Question

sports car or convertible? the following table presents the fuel efficiency, in miles per gallon, for a sample of convertibles and a sample of sp
convertible model mpg sports model mpg
volvo c70 20 honda civic si 27
ford mustang v6 25 bmw 135i 23
mini cooper 25 mazda mazdaspeed 24
saab 9-3 24 subaru impreza wrx sti 21
ford mustang v6 21 mazda rx-8 18
bmw 328i 21 mitsubishi lancer evolution 21
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part: 0 / 2
part 1 of 2
(a) find the sample standard deviation of the mileage for the sample of convertibles. round the answer to at least one decimal place.
the sample standard deviation of the mileage for the sample of convertibles is 2.2

Explanation:

Step1: Recall sample - standard - deviation formula

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data points, $\bar{x}$ is the sample mean, and $n$ is the sample size.
For the convertibles data: $x = \{20,25,25,24,21,21\}$, $n = 6$.

Step2: Calculate the sample mean $\bar{x}$

$\bar{x}=\frac{20 + 25+25+24+21+21}{6}=\frac{136}{6}\approx22.67$.

Step3: Calculate $(x_{i}-\bar{x})^{2}$ for each $x_{i}$

$(20 - 22.67)^{2}=(-2.67)^{2}=7.1289$;
$(25 - 22.67)^{2}=(2.33)^{2}=5.4289$;
$(25 - 22.67)^{2}=(2.33)^{2}=5.4289$;
$(24 - 22.67)^{2}=(1.33)^{2}=1.7689$;
$(21 - 22.67)^{2}=(-1.67)^{2}=2.7889$;
$(21 - 22.67)^{2}=(-1.67)^{2}=2.7889$.

Step4: Calculate $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$

$\sum_{i = 1}^{6}(x_{i}-\bar{x})^{2}=7.1289+5.4289+5.4289+1.7689+2.7889+2.7889 = 25.3334$.

Step5: Calculate the sample standard deviation $s$

$s=\sqrt{\frac{25.3334}{6 - 1}}=\sqrt{\frac{25.3334}{5}}=\sqrt{5.06668}\approx2.2$.

Answer:

$2.2$