Since 1965, dimes are composed of copper with 25% nickel on the outside. A Roosevelt Type dime (1946 to 1964), designed by John R Sionockis, is composed of 90.0% silver and 10.0% copper. The composition changed when the dime cost more in silver than it was worth. A 1963 dime is weighed on ten different balances, and the mass is recorded. Balance Number Mass (g) = Xm d = Xm- d2
1 2.495 g
2 2.509 g
3 2.507 g
4 2.511 g
5 2.508 g
6 2.538 g
7 2.512 g
8 2.501 g
9 2.510 g
10 2.490 g
a) Solve for the average value, 8:
b) Fill in the chart for all the d and d2 values.
c) Solve for the standard deviation, s. S- n-1
d) Solve for the range, * +2s.
e) Check all data points against the range. Identify values outside the range that may be unreliable and discarded:
f) Do you suspect the differing values are due to random errors or systematic errors or possibly both? Explain. How might you test your hypothesis?
g) Solve for the new average value, I, removing values outside the range in part (e).