Question

(1 point) the following are boxplots of the numbers of hits at a certain website for the different days of the week. it is found that the number of hits on friday apr 9 was mistakenly recorded. the correct figure should be 1400 hits. how will the iqr change corrected? a. the iqr will stay the same. b. the iqr will increase. c. the iqr will decrease.

Explanation:

The Inter - Quartile Range (IQR) is calculated as \(IQR = Q_3 - Q_1\), where \(Q_1\) is the first quartile (the median of the lower half of the data) and \(Q_3\) is the third quartile (the median of the upper half of the data). An outlier or a single data point correction (when the data point is an outlier or not affecting the quartiles) does not change the values of \(Q_1\) and \(Q_3\) because quartiles are based on the order of the data and the division of the data set into four equal - sized parts. In this case, the correction of the number of hits on Friday (a single data point) will not change the positions of \(Q_1\) and \(Q_3\) in the data set of website hits per day of the week. So, the IQR, which depends on \(Q_3\) and \(Q_1\), will stay the same.

Answer:

A. The IQR will stay the same.