(08.06)Data are collected about the amount of time, in minutes, each member of the lacrosse team spends practicing. How does a single outlier change the mean of the collected data?

A single outlier causes the value of the mean to move slightly toward the outlier.

A single outlier causes the value of the mean to move slightly away from the outlier.

A single outlier does not affect the value of the mean.

A single outlier doubles the value of the mean.

A single outlier causes the value of the mean to move slightly toward the outlier.

Step-by-step explanation:

Hello!

The mean is a measurement of position, it gives you an idea of where the center of the data distribution lies. It is calculated as the summary of all observed values by the number of observations, X[bar]= ∑Xn, it takes a value within the range of definition of the variable but it does not necessarily coincide with an observed value. The mean is greatly affected by outliers, its value always moves in the direction of the outlier. And the greater is the value of the outlier is, the further away the mean is, regarding the rest of the observations.

Consider the following example,

You have the information about training time, in minutes, of 10 team members:

118, 120, 126, 131, 134, 137, 139, 146, 147, 148

The sample mean is X[bar]= ∑X/n= 1346/10= 134.6min

Now let's say that all members train the same except one that slacks off and train much less than the others:

34, 118, 120, 126, 131, 134, 137, 139, 146, 147

∑X/n= 1232/10= 123.2min

As you can see, the mean moved towards the extreme value.

I hope this helps!

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