Problem 69E

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, 1.91.

(a) Calculate the sample mean, sample variance, and sample standard deviation.

(b) Construct a box plot of the data.

Answer

Step 1 of 2

(a)

The following times (in seconds) were obtained for a test vehicle:

We are asked to find the sample mean, sample variance and standard deviation.

If the observations in a sample are denoted by the sample mean is,

……..(1)

Let be the cold start ignition time ( in seconds)

The number of measurements is

The sample variance,

……….(2)

We can rewrite equation (2) as,

[ from the data]

Hence the sample mean, sample standard deviation and sample variance of the cold start ignition time are respectively.