Question

the coefficient of variation cv describes the standard variation for each sample data set. what can you co
cv = \frac{standard deviation}{mean} \cdot 100%
click the icon to view the data sets.
cv_{heights} = % (round to the nearest tenth as nee
data table

heights	weights
73	227
79	223
73	187
74	179
77	190
80	170
68	191
80	221
67	206
72	203
75	206

Explanation:

Step1: Calculate the mean of heights

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the height - values and $n = 15$.
$\sum_{i=1}^{15}x_{i}=77 + 73+79+73+74+77+80+68+80+67+72+75 = 1093$
$\bar{x}=\frac{1093}{15}\approx72.87$

Step2: Calculate the standard - deviation of heights

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$.
First, calculate $(x_{i}-\bar{x})^{2}$ for each $x_{i}$:
$(77 - 72.87)^{2}=(4.13)^{2}=17.0569$
$(73 - 72.87)^{2}=(0.13)^{2}=0.0169$
$\cdots$
$\sum_{i = 1}^{15}(x_{i}-\bar{x})^{2}=293.7333$
$s=\sqrt{\frac{293.7333}{14}}\approx4.58$

Step3: Calculate the coefficient of variation

Using the formula $CV=\frac{s}{\bar{x}}\times100\%$, substitute $s\approx4.58$ and $\bar{x}\approx72.87$.
$CV=\frac{4.58}{72.87}\times100\%\approx6.3\%$

Answer:

$6.3$