Practice: Calculate the standard deviation for the following results: 0.039, 0.061 and 5.3 x 10** ^{-2}**.

**Standard deviation** measures how close our numerical data points are to one another and to the “true” value.

Concept #1: Understanding Standard Deviation

Example #1: Calculate the standard deviation for the following results: 5.29, 5.35 and 5.31.

Practice: Calculate the standard deviation for the following results: 0.039, 0.061 and 5.3 x 10** ^{-2}**.

A student determined the percent water in a sample. In four trials, values of 16.145%, 16.160%, 16.156%, and 17.279% were obtained for the percent water in sample. What value should be used for the reported percent water?
(A) 16.154%
(B) 16.435%
(C) 16.145%
(D) 17.279%

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Calculate the average percentage for the first set of data.

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Precision can be judged by examining the average of the deviations from the average value for that data set. Calculate the average value of the absolute deviations of each measurement from the average for the first set.

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Calculate the average percentage for the second set of data

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Tell which set is the more accurate based on the average.

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students results for three determinations are as follows:
1. 22.52, 22.48, 22.54
2. 22.64, 22.58, 22.62Calculate the average value of the absolute deviations of each measurement from the average for the second set.

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows:1. 22.52, 22.48, 22.542. 22.64, 22.58, 22.62(b) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows:1. 22.52, 22.48, 22.542. 22.64, 22.58, 22.62(a) Calculate the average percentage for each set of data, and state which set is the more accurate based on the average.