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 formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\).
Here \(n = 7\), \(x_{1}=26\), \(x_{2}=26\), \(x_{3}=21\), \(x_{4}=22\), \(x_{5}=20\), \(x_{6}=25\), \(x_{7}=35\).
\(\bar{x}=\frac{26 + 26+21+22+20+25+35}{7}=\frac{175}{7}=25\)

Step2: Calculate the variance

The formula for the variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n}\)
\((26 - 25)^{2}=1\), \((26 - 25)^{2}=1\), \((21 - 25)^{2}=16\), \((22 - 25)^{2}=9\), \((20 - 25)^{2}=25\), \((25 - 25)^{2}=0\), \((35 - 25)^{2}=100\)
\(s^{2}=\frac{1+1 + 16+9+25+0+100}{7}=\frac{152}{7}\approx21.71\)

Step3: Calculate the standard deviation

The formula for the standard deviation \(s=\sqrt{s^{2}}\)
\(s=\sqrt{\frac{152}{7}}\approx\sqrt{21.71}\approx4.66\)

Answer:

4.66 pounds