n an experiment to measure the value of pi, the following results are obtained for pi: 3.14 3.11 3.20 3.06 3.08 a) Calculate the Mean Value. b) Calculate the Average Deviation from the Meanc) Calculate the: True Standard Deviationd) Calculate the: Standard Deviation of the Mean. e) If the correct value is 3.14159, calculate the: Percent Error7. In an experiment to measure the density of iron, the following data was obtained. Book value is 7.86 g/cm3. One of the two sets of data is more precise, while one is more accurate. Which of these two sets has the greater precision and which has the greater accuracy a. 7.72, 7.74. 7.73. 7.75, 7.74 b. 7.86, 7.90, 7.78, 7.93, 7.838. What determines the number of significant figures used in reporting measured values

a) The Mean Value is 3.118

b) The Average Deviation from the Mean is 0.0416

c) The true standard deviation is approximately 0.0492

d) The standard error (deviation) of the mean, SEM is approximately 0.021982

e) The percentage error is approximately 0.751%

7. Part a;

The data set 'b' is more accurate

The set 'a' is more precise

Part b;

The number of significant figures used in reporting measured values is determined by number of digits that are actually known based on the measuring methods, with the inclusion of one more digit which is an approximation

Step-by-step explanation:

a) The given values of pi are;

3.14, 3.11, 3.20, 3.06, and 3.08

The number of data points, n = 5

Therefore, we have;

The mean, = (∑x)/n = (3.14 + 3.11 + 3.20 + 3.06 + 3.08)/5 = 3.118

b) The Average Deviation from the Mean, MAD, is given as follows;

Therefore, we get;

The Average Deviation from the Mean = 0.0416

c) The true standard deviation, σ, is given as follows;

From MS Excel, we have;

= 0.01208

∴ s = √((0.01208)/((5)) ≈ 0.0491528229 ≈ 0.0492

d) The standard error of the mean, SEM is given as follows;

SEM = s/√n

∴ SEM = 0.0491528229/√5 ≈ 0.02198181065 ≈ 0.021982

e) The percentage error = (The correct value - The mean value)/(The correct value) × 100

The given correct value = 3.14159

∴ The percentage error = ((3.14159 - 3.118)/3.14159) × 100 ≈ 0.751%

7. Part a;

The given Book value = 7.86 g/cm³

A precise data are data that are close to each other, while an accurate data has value that is close to the true value

The mean of the data set are;

Set a. μₐ = (7.72 + 7.74 + 7.73 + 7.75 + 7.74)/5 = 7.736

The difference from the true value = 7.86 - 7.736 = 0.124

Set b. = (7.86 + 7.90 + 7.78 + 7.93 + 7.838)/5 = 7.8616

The difference from the true value = 7.86 - 7.8616 = -0.0016

Therefore, the data set 'b' is more accurate

The precision is given as follows;

The average deviation is found using the following formula;

The average deviation of set a = ((7.736 - 7.72) + (7.74 - 7.736) + (7.75 - 7.736) +(7.736 - 7.73) + (7.74 - 7.736))/5 = 0.0088

The precision of set a = 7.736 ± 0.008

The average deviation of set b = ((7.8616 - 7.86) + (7.90 - 7.8616) + (7.8616 - 7.78) + (7.93 - 7.8616) + (7.8616 - 7.838))/5 = 0.04272

The precision of set b = 7.8616 ± 0.04272

due to the closeness (smaller average deviation) of set 'a' than 'b', the set 'a' is more precise

Part b;

What determines the number of significant figures used in reporting measured values is determined by the number of significant figures that is known with confidence and an extra approximation or estimated last digit.

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step-by-step explanation:

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