alicia received the following seven scores on her math assignments. 80, 90, 10, 75, 90, 95, 99. find the…

alicia received the following seven scores on her math assignments. 80, 90, 10, 75, 90, 95, 99. find the mean and median. which measure of center best represents the data? the mean the median both the mean and the median neither the mean nor the median

alicia received the following seven scores on her math assignments. 80, 90, 10, 75, 90, 95, 99. find the mean and median. which measure of center best represents the data? the mean the median both the mean and the median neither the mean nor the median

Answer

Answer:

  1. Mean: 77
  2. Median: 90
  3. B. the median

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 7$, and $\sum_{i=1}^{7}x_{i}=80 + 90+10+75+90+95+99=539$. So, $\bar{x}=\frac{539}{7}=77$.

Step2: Calculate the median

First, order the data set: $10,75,80,90,90,95,99$. Since $n = 7$ (an odd number), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{7+1}{2}=4$-th value. So the median is 90.

Step3: Determine the best measure of center

The value 10 is an out - lier. The mean is affected by outliers, while the median is not. So the median best represents the data.