students in a science class roll a model car down a ramp. they repeat this process for 5 trials, recording…

Explanation:

Step1: Calculate the mean of the original data set

The original data set is (3,6,7,5,6). The mean (\bar{x}_1=\frac{3 + 6+7+5+6}{5}=\frac{27}{5} = 5.4).

Step2: Calculate the variance of the original data set

The variance (s_1^{2}=\frac{(3 - 5.4)^{2}+(6 - 5.4)^{2}+(7 - 5.4)^{2}+(5 - 5.4)^{2}+(6 - 5.4)^{2}}{5}) [ \begin{align*} &=\frac{(- 2.4)^{2}+(0.6)^{2}+(1.6)^{2}+(-0.4)^{2}+(0.6)^{2}}{5}\ &=\frac{5.76+0.36 + 2.56+0.16+0.36}{5}\ &=\frac{9.2}{5}=1.84 \end{align*} ] The standard - deviation (s_1=\sqrt{1.84}\approx1.36).

Step3: Calculate the mean of the new data set (after removing Trial 1)

The new data set is (6,7,5,6). The mean (\bar{x}_2=\frac{6 + 7+5+6}{4}=\frac{24}{4}=6).

Step4: Calculate the variance of the new data set

The variance (s_2^{2}=\frac{(6 - 6)^{2}+(7 - 6)^{2}+(5 - 6)^{2}+(6 - 6)^{2}}{4}) [ \begin{align*} &=\frac{(0)^{2}+(1)^{2}+(-1)^{2}+(0)^{2}}{4}\ &=\frac{0 + 1+1+0}{4}=\frac{2}{4}=0.5 \end{align*} ] The standard - deviation (s_2=\sqrt{0.5}\approx0.71).

Answer:

The standard deviation of the data will decrease if the Trial 1 value is removed. This is because the value of 3 in Trial 1 is an out - lier relative to the other values, and removing it makes the data more clustered around the mean.