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

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. model car trials table with trial 1: 3, trial 2: 6, trial 3: 7, trial 4: 5, trial 5: 6 for feet traveled 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...

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. model car trials table with trial 1: 3, trial 2: 6, trial 3: 7, trial 4: 5, trial 5: 6 for feet traveled 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...

Answer

Explanation:

Step1: Recall Standard Deviation Concept

Standard deviation measures the spread of data from the mean. A lower spread (less variation) means a smaller standard deviation, and vice versa.

Step2: Analyze Original Data (Including Trial 1)

Data: ( 3, 6, 7, 5, 6 ) Mean ((\mu_1)): ( \frac{3 + 6 + 7 + 5 + 6}{5} = \frac{27}{5} = 5.4 ) Deviations from mean: ( |3 - 5.4| = 2.4 ), ( |6 - 5.4| = 0.6 ), ( |7 - 5.4| = 1.6 ), ( |5 - 5.4| = 0.4 ), ( |6 - 5.4| = 0.6 ) These deviations contribute to the spread. The value ( 3 ) is far from the mean, increasing the spread.

Step3: Analyze Data Without Trial 1

New data: ( 6, 7, 5, 6 ) Mean ((\mu_2)): ( \frac{6 + 7 + 5 + 6}{4} = \frac{24}{4} = 6 ) Deviations from mean: ( |6 - 6| = 0 ), ( |7 - 6| = 1 ), ( |5 - 6| = 1 ), ( |6 - 6| = 0 ) The deviations are smaller and more consistent (less spread) without the outlier ( 3 ).

Step4: Determine Change in Standard Deviation

Since removing ( 3 ) (an outlier) reduces the spread of the data around the mean, the standard deviation will decrease. This is because standard deviation is sensitive to outliers; removing an outlier that is far from the mean reduces the overall variation in the data set.

Answer:

The standard deviation of the data will decrease if the Trial 1 value is removed. This is because the value ( 3 ) (from Trial 1) is an outlier that increases the spread of the data; removing it reduces the variation in the data set.