some teenagers collected trash for a beach cleanup. the data for the number of pounds of trash collected by…

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

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

Answer

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{26 + 26+21+22+20+25+35}{7}=\frac{175}{7}=25$

Step2: Calculate the squared - differences

$(26 - 25)^2=1$, $(26 - 25)^2 = 1$, $(21 - 25)^2=16$, $(22 - 25)^2 = 9$, $(20 - 25)^2=25$, $(25 - 25)^2 = 0$, $(35 - 25)^2=100$

Step3: Calculate the variance

$s^{2}=\frac{1+1+16+9+25+0+100}{7}=\frac{152}{7}\approx21.71$

Step4: Calculate the standard deviation

$s=\sqrt{\frac{152}{7}}\approx4.66$

Answer:

4.66 pounds