Question

Working with the Concepts.Sports car or convertible? The following table presents the fuel efficiency, in miles per gallon, for a sample of convertibles sports cars.Convertible Model MPGVolkswagen Eos 25Mini Cooper 25Saab 24BMW 21Toyota 21Volvo 21Ford Mustang 20Find the sample standard deviation of the mileage for the sample of convertibles.

Answer 1

Standard Deviation

The standard deviation for a sample of size n is given by:

`\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_i-\bar{x})^2}{n-1}}`

Where xi represents each value of the sample, x(bar) is the mean of all the values, and n is the number of values of the sample.

For the convertible models, the values are:

25, 25, 24, 21, 21, 21, 20

The mean value is:

`\begin{gathered} \bar{x}=(25+25+24+21+21+21+20)/(7) \\ \bar{x}=(157)/(7) \\ \bar{x}=22.4286 \end{gathered}`

The calculations involved in this formula are too long to display here, so we show the result:

`\sigma=2.149`

Following the same procedure for the sport models:

`\begin{gathered} \bar{x}=(23+24+21+18+21+25+27)/(7) \\ \bar{x}=(159)/(7) \\ \bar{x}=22.7143 \end{gathered}`

The second standard deviation is:

`\sigma=2.9841`