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I am confused on the correct answers to this problem.

The data is given by the age of the first 44 presidents upon inauguration -$(57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,51,47,55,55,54,42,51,56,55,51,54,51,60,61,43,55,56,61,52,69,64,46,54,47)$

1.For 1. would the answer be $.2$ or $.22$? Where should I read the value off on the graph? I know the cumulative distribution function is right continuous and if $F$ is the cumulative distribution function then $F_{44}(50)=\frac{1}{44}\{\text{number of observations less than or equal to 50}\}$. I'm guessing it should be around $.22$.

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Any suggestions?

  1. Again I am confused because of the right continuity of the graph. Would the answer be $.2$ or $.22$? I am guessing it should be exactly $.2$.

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  1. I suppose the answer would be about $51$ based on the graph. Is this correct?

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ernesto
  • 549

1 Answers1

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For a discrete random variable (which is the case here) the vertical rise at a point on the x-axis is the probability of observing that point, and a flat line means that the probability of those values is $0$. Using this information, the proportion that was 50 years old or younger should be counted from the top of the 50-year-old vertical line (so approximately 22% as you say). The fraction older than 60 should be the space from the top of the cdf (e.g. 1) to the top of the vertical line at 60, so say approximately 20%. Finally, I believe your answer for c is correct, and any age 51 or younger would be in the lower 1/3 of presidential ages.

Vons
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