Question

question 1 the following refer to the following data - set: 70 106.9 62.8 81.4 91.8 87.2 106.9 86.6 106.9 71.7 what is the mean of this data - set? mean = what is the median of this data - set? median =

Explanation:

Step1: Calculate the mean

First, sum all data values: $70 + 106.9+62.8 + 81.4+91.8+87.2+106.9+86.6+106.9+71.7=872.2$. There are $n = 10$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{872.2}{10}=87.22$.

Step2: Calculate the median

Arrange the data in ascending order: $62.8,70,71.7,81.4,86.6,87.2,91.8,106.9,106.9,106.9$. Since $n = 10$ (an even number of data - points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The median $M=\frac{86.6 + 87.2}{2}=86.9$.

Answer:

Mean: $87.22$, Median: $86.9$