Exact and grouped call-duration statistics

Exact and grouped call-duration statistics

Secondary 2
TGM Original Questions

Call durations (min) are 2,4,5,5,7,8,9,10,12,13,15,15,18,20.

  1. Find the exact mean, median and mode(s).
  2. Group them into \(0<t\le5,5<t\le10,10<t\le15,15<t\le20\), state the frequencies, draw a histogram, and estimate the mean using midpoints. Compare the estimate with the exact mean.
  3. Find \(P(t>10)\) and \(P(5\le t\le15)\).
  4. For 14 calls per day over 14 days, estimate how many exceed 15 min.

Solution:

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Answer:(a) mean \(143/14\), median \(9.5\), modes \(5,15\); (b) histogram heights \(4,4,4,2\), estimate \(125/14\approx8.93\), about \(1.29\) below exact; (c) \(3/7,5/7\); (d) \(28\).

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