Question

latesh a and bernard are playing a game. their scores for five games are shown in the table. latesh as and bernards scores latesh as scores 92 45 67 36 80 bernards scores 63 68 62 69 53 which statement comparing the means to the ranges is true? the means differ by 1, but the ranges differ by 2. the means differ by 5, but the ranges differ by 2. the means differ by 1, but the ranges differ by 40. the means differ by 5, but the ranges differ by 40.

Explanation:

Step1: Calculate LaTasha's mean

The formula for the mean is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For LaTasha's scores \(x=\{92,45,67,36,80\}\), \(n = 5\).

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Step2: Calculate LaTasha's range

The range formula is \(R=\text{Max}-\text{Min}\). For LaTasha's scores, \(\text{Max}=92\), \(\text{Min}=36\).

$$R_{LaTasha}=92 - 36=56$$

Step3: Calculate Bernard's mean

For Bernard's scores \(x=\{63,68,62,69,53\}\), \(n = 5\).

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Step4: Calculate Bernard's range

For Bernard's scores, \(\text{Max}=69\), \(\text{Min}=53\).

$$R_{Bernard}=69 - 53 = 16$$

Step5: Compare means and ranges

The difference in means: \(|\bar{x}_{LaTasha}-\bar{x}_{Bernard}|=|64 - 63|=1\).
The difference in ranges: \(|R_{LaTasha}-R_{Bernard}|=|56 - 16|=40\).

Answer:

The means differ by 1, but the ranges differ by 40.