4. In a study of how students use their mobile telephones, the phone usage of a random sample of 11 students was examined for a particular week.
The total length of calls, \(y\) minutes, for the 11 students were
$$17,23,35,36,51,53,54,55,60,77,110$$
- Find the median and quartiles for these data.
A value that is greater than \(Q _ { 3 } + 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\) or smaller than \(Q _ { 1 } - 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\) is defined as an outlier.
- Show that 110 is the only outlier.
- Using the graph paper on page 15 draw a box plot for these data indicating clearly the position of the outlier.
The value of 110 is omitted.
- Show that \(S _ { y y }\) for the remaining 10 students is 2966.9
These 10 students were each asked how many text messages, \(x\), they sent in the same week.
The values of \(S _ { x x }\) and \(S _ { x y }\) for these 10 students are \(S _ { x x } = 3463.6\) and \(S _ { x y } = - 18.3\).
- Calculate the product moment correlation coefficient between the number of text messages sent and the total length of calls for these 10 students.
A parent believes that a student who sends a large number of text messages will spend fewer minutes on calls.
- Comment on this belief in the light of your calculation in part (e).
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