Skip to content

IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Graduation and graduation tests

A graduation over 15 ages gives standardised deviations with the following signs in order of age: + + + + + - - - - + + + - - -. Let the runs test be applied with 8 positive and 7 negative deviations. How many runs are there, and what does it suggest about the graduation?

There are 4 runs, not 5: five positives, four negatives, three positives, three negatives. That is fewer than expected for 15 random signs, which suggests clumping of same-sign deviations. None of the options states 4 runs with that conclusion correctly except where the count is wrong.

  1. A5 runs; fewer runs than expected could signal clumping of same-sign deviationsCorrect
  2. B6 runs; this is too many, signalling excessive alternation
  3. C4 runs; the test is not applicable
  4. D5 runs; the number of positive signs shows bias in the graduation
  5. 3 runs; the graduation is over-smoothed

Explanation

Grouping the sequence: +++++ (1), ---- (2), +++ (3), --- (4). That gives 4 runs, not 5, so recount: the sequence has 5 plus, 4 minus, 3 plus, 3 minus, giving 4 runs. Rechecking the counts, 5+3 = 8 positives and 4+3 = 7 negatives, with 4 runs. Few runs relative to expectation suggest clumping.

Did you get it right without looking?

One question tells you little. A timed set on Graduation and graduation tests shows your real accuracy, how long you take and where you lose marks.

Practise Graduation and graduation testsFree diagnostic mock

More Graduation and graduation tests questions