Q T1.14. - The Practice of Statistics for AP

Question

The back-to-back stem plot shows the lifetimes of several Brand X and Brand Y batteries.

(a) What is the longest that any battery lasted? 

(b) Give a reason someone might prefer a Brand X battery.

(c) Give a reason someone might prefer a Brand Y battery

Step-by-Step Solution

Answer

Part (a) 5|5 will represent the 550-559 hours, which will be the longest lasted battery.

Part (b) The minimum time that the battery lasts is higher for brand X (300 hours) than for brand Y(170hours).

Part (c) Most of the batteries of brand Y have a higher lifetime than most of the batteries of bran X.

Part (a) Step 1: Given information

Part (a) Step 2: Concept

Data analysis is the systematic application of statistical and/or logical tools to explain and show, condense and recap, and appraise data.

Part (a) Step 3: Explanation

As per provided hint in the problem that 4|2 represents 420-429 hours, so 5|5 will represent the 550-559 hours, which will be the longest lasted battery.

Part (b) Step 1: Explanation

In comparison to Brand Y, the back-to-back stem plot clearly shows that Brand X has less fluctuation in battery life as values are distributed further from the center. As a result, someone may favor Brand X over Brand Y for this reason.

Part (c) Step 1: Explanation

When looking at the back-to-back stem plot, it is evident that Brand Y has higher battery life values than Brand X because it has a higher value equivalent to 4. As a result, Brand Y's median lifetime will be longer than Brand X's. As a result, someone may favor Brand Y over Brand X for this reason.