Question

select the outlier in the data set.
40 50 58 61 62 76 78 214
if the outlier were removed from the data set, would the mean increase or decrease?
increase decrease
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Explanation:

Step1: Identify the outlier

An outlier is a data point that is significantly different from other data points. In the data set \(40,50,58,61,62,76,78,214\), \(214\) is much larger than the other values.

Step2: Analyze the effect on the mean

The mean of a data set is calculated as \(\text{Mean}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Let \(n = 8\) and the sum of the original data set \(S_{1}=40 + 50+58+61+62+76+78+214=639\), so the original mean \(\bar{x}_{1}=\frac{639}{8}=79.875\).
If we remove the outlier (\(214\)), \(n = 7\) and the new sum \(S_{2}=40 + 50+58+61+62+76+78=425\), the new mean \(\bar{x}_{2}=\frac{425}{7}\approx60.71\)

Answer:

The outlier is \(214\). If the outlier were removed, the mean would decrease.