denise and sandra are playing a target game. the object of the game is to get an object as close to the…

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.\ndenises scores: 112, 116, 125, 119, 131\nsandras scores: 124, 120, 110, 126, 118\nwhich explains who is winning the game?\ndenise is winning because she has the greater mean.\ndenise is winning because she is generally closer to the center.\nsandra is winning because she has the greater mean.\nsandra is winning because she is generally closer to the center.

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.\ndenises scores: 112, 116, 125, 119, 131\nsandras scores: 124, 120, 110, 126, 118\nwhich explains who is winning the game?\ndenise is winning because she has the greater mean.\ndenise is winning because she is generally closer to the center.\nsandra is winning because she has the greater mean.\nsandra is winning because she is generally closer to the center.

Answer

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). [ \begin{align*} \bar{x}_{Denise}&=\frac{112 + 116+125+119+131}{5}\ &=\frac{603}{5}\ & = 120.6 \end{align*} ]

Step2: Calculate Sandra's mean

For Sandra's scores (x=[124,120,110,126,118]), (n = 5) [ \begin{align*} \bar{x}_{Sandra}&=\frac{124+120 + 110+126+118}{5}\ &=\frac{608}{5}\ &=121.6 \end{align*} ] 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.