Question

Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.

Sample Mean car 1: 250.3 mi/ 10 gal
Sample mean car 2: 246.1 mi/10 gal

Question: Find the medians for Car 2 and Car 2

Answer 1

Answers in bold

Median of car 1: 249

Median of car 2: 251

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Step-by-step explanation:

This is the data set for car 1

`\begin{array}c \cline{1-5}202 & 247 & 241 & 223 & 246\\\cline{1-5}253 & 271 & 241 & 291 & 249\\\cline{1-5}259 & 257 & 261 & 246 & 268\\\cline{1-5}\end{array}`

Which when written out as a single long line, we have this:

202, 247, 241, 223, 246, 253, 271, 241, 291, 249, 259, 257, 261, 246, 268

Sort those values from smallest to largest to get this set

202, 223, 241, 241, 246, 246, 247, 249, 253, 257, 259, 261, 268, 271, 291

There are n = 15 items in that set.

n/2 = 15/2 = 7.5 which rounds to 8

The middle-most item, aka median, is in slot 8.

There are 7 items below the median, and 7 items above it. Giving us 7+1+7 = 15 items total.

Start at "202" and count 8 slots to the right until you arrive at 249 which is the median of the car 1 data set. Make sure you are looking at the sorted data set.

Follow similar steps for the car 2 data set. You should get 251 as the median of the car 2 data set.