Question

1. your math teacher allows you to choose the most favorable measure of central tendency of your test scores to determine your grade for the term. do not include your scores of 89, 81, 85, 82, 89, and 89. what is your grade to the nearest whole number, and which measure of central tendency should you choose?

87; the median
91; the mode
89; the mean
89; the mode

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $x_{i}$ are the scores \(89,81,85,82,89,89\) and \(n = 6\).

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Step2: Calculate the median

First, order the data: \(81,82,85,89,89,89\). Since \(n = 6\) (even), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here, \(x_{3}=85\) and \(x_{4}=89\)

$$ M=\frac{85 + 89}{2}=\frac{174}{2}=87 $$

Step3: Calculate the mode

The mode is the most - frequently occurring value. The score \(89\) occurs \(3\) times, more frequently than other scores.

Answer:

A. 89; the mode