Question

some teenagers collected trash for a beach cleanup. the data for the number of pounds of trash collected by each teenager are shown below 26, 26, 21, 22, 20, 25, 35 what is the standard deviation of the data? 0 pounds 4.66 pounds 5.03 pounds 25.33 pounds

Explanation:

Step1: Calculate the mean

The mean $\bar{x}$ of a data set $x_1,x_2,\cdots,x_n$ is given by $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.
Here, $n = 7$, and $\sum_{i=1}^{7}x_i=26 + 26+21+22+20+25+35=175$.
So, $\bar{x}=\frac{175}{7}=25$.

Step2: Calculate the squared - differences

The formula for the squared - difference $(x_i-\bar{x})^2$:
For $x_1 = 26$: $(26 - 25)^2=1$; for $x_2 = 26$: $(26 - 25)^2=1$; for $x_3 = 21$: $(21 - 25)^2=16$; for $x_4 = 22$: $(22 - 25)^2=9$; for $x_5 = 20$: $(20 - 25)^2=25$; for $x_6 = 25$: $(25 - 25)^2=0$; for $x_7 = 35$: $(35 - 25)^2=100$.
The sum of squared - differences $\sum_{i = 1}^{n}(x_i-\bar{x})^2=1+1+16+9+25+0+100 = 152$.

Step3: Calculate the variance

The variance $s^2$ (for a sample, we use $n$ instead of $n - 1$ if we assume it's a population - like in basic standard deviation calculation for such problems) is $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n}$.
So, $s^2=\frac{152}{7}\approx21.71$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{s^2}$.
$s=\sqrt{\frac{152}{7}}\approx\sqrt{21.71}\approx4.66$.

Answer:

4.66 pounds