Problems A
59
Calculator Tips
Equation 5-3, which defines the standard deviation, can be rewritten in the form
The advantage of this form is that you need not find the average before proceeding to find the deviations. If you use a calculator that doesn't have a built-in
program for finding . s and x directly, you can easily enter each of your measurements in a way that accumulates tx t in one memory storage and ^,x'\ in
another. After entering all of the data, you can use S.v, and tx'] in Equation 5-7
to get s, and furthermore you can divide ~S,x t by n to obtain x, even though you
didn't have to find it to calculate s.
EPILOGUE
In an age requiring closer looks at the factors that affect our health, safety,
environment, and life style, it will become more and more important to examine
carefully and intelligently the statistical significance of the data on which important decisions are based. The intelligent use of your calculator can be of enormous help in these kinds of evaluations. You must always resist the urge to
include far more figures in your reported results than the data justify. Calculations and computers cannot improve experimental reliability, and it is your
responsibility to round off the final answer to the proper number of significant
figures.
PROBLEMS A
1. State the number of significant figures in each of the following measurements.
(a) 374; (b) 0.0374; (c) 3074; (d) 0.0030740; (e) 3740 (f) 3.74 x 10
5
; (g) 75
million; (h) 21 thousand; (i) 6 thousandths; (j) 2 hundredths.
2. Express the answer in each of the following calculations to the proper number
of significant figures (assume that the numbers represent measurements).
(a) 3.196 + 0.0825 + 12.32 + 0.0013
(b) 721.56 - 0.394
(c) 525.3 + 326.0 + 127.12 + 330.0
(d) 5.23 x 10~
J + 6.01 x 1Q-" + 8 x K)-1 + 3.273 x 10~3.21 x 432 x 650
(f)
563
8.57 x IP'
2 x 6.02 x 10*' x 2.543
361 x 907
59
Calculator Tips
Equation 5-3, which defines the standard deviation, can be rewritten in the form
The advantage of this form is that you need not find the average before proceeding to find the deviations. If you use a calculator that doesn't have a built-in
program for finding . s and x directly, you can easily enter each of your measurements in a way that accumulates tx t in one memory storage and ^,x'\ in
another. After entering all of the data, you can use S.v, and tx'] in Equation 5-7
to get s, and furthermore you can divide ~S,x t by n to obtain x, even though you
didn't have to find it to calculate s.
EPILOGUE
In an age requiring closer looks at the factors that affect our health, safety,
environment, and life style, it will become more and more important to examine
carefully and intelligently the statistical significance of the data on which important decisions are based. The intelligent use of your calculator can be of enormous help in these kinds of evaluations. You must always resist the urge to
include far more figures in your reported results than the data justify. Calculations and computers cannot improve experimental reliability, and it is your
responsibility to round off the final answer to the proper number of significant
figures.
PROBLEMS A
1. State the number of significant figures in each of the following measurements.
(a) 374; (b) 0.0374; (c) 3074; (d) 0.0030740; (e) 3740 (f) 3.74 x 10
5
; (g) 75
million; (h) 21 thousand; (i) 6 thousandths; (j) 2 hundredths.
2. Express the answer in each of the following calculations to the proper number
of significant figures (assume that the numbers represent measurements).
(a) 3.196 + 0.0825 + 12.32 + 0.0013
(b) 721.56 - 0.394
(c) 525.3 + 326.0 + 127.12 + 330.0
(d) 5.23 x 10~
J + 6.01 x 1Q-" + 8 x K)-1 + 3.273 x 10~3.21 x 432 x 650
(f)
563
8.57 x IP'
2 x 6.02 x 10*' x 2.543
361 x 907