Question

13 what is the sample standard deviation of the following dataset? 67, 70, 72, 75, 76 a 10.8 b 13.5 c 3.29 d 3.67

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{67 + 70+72+75+76}{5}=\frac{360}{5}=72$

Step2: Calculate the squared differences

$(67 - 72)^2=(-5)^2 = 25$, $(70 - 72)^2=(-2)^2=4$, $(72 - 72)^2=0^2 = 0$, $(75 - 72)^2=3^2=9$, $(76 - 72)^2=4^2 = 16$

Step3: Calculate the sum of squared differences

$25+4+0+9+16=54$

Step4: Calculate the sample variance

The sample variance $s^2=\frac{54}{5 - 1}=\frac{54}{4}=13.5$

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{13.5}\approx3.67$

Answer:

D. 3.67