
Finally, s = ∑ i = 1 n ( x i − μ ) 2 n − 1 = 29789 175 = 208523 35 s = \sqrt{\frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1}} = \sqrt{\frac{29789}{175}} = \frac{\sqrt{208523}}{35} s = n − 1 ∑ i = 1 n ( x i − μ ) 2 = 175 29789 = 35 208523
Answer The sample standard deviation is s = 208523 35 ≈ 13.04694819269461 s = \frac{\sqrt{208523}}{35}\approx 13.04694819269461 s = 35 208523 ≈ 13.04694819269461 A .
