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. on six tests you earn 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 mode
89, the mean

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 6$, and $x_{i}$ are the test scores: $89,91,85,87,89,89$.
$\sum_{i=1}^{6}x_{i}=89 + 91+85 + 87+89+89=520$.
$\bar{x}=\frac{520}{6}\approx87$.

Step2: Find the median

First, order the data set: $85,87,89,89,89,91$.
Since $n = 6$ (even), the median $M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}$.
$x_{3}=89$, $x_{4}=89$.
$M=\frac{89 + 89}{2}=89$.

Step3: Find the mode

The mode is the most - frequently occurring value. In the data set $85,87,89,89,89,91$, the mode is $89$.

Answer:

89, the mode