Question

Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the current population of all people? 9.9 8.7 10.1 9.2 9.2 9.9 0.1 9.4 9.1 9.3 10.2 The range of the sample data is (Type an integer or a decimal. Do not round.) The standard deviation of the sample data is (Round to two decimal places as needed.) people inches2 inches. people. The variance of the sample data is (Round to two decimal places as needed.) Are the statistics representative of the current por A. Since the measurements were made in 15 le? sarily representative of the population today B. The statistics are representative because te snuaru uevation of the sample data is less than 1 C. The statistics are not representative because a smaller sample is needed to represent the population D. The statistics are representative because they are taken from a random sample

Answer 1

`Range= Max-Min= 10.2-8.7=1.5 inches`

`s =\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

And if we replace we got
`s = 0.50 inches`

`s^2 = 0.503^2 = 0.25 in^2`

D. The statistics are representative because they are taken from a random sample

Explanation:

For this case we have the following data:

9.9 8.7 10.1 9.2 9.2 9.9 10.1 9.4 9.1 9.3 10.2

The data was colledted from a random sample of people selected in 1988.

We can order the dataset on increasing way and we got:

8.7 9.1 9.2 9.2 9.3 9.4 9.9 9.9 10.1 10.1 10.2

The range is defined as
`Range= Max-Min= 10.2-8.7=1.5 inches`

The mean is defined as:

`\bar X =(\sum_(i=1)^n X_i)/(n)= 9.555 inches`

The standard deviation can be calculated with the following formula:

`s =\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

And if we replace we got
`s = 0.50 inches`

The sample variance would be just the deviation squared:

`s^2 = 0.503^2 = 0.25 in^2`

And since the data comes from a random sample then is representative fo the population data in 1988. So then the best answer for this case would be:

D. The statistics are representative because they are taken from a random sample