In Exercises, find the range, variance, and standard deviation for the given samph data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Then answer the given questions.

JFK to LAX Flight Delays Listed below are the arrival delay times (in minutes) of randomly selected American Airline flights from New York’s JFK airport to Los Angeles (LAX). Negative values correspond to flights that arrived early before the scheduled arrival time, and positive values represent lengths of delays. (The data are from the Bureau of Transportation, and more data are listed in Data Set 15.) Some of the sample values are negative, but can the standard deviation ever be negative?

Answer :

Step 1 of 1 :

Given JFK to LAX Flight Delays Listed below are the arrival delay times (in minutes) of randomly selected American Airline flights from New York’s JFK airport to Los Angeles (LAX). Negative values correspond to flights that arrived early before the scheduled arrival time, and positive values represent lengths of delays.

-15 , -18 , -32 , -21 , -9 , -32 , 11 , 2

Now we have to find the range, variance, and standard deviation for the given sample data.

The range is a simple measure of variation in a set of random variables. It is difference between the biggest and smallest random variable.

Range = Maximum value - Minimum value

Given data

-15 , -18 , -32 , -21 , -9 , -32 , 11 , 2

Range = Maximum value - Minimum value

Range = 11 + 32

Range = 43

Therefore range is 43 min.

Sample variance :

The variance of a sample is defined by slightly different formula:

The sample variance is the square difference of the data value to the mean divided by the number of values.

s2 =

where s2 is the sample variance.

x is the sample mean.

xi is the ith element from the sample and

n is the number of elements in the sample.

-15 + -18 + -32 + -21 + -9 + -32 + 11 + 2 = -114

=

=...