Question

The average mark of candidates in an aptitude test was 128.5 with a standard deviation of

8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the

extracted scores that are extreme values (outliers)?

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Answer 1

Explanation:

Hello!

The variable of interest is

X: mark obtained in an aptitude test by a candidate.

This variable has a mean μ= 128.5 and standard deviation σ= 8.2

You have the data of three scores extracted from the pool of aptitude tests taken.

148, 102, 152

An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.

Using the mean and the standard deviation, an outlier is any value that is three standard deviations away from the mean: μ±3σ

Using the population values you can calculate the limits that classify an observed value as outlier:

μ±3σ

128.5±3*8.2

(103.9; 153.1)

This means that any value below 103.9 and above 153.1 can be considered an outlier.

For this example, there is only one outlier, that this the extracted score 102

I hope this helps!