Question

denise and sandra are playing a target game. the object of the game is to get an object as close to the center as possible. each players score is the number of inches away from the center. their scores are shown below.
denises scores: 112, 116, 125, 119, 131
sandras scores: 124, 120, 110, 126, 118
which explains who is winning the game?
denise is winning because she has the greater mean.
denise is winning because she is generally closer to the center.
sandra is winning because she has the greater mean.
sandra is winning because she is generally closer to the center.

Explanation:

Step1: Calculate Denise's mean

The formula for the mean is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Denise's scores \(x = [112,116,125,119,131]\), \(n = 5\).

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Step2: Calculate Sandra's mean

For Sandra's scores \(x=[124,120,110,126,118]\), \(n = 5\)

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Since \(120.6<121.6\), Sandra has a higher mean. But in the game, a lower score (closer to the center) is better.
Let's check the general closeness. We can also think about the sum of deviations from a central value (or just compare the means in the context of the game rules: lower score is better). Since \(120.6<121.6\), Denise has a lower mean (is generally closer to the center as \(120.6\) inches away on average compared to \(121.6\) inches for Sandra)

Answer:

Denise is winning because she is generally closer to the center.