Question

question for the following set of data, find the sample standard deviation, to the nearest hundredth. 214, 68, 146, 186, 37, 77, 158, 113, 41 answer attempt 1 out of 2

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{214 + 68+146+186+37+77+158+113+41}{9}=\frac{1030}{9}\approx114.44$

Step2: Calculate the squared - differences

$(214 - 114.44)^2=(99.56)^2 = 9912.1936$
$(68 - 114.44)^2=(-46.44)^2 = 2156.6736$
$(146 - 114.44)^2=(31.56)^2 = 995.0336$
$(186 - 114.44)^2=(71.56)^2 = 5121.8336$
$(37 - 114.44)^2=(-77.44)^2 = 5996.9536$
$(77 - 114.44)^2=(-37.44)^2 = 1401.7536$
$(158 - 114.44)^2=(43.56)^2 = 1897.4736$
$(113 - 114.44)^2=(-1.44)^2 = 2.0736$
$(41 - 114.44)^2=(-73.44)^2 = 5393.4336$

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{9}(x_i-\bar{x})^2=9912.1936+2156.6736 + 995.0336+5121.8336+5996.9536+1401.7536+1897.4736+2.0736+5393.4336=32877.4232$

Step4: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{32877.4232}{9 - 1}=\frac{32877.4232}{8}=4109.6779$

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{4109.6779}\approx64.00$

Answer:

$64.00$