6-23. The f ollowing data are the numbers of cycles to fail- ure of aluminum tes

Question

6-23. The f ollowing data are the numbers of cycles to fail- ure of aluminum test coupons subjected to repeated alternating stress at 144,790 kN/m, 18 cycles per second. 1115 865 1015 885 1594 1000 1416 1501 1310 2130 845 1223 2023 1820 1560 1238 1540 1421 1674 375 1315 1940 1055 990 1502 1109 1016 2265 1269 1120 1764 1468 1258 1481 1102 1910 1260 910 1330 1512 1315 1567 1605 1018 1888 1730 1608 1750 1085 1883 706 1452 1782 1102 1535 1642 798 1203 2215 1890 1522 1578 1781 1020 1270 785 2100 1792 758 1750 Construct a stem-and-leaf display for these data. Calculate the median and quartiles of these data. Does it appear likely that a coupon w ive" beyond 1500 cycles? Justify your answer.

Explanation / Answer

A)

Stem-and-Leaf Display: data

Stem-and-leaf of data : N = 70
Leaf Unit = 100

1    0 3
1    0
5    0 7777
10   0 88899
22   1 000000011111
33   1 22222223333
(15) 1 444445555555555
22   1 66667777777
11   1 888899
5    2 011
2    2 22

B)

median(Q2)=1436.5

Q1 =1097.8

Q3=1735

C) Now we can see that out of 70 data points 32 of them will survive beyond 1500 cycles. So probability of survival beyond 1500 cycles is=32/70= 0.46 which is less than 0.5. Thus it means that this possibility is moderate. It can happen or it cannot happen. [Since probability is close to 1/2]

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