Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
June 2015 p62 q3
2470
In an open-plan office there are 88 computers. The times taken by these 88 computers to access a particular web page are represented in the cumulative frequency diagram.
(i) On graph paper draw a box-and-whisker plot to summarise this information.An ‘outlier’ is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.
(ii) Show that there are no outliers.
Solution
(i) From the cumulative frequency diagram, determine the quartiles: \(Q_1 = 2.6\), \( median= 3.8 \text{ to } 3.85 \), \(Q_3 = 6.4 \text{ to } 6.6\). Draw a box-and-whisker plot using these values. Ensure the axis is labeled with time in seconds and is linear from 2 to 10.
(ii) Calculate the interquartile range (IQR): \(IQR = Q_3 - Q_1 = 6.5 - 2.6 = 3.9\).Calculate \(1.5 \times IQR = 1.5 \times 3.9 = 5.85\).Check for outliers: \(Q_1 - 5.85 = -3.25\) (negative, so no lower outliers) and \(Q_3 + 5.85 = 12.35\) (greater than 10, so no upper outliers).