Question

students in a science class roll a model car down a ramp. they repeat this process for 5 trials, recording the number of whole feet the car travels during each trial in the table below.
the students want to count the first trial as practice and remove its value from the data set. how will the standard deviation of the data in the table change if they remove the trial 1 value? use the drop - down menus to explain.

feet traveled	trial 1	trial 2	trial 3	trial 4	trial 5

model car trials

click the arrows to choose an answer from each menu.

the standard deviation of the data will choose... if the trial 1 value is removed. this is because choose... .

Explanation:

Step1: Calculate mean with all data

Data: 3, 6, 7, 5, 6. Mean $\mu_1 = \frac{3 + 6 + 7 + 5 + 6}{5} = \frac{27}{5} = 5.4$.
Deviations squared: $(3 - 5.4)^2 = 5.76$, $(6 - 5.4)^2 = 0.36$, $(7 - 5.4)^2 = 2.56$, $(5 - 5.4)^2 = 0.16$, $(6 - 5.4)^2 = 0.36$.
Variance $\sigma_1^2 = \frac{5.76 + 0.36 + 2.56 + 0.16 + 0.36}{5} = \frac{9.2}{5} = 1.84$.
Standard deviation $\sigma_1 = \sqrt{1.84} \approx 1.356$.

Step2: Calculate mean without Trial 1

Data: 6, 7, 5, 6. Mean $\mu_2 = \frac{6 + 7 + 5 + 6}{4} = \frac{24}{4} = 6$.
Deviations squared: $(6 - 6)^2 = 0$, $(7 - 6)^2 = 1$, $(5 - 6)^2 = 1$, $(6 - 6)^2 = 0$.
Variance $\sigma_2^2 = \frac{0 + 1 + 1 + 0}{4} = \frac{2}{4} = 0.5$.
Standard deviation $\sigma_2 = \sqrt{0.5} \approx 0.707$.

Step3: Compare standard deviations

$\sigma_2 < \sigma_1$, so standard deviation decreases. Trial 1 (3) is an outlier (far from other values: 5, 6, 6, 7), removing it reduces data spread.

Answer:

The standard deviation of the data will decrease if the Trial 1 value is removed. This is because removing the outlier (Trial 1) reduces the spread of the data.