Question

question 1 - 6
chelsea received the following test scores in her algebra class: {77, 81, 81, 85, 89, 90, 93}
what are the mean, median, and mode of these test scores?
o mean: 85.14, median: 85, mode: 81
o mean: 85, median: 81, mode: 85.14
o mean: 81, median: 85.14, mode: 85
o mean: 81, median: 85, mode: 85.14

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 7$, and the data - set is $\{77,81,81,85,89,90,93\}$. So, $\sum_{i=1}^{7}x_i=77 + 81+81+85+89+90+93=596$, and $\bar{x}=\frac{596}{7}\approx85.14$.

Step2: Calculate the median

First, order the data - set: $\{77,81,81,85,89,90,93\}$. Since $n = 7$ (an odd number), the median is the middle value. The middle value is the 4th value when the data is ordered, so the median is $85$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. The number $81$ appears twice, and all other numbers appear only once, so the mode is $81$.

Answer:

mean: 85.14, median: 85, mode: 81