1). Rata-rata (mean) dan standar deviasi (deviation) 2). Ketepatan (accuracy) dan ketelitian (precision)

Rata-rata (mean) The mean, X, is the numerical average obtained by dividing the sum of the individual measurements by the number of measurements

Table Berat Uang Koin What is the mean for the data in Table above? Answer: =

Standard Deviation) The absolute standard deviation, s, describes the spread of individual measurements about the mean Relative Standard Deviation X 100%

What are the standard deviation, the relative standard deviation, and the percent relative standard deviation for the data in Table above ? Table Berat Uang Koin

Hasil pengukuran berat koin bisa dituliskan sbb: Berat koin = 3.117±0.051g

Accuracy and Precision Much of science has to do with the collection and manipulation of quantitative or numerical data. Much of science has to do with the collection and manipulation of quantitative or numerical data. The value of computations using numerical data is greatly dependent on the accuracy and precision of that data. The value of computations using numerical data is greatly dependent on the accuracy and precision of that data.

Conceptual illustration Accuracy and Precision

Conceptual illustration Accuracy and Precision

Accuracy and precision can not be considered independently Accuracy and precision can not be considered independently A number can be accurate and not precise A number can be accurate and not precise A number can be precise and not accurate A number can be precise and not accurate A number can be precise and accurate A number can be precise and accurate

ACCURACY Accuracy can be defined as how close a number is to what it should be. Accuracy can be defined as how close a number is to what it should be. Accuracy is determined by comparing a number to a known or accepted value. Accuracy is determined by comparing a number to a known or accepted value. Assessing Accuracy

PRECISION Precision: The closeness of agreement between independent test results obtained under stipulated conditions repeatability: precision under similar conditions reproducibility: precision under different conditions

Assessing Precision Measurement of precision for a data set is the standard deviation ( s ) For data sets that have more than 20 points For data sets < 20 points Relative Standard Deviation X 100%

Example 1: How old are you? How old are you?  I am 22 years old (1)  I am 22 years and 8 months old (2)  I am 22 years, 8 months, and 5 days old (3)  I am 22 years, 8 months, 5 days, and 10 hours old (4)

Accuracy vs. Precision for Example 1 Statement (2) is more accurate and more precise that statement (1). Statement (2) is more accurate and more precise that statement (1). Statement (3) is more accurate and more precise than statement (2). Statement (3) is more accurate and more precise than statement (2). Statement (4) is more accurate and more precise than statement (3). Statement (4) is more accurate and more precise than statement (3).

Example 2: How long is a string ? How long is a string ?  Student A measures the string at 2.63 ± 0.02 m.  Using the same ruler, Student B measures the string at 1.98 ± 0.01 m.  Who is most precise?  Who is most accurate?

Accuracy vs. Precision for Example 2 The actual measurement is 2.65 m. The actual measurement is 2.65 m. Student A is fairly accurate and also very precise. Student A is fairly accurate and also very precise. Student B is very precise, however, he is not very accurate. The lack of accuracy is due to using the ruler incorrectly. Student B is very precise, however, he is not very accurate. The lack of accuracy is due to using the ruler incorrectly.

Example 3 Using a centigram balance, Using a centigram balance,  Student A measured a sample at 3 ±0 g.  Student B measured the same sample at 3.00 ±0.01 g.  Who is most precise?  Who is most accurate?

Accuracy vs. Precision for Example 3 The actual measurement is 3.01 g. The actual measurement is 3.01 g. Student A is reasonably accurate. He/She was not very precise because the balance was not capable of measuring to two decimal places. Student A is reasonably accurate. He/She was not very precise because the balance was not capable of measuring to two decimal places. Student B is much more accurate because of the precision of his/her measurement and closeness of her value to the actual value. Student B is much more accurate because of the precision of his/her measurement and closeness of her value to the actual value.