# the impact of an outlier on the mean

Given a sample of 50 IQ scores ranging from 80 to 145, if the 145 were accidentally typed in error as a 415, what would be the impact on the following statistics? (Answer with increase, decrease or remains the same.)

The mean.

The median.

The standard deviation.

The range.

https://brainmass.com/statistics/dispersion-and-spread-of-data/impact-outlier-mean-183525

#### Solution Preview

The 50 IQ scores are first listed from small to larger as x1, x2, ..., x50

where x1 = 80, and x50 = 145

However, x50 = 415 now.

1) the mean: increase

the mean = (x1 + x2 + ... + x49 + x50) / 50 = (x1 + x2 + ... + x49 ) / 50 + x50/50

since x50 is larger, ...

#### Solution Summary

It analyzes how an outliner in an IQ scores samples impacts the mean, median, standard deviation, and range.

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