Introducci´on a la Estad´ıstica Curso 2012-2013 Fac. Comercio, Turismo y CC. Sociales Jovellanos
1. Two olympic athletes, Peter and Paul, recorded their 100m sprinting time in fifty rep-
etitions. Below, several statistics about the recorded times (in seconds) are provided:
arith. mean std. dev. percentile 25 percentile 50 percentile 75
Peter 10.30 0.06 10.26 10.31 10.34
Paul 10.22 0.10 10.15 10.22 10.29
Who has been more regular during the last 50 repetitions, Peter or Paul? Justify your
answer.
Solution.- Peter has been more regular than Paul (Peter’s sprint times have been less
spread out than those of Paul). We can note it by looking of the values of all the available
dispersion measures. The values of the standard deviation, coefficient of variation,
interquartile range and variance are lower in Peter’s records than in Paul’s ones. Those
values are provided below:
std. dev. I.R. C.V. Variance
Peter 0.06s 10.34s-10.26s=0.08s 0.06
10.30 ≈0.00583 0.036s2
Paul 0.10s 10.29s-10.15s=0.14s 0.10
10.22 ≈0.00978 0.01s2
2. A superstore has organized a prize draw. Prizes range from $5 to $100 and they are
distributed as follows:
•10 white gift cards, $5 each.
•5 red gift cards, $20 each.
•3 silver gift cards, $50 each.
•2 golden gift cards, $100 each.
(a) Complete the following table:
xiniNiPi(cum %) xiniPi
j=1 xjnjQi(cum. % of income)
5 10 10 50% 50 50 10%
20 5
50 3
100 2
Solution.- The complete table is:
xiniNiPi(cum %) xiniPi
j=1 xjnjQi(cum. % of income)
5 10 10 50% 50 50 10%
20 5 15 75% 100 150 30%
50 3 18 90% 150 300 60%
100 2 20 100% 200 500 100%
(b) How much money has been given out? (What has been the total amount of money
spent by the superstore?) The total amount of money is P4
j=1 xini= $500.
