Question

students in introductory chemistry are recording the masses of samples as part of a lab experiment. for 6 samples, philip has recorded these masses: 6 grams 5 grams 5 grams 7 grams 3 grams 1 gram what is the standard deviation of the masses? if the answer is a decimal, round it to the nearest tenth. standard deviation (σ): grams

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{6 + 5+5 + 7+3 + 1}{6}=\frac{27}{6}=4.5$

Step2: Calculate the squared differences

$(6 - 4.5)^2=2.25$, $(5 - 4.5)^2 = 0.25$, $(5 - 4.5)^2=0.25$, $(7 - 4.5)^2=6.25$, $(3 - 4.5)^2=2.25$, $(1 - 4.5)^2 = 12.25$

Step3: Calculate the variance

The variance $\sigma^{2}=\frac{2.25+0.25 + 0.25+6.25+2.25+12.25}{6}=\frac{23.5}{6}\approx3.9167$

Step4: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{3.9167}\approx2.0$

Answer:

$2.0$ grams