Question

A car owner conducts an experiment by filling up their car with 10 gallons of gas and drives until it runs out of gas. The number of miles driven from the 10 times of doing this experiment is shown below:

275 240 303 243 259 187 311 276 251 263

Find the following: Show ALL necessary work

a) Median

b) Lower and Upper Quartiles

c) IQR

d) State the mild outliers, if any. If there are no outliers, then state "no outliers".

Answer 1

The number of miles in the ascending order is

187 240 243 251 259 263 275 276 303 311

Here, n = total number of time the experiment is done = 10

a) Answer :

Median = ((n + 1) / 2)th observation

             = 5.5th observation

             = (5th + 6th observations) / 2

             = (259 + 263) / 2

             = 261

Therefore, median is 261 miles.

b) Answer :

Lower Quartile = Q1 = ((n + 1) / 4)th observation

                                 = 2.75th observation

                                 = 2nd observation + (3/4) * (3rd observation - 2nd observation)

                                 = 240 + (3/4) * (243 - 240)

              Q1 = 242.25

Upper Quartile = Q3 = (3*(n + 1) / 4)th observation

                                 = 8.25th observation

                                 = (8th observation + (1/4) * (9th observation - 8th observation)

                                 = 276 + (1/4) * (303 - 276)

                       Q3 = 282.75

Therefore, the lower and upper quartiles are 242.25 miles and 282.25 miles respectively.

c) Answer :

IQR = Q3 - Q1

       = 282.75 - 242.25

       = 40.5

Therefore, the IQR is 40.5 miles.

d) Answer :

There is one mild outlier. Its value is 187 miles.

Therefore, the mild outlier is 187 miles.