for the data shown, answer the questions, round to 1 decimal place.\nfind the mean\nfind the median\nfind…

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, $n = 7$, and $\sum_{i=1}^{7}x_{i}=12.3 + 8.1+16.4 + 20.5+22.3+25.3+11.3=116.2$. So, $\bar{x}=\frac{116.2}{7}\approx16.6$.

Step2: Calculate the median

First, order the data: $8.1,11.3,12.3,16.4,20.5,22.3,25.3$. Since $n = 7$ (odd), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{7+1}{2}=4$-th value. So the median is $16.4$.

Step3: Calculate the sample standard deviation

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$. $(12.3-16.6)^{2}=(-4.3)^{2}=18.49$; $(8.1 - 16.6)^{2}=(-8.5)^{2}=72.25$; $(16.4-16.6)^{2}=(-0.2)^{2}=0.04$; $(20.5 - 16.6)^{2}=(3.9)^{2}=15.21$; $(22.3-16.6)^{2}=(5.7)^{2}=32.49$; $(25.3-16.6)^{2}=(8.7)^{2}=75.69$; $(11.3-16.6)^{2}=(-5.3)^{2}=28.09$. $\sum_{i = 1}^{7}(x_{i}-\bar{x})^{2}=18.49+72.25 + 0.04+15.21+32.49+75.69+28.09=242.26$. $s=\sqrt{\frac{242.26}{7 - 1}}=\sqrt{\frac{242.26}{6}}\approx6.4$.

Answer:

Mean: $16.6$ Median: $16.4$ Sample standard deviation: $6.4$