for the data shown above, find the following.\nround answer in the first blank to 1 decimal place(s).\nin…

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. $n = 15$, and $\sum_{i=1}^{15}x_{i}=64 + 64+138+145+209+80+169+209+64+90+161+72+288+95+48=2005$ $\bar{x}=\frac{2005}{15}\approx133.7$

Step2: Calculate the median

First, order the data: $48,64,64,64,72,80,90,95,138,145,161,169,209,209,288$. Since $n = 15$ (odd), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{15+1}{2}=8$-th value, so the median is $95$.

Step3: Calculate the range

The range is the difference between the maximum and minimum values. Range$=288 - 48=240$

Step4: Calculate the variance

The variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$. $(x_1-\bar{x})^2=(64 - 133.7)^2=(-69.7)^2 = 4858.09$, $(x_2-\bar{x})^2=(64 - 133.7)^2=4858.09,\cdots$ $\sum_{i = 1}^{15}(x_{i}-\bar{x})^{2}=40089.2$ $s^{2}=\frac{40089.2}{14}\approx2863.5$

Step5: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}$. $s=\sqrt{2863.5}\approx53.5$

Answer:

Find the mean: $133.7$ km Find the median: $95.0$ km Find the range: $240.0$ km Find the variance: $2863.5$ $(km)^2$ Find the standard deviation: $53.5$ km