Question

question for the following set of data, find the population standard deviation, to the nearest hundredth. 124, 36, 26, 133, 76, 73, 115 answer attempt 1 out of 2

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{124 + 36+26+133+76+73+115}{7}=\frac{583}{7}\approx83.29$

Step2: Calculate the squared - differences

$(124 - 83.29)^2=(40.71)^2 = 1657.2041$
$(36 - 83.29)^2=(-47.29)^2 = 2236.3441$
$(26 - 83.29)^2=(-57.29)^2 = 3282.1441$
$(133 - 83.29)^2=(49.71)^2 = 2471.0841$
$(76 - 83.29)^2=(-7.29)^2 = 53.1441$
$(73 - 83.29)^2=(-10.29)^2 = 105.8841$
$(115 - 83.29)^2=(31.71)^2 = 1005.5241$

Step3: Calculate the variance

The population variance $\sigma^{2}=\frac{1657.2041+2236.3441+3282.1441+2471.0841+53.1441+105.8841+1005.5241}{7}=\frac{10811.3337}{7}\approx1544.48$

Step4: Calculate the standard deviation

The population standard deviation $\sigma=\sqrt{1544.48}\approx39.30$

Answer:

$39.30$