find the mean, median, and modes of the data set: 91, 93, 89, 97, 89, 98, 94, 93. (2 points)\nthe mean is…

Explanation:

Step1: Calculate the mean

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, $n = 8$, and $\sum_{i=1}^{8}x_{i}=91 + 93+89+97+89+98+94+93=744$. So, $\bar{x}=\frac{744}{8}=93$.

Step2: Arrange data for median

Arrange the data in ascending order: $89,89,91,93,93,94,97,98$. Since $n = 8$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 93 and the 5th value is 93. So, the median $=\frac{93 + 93}{2}=93$.

Step3: Find the mode

The mode is the value(s) that occur most frequently in the data - set. The number 89 appears 2 times and 93 appears 2 times, and other numbers appear only once. So the modes are 89 and 93.

Answer:

The mean is 93. The median is 93. The first mode in the data set is 89. The second mode in the data set is 93.