Question

sports car or convertible? the following table presents the fuel efficiency, in miles per gallon, for a sample of convertibles and

convertible model	mpg	sports model	mpg
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

send data to excel

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
the sample standard deviation of the mileage for the sample of convertibles is 2.2.

part: 1 / 2

part 2 of 2

(b) find the sample standard deviation of the mileage for the sample of sports cars. round the answer to at least one decimal p
the sample standard deviation of the mileage for the sample of sports car is .

Explanation:

Step1: Calculate mean for sports cars

Let the MPG values for sports cars be $x_1 = 27,x_2=23,x_3 = 24,x_4=21,x_5=18,x_6=21$. The mean $\bar{x}=\frac{27 + 23+24+21+18+21}{6}=\frac{134}{6}\approx22.33$.

Step2: Calculate squared - differences

$(x_1-\bar{x})^2=(27 - 22.33)^2=(4.67)^2 = 21.8089$, $(x_2-\bar{x})^2=(23 - 22.33)^2=(0.67)^2=0.4489$, $(x_3-\bar{x})^2=(24 - 22.33)^2=(1.67)^2 = 2.7889$, $(x_4-\bar{x})^2=(21 - 22.33)^2=(-1.33)^2 = 1.7689$, $(x_5-\bar{x})^2=(18 - 22.33)^2=(-4.33)^2 = 18.7489$, $(x_6-\bar{x})^2=(21 - 22.33)^2=(-1.33)^2 = 1.7689$.

Step3: Calculate sum of squared - differences

$\sum_{i = 1}^{6}(x_i-\bar{x})^2=21.8089+0.4489+2.7889+1.7689+18.7489+1.7689 = 47.3334$.

Step4: Calculate sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{47.3334}{6 - 1}=\frac{47.3334}{5}=9.46668$.

Step5: Calculate sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{9.46668}\approx3.1$.

Answer:

$3.1$