Question

Answer the following:

1a. What are the rules for counting significant figures?

1b. What are the rules of significant figures when multiplying or dividing numbers?

1c. What are the rules of significant figures when adding or subtracting numbers?

1d. What is the formula for an average?

1e. What is the formula for a standard deviation (assuming small sample size), also called the square root of the variance?

1f. How many significant figures should a standard deviation have?

1g. If you have an average which is 7.352 and a standard deviation which is 0.137, how would you report your average?

1h. In a statistics and error analysis, why is the result never just a number?

Answer 1

a)

RULES

1. All non-zero numbers ARE significant. The number 41.5 has THREE significant figures because all of the digits present are non-zero.

2. Zeros between two non-zero digits ARE significant. 3502has FOUR significant figures. The zero is between 5 and 2

Trailing zeros in a whole number with no decimal shown are NOT significant. 350 indicates that the zero is NOT significant, and there are only TWO significant figures in this value.

3. Leading zeros are NOT significant.-The number 0.61 has only TWO significant figures. 0.00079 also has TWO significant figures. All of the zeros are leading.

4. Trailing zeros to the right of the decimal ARE significant. There are four significant figures in 85.00.

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b)

Multiplication and division-The final answer is rounded to the least number of significant figures.

2.5 x 3.42=8.6

2.5 has two significant figures while 3.42 has three. Two significant figures is less precise than three, so the answer has two significant figures

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c)addition and subtraction: The final answer is rounded to the least precise decimal place.

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d)average=sum of all numbers in sample / total numbers

e)formula

formula for Sample Standard Deviation: