Question

consider the following sets of sample data:
a: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312
b: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41

step 1 of 2: for each of the above sets of sample data, calculate the coefficient of variation, cv. round to one decimal place.

answer
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cv for data set a: ______ %
cv for data set b: ______ %

Explanation:

Step1: Calculate mean of Set A

First, sum all values in Set A, then divide by the number of values ($n=15$):
Sum = $431+447+306+413+315+432+312+387+295+327+323+296+441+312 = 5537$
$\bar{x}_A = \frac{5537}{15} \approx 369.1333$

Step2: Calculate sample std dev of Set A

Use sample standard deviation formula: $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$
After calculation, $s_A \approx 61.224$

Step3: Compute CV for Set A

CV = $\frac{s}{\bar{x}} \times 100\%$
$CV_A = \frac{61.224}{369.1333} \times 100\% \approx 16.6\%$

Step4: Calculate mean of Set B

Sum all values in Set B, divide by $n=11$:
Sum = $1.35+1.82+1.82+2.72+1.07+1.86+2.71+2.61+1.13+1.20+1.41 = 19.70$
$\bar{x}_B = \frac{19.70}{11} \approx 1.7909$

Step5: Calculate sample std dev of Set B

Using sample standard deviation formula, $s_B \approx 0.602$

Step6: Compute CV for Set B

$CV_B = \frac{0.602}{1.7909} \times 100\% \approx 33.6\%$

Answer:

CV for Data Set A: 16.6 %
CV for Data Set B: 33.6 %