Question

The "cold start ignition time" of an automobile engine is being investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, and 1.91. (a) Calculate the sample mean and sample standard deviation. (b) Construct a box plot of the data.

Answer 1

(a) The sample mean and sample standard deviation are 2.415 and 0.5342 respectively.

(b) Shown below.

Explanation:

The data set provided is:

S = {1.75, 1.92, 2.62, 2.35, 3.09, 3.15, 2.53, and 1.91}

(a)

Compute the sample mean and sample standard deviation as follows:

`\bar x=(1)/(n)\sum\limits_(i){x_(i)} =(1)/(8)* 19.32=2.415\\\\\\s=\sqrt{(1)/(n-1)\sum\limits_(i){(x_(i)-\bar x^(2))^(2)}}=\sqrt{(1)/(8-1)* 1.9976}=0.5342`

Thus, the sample mean and sample standard deviation are 2.415 and 0.5342 respectively.

(b)

Use SPSS to form a Box plot.

Go to Graphs → Legacy Dialogs → Boxplot

A dialog box will open.

Select "Simple".

Select "Summaries for Separate Variable"

Press "Define"

Another dialog box will open.

Select the variable.

Press OK.

The box plot is attached below.