Question

this data is from a sample. calculate the mean, standard deviation, and coefficient of variation.
17.6, 22.9, 38.4, 11.8, 24.5, 30.1, 23.1, 23.7, 47.2
please show the following answers to 2 decimal places.
mean =
enter an integer or decimal number more..
standard deviation =
coefficient of variation = % (please enter a whole number.)

Explanation:

Step1: Calculate the mean

The formula for the sample mean $\bar{x}$ is $\bar{x} = \frac{\sum_{i = 1}^{n} x_i}{n}$, where $x_i$ are the data points and $n$ is the number of data points.
First, sum the data points: $17.6 + 22.9 + 38.4 + 11.8 + 24.5 + 30.1 + 23.1 + 23.7 + 47.2$.
Let's calculate the sum:
$17.6+22.9 = 40.5$; $40.5+38.4 = 78.9$; $78.9+11.8 = 90.7$; $90.7+24.5 = 115.2$; $115.2+30.1 = 145.3$; $145.3+23.1 = 168.4$; $168.4+23.7 = 192.1$; $192.1+47.2 = 239.3$.
There are $n = 9$ data points. So the mean $\bar{x}=\frac{239.3}{9}\approx26.59$.

Step2: Calculate the sample standard deviation

The formula for the sample standard deviation $s$ is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i - \bar{x})^2}{n - 1}}$.
First, calculate $(x_i - \bar{x})^2$ for each data point:

• For $x_1 = 17.6$: $(17.6 - 26.59)^2=(-8.99)^2 = 80.8201$
• For $x_2 = 22.9$: $(22.9 - 26.59)^2=(-3.69)^2 = 13.6161$
• For $x_3 = 38.4$: $(38.4 - 26.59)^2=(11.81)^2 = 139.4761$
• For $x_4 = 11.8$: $(11.8 - 26.59)^2=(-14.79)^2 = 218.7441$
• For $x_5 = 24.5$: $(24.5 - 26.59)^2=(-2.09)^2 = 4.3681$
• For $x_6 = 30.1$: $(30.1 - 26.59)^2=(3.51)^2 = 12.3201$
• For $x_7 = 23.1$: $(23.1 - 26.59)^2=(-3.49)^2 = 12.1801$
• For $x_8 = 23.7$: $(23.7 - 26.59)^2=(-2.89)^2 = 8.3521$
• For $x_9 = 47.2$: $(47.2 - 26.59)^2=(20.61)^2 = 424.7721$

Now sum these squared differences:
$80.8201+13.6161 = 94.4362$; $94.4362+139.4761 = 233.9123$; $233.9123+218.7441 = 452.6564$; $452.6564+4.3681 = 457.0245$; $457.0245+12.3201 = 469.3446$; $469.3446+12.1801 = 481.5247$; $481.5247+8.3521 = 489.8768$; $489.8768+424.7721 = 914.6489$.

Now, divide by $n - 1=8$: $\frac{914.6489}{8}=114.3311125$.

Take the square root: $s=\sqrt{114.3311125}\approx10.69$.

Step3: Calculate the coefficient of variation (CV)

The formula for the coefficient of variation is $CV=\frac{s}{\bar{x}}\times100\%$.
We have $s\approx10.69$ and $\bar{x}\approx26.59$.
So $CV=\frac{10.69}{26.59}\times100\%\approx40.20\%$, and as a whole number, it is $40\%$.

Answer:

Mean = $26.59$
Standard Deviation = $10.69$
Coefficient of Variation = $40$%