Question

researchers decided to investigate which of two popular brands of camera battery lasts longer. they took separate random samples of 40 camera batteries of each brand, and recorded how long each battery lasted (in hours of use). the back - to - back stemplot displays the data.
brand x: 6|86200; 7|99988640; 8|887531110; 9|966422200; 10|8753111; 11|42;
brand y: 6|9; 7|35; 8|248; 9|014559; 10|00258899; 11|001133679; 12|14666788; 13|35; 14|6;
key: 6|9 = 69 hours
shape: the shape of the distributions of battery lifespan (hours) for brand x is
outliers: and for brand y is
center: brand x batteries tend not to last as long (median = ) as brand y batteries (median = )
compare the two distributions.

Explanation:

Step1: List all Brand X data

Data: 68, 62, 60, 60, 79, 79, 79, 78, 78, 76, 74, 70, 88, 87, 85, 83, 81, 81, 81, 80, 99, 96, 96, 94, 92, 92, 92, 90, 90, 108, 107, 105, 103, 101, 101, 101, 101, 114, 112, 146

Step2: Find Brand X median

For n=40, median = average of 20th & 21st values:
$\text{Median}_X = \frac{80 + 99}{2} = 89.5$

Step3: List all Brand Y data

Data: 69, 73, 75, 82, 84, 88, 90, 91, 94, 95, 95, 99, 100, 100, 102, 105, 108, 108, 109, 109, 110, 110, 101, 111, 113, 113, 116, 117, 119, 121, 124, 126, 126, 126, 127, 128, 128, 133, 135, 146

Step4: Find Brand Y median

For n=40, median = average of 20th & 21st values:
$\text{Median}_Y = \frac{109 + 110}{2} = 109.5$

Step5: Analyze distribution shape

Brand X: Most data clustered at lower stems (6-10), tail right.
Brand Y: Data spread evenly, symmetric around center.

Step6: Check for outliers

Brand X: IQR = $Q_3 - Q_1 = 99 - 78 = 21$. Upper fence = $99 + 1.5\times21=130.5$. 146 > 130.5, so outlier.
Brand Y: IQR = $Q_3 - Q_1 = 126 - 95 = 31$. Upper fence = $126 + 1.5\times31=172.5$, lower fence = $95 - 1.5\times31=48.5$. All data within range, no outliers.

Answer:

Shape:

The shape of the distributions of battery lifespan (hours) for Brand X is right-skewed, and for Brand Y is roughly symmetric.

Center:

Brand X batteries tend not to last as long (median = 89.5 hours) as Brand Y batteries (median = 109.5 hours).

Outliers:

Brand X has one outlier at 146 hours; Brand Y has no outliers.