Answer :

According to the 1.5 × IQR rule, there are zero outliers in the given data set (167, 180, 188, 177, 181, 185, 189)

To calculate the number of outliers in the given set of data we need to establish data central tendency and dispersion. We may calculate the mean, median, and interquartile range (IQR).

To calculate the mean value first sum all the values and then divide it by the number of values-(167 + 180 + 188 + 177 + 181 + 185 + 189) / 7 = 180.

In this case, the Median is 181, it is the midpoint where data is arranged in ascending order.

For calculating IQR value, we need to arrange the data set value in ascending order which is -167, 177, 180, 181, 185, 188, 189. The first quartile is the median of the lower half which is-(167 + 177) / 2 = 172 and the third quartile is the median of the upper half which is- (185 + 188) / 2 = 186. So the IQR value is 186 - 172 = 14.

According to the question, the lower outlier threshold is 172 - 1.5 * 14 = 151 and the upper outlier threshold is 186 + 1.5 × 14 = 207, As we know the outlier is defined as any result that is less than Q1 - 1.5 × IQR and larger than Q3 + 1.5 × IQR.

By observing the given data set we cannot see any number below 151 and above 207. As a result, there are no outliers in the given data set.

To know about the 1.5×IQR rule refers to:

https://brainly.com/question/29069084

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