Question

A student determines the density of a chunk of metal to be 5.1 g/cm3. She then repeats the measurement four more times on the same chunk of metal and obtains values of 5.0, 4.9, 5.4, and 5.2 g/cm3 for the density. What is the standard deviation of the five measurements?

A. 0.148
B. 0.19
C. 0.037
D. 0.22
E. 0.17

Answer 1

E. 0.17

Explanation:

Mean:

Sum of all values divided by the number of values, so:

`\overline{x} = (5.1 + 5 + 4.9 + 5.4 + 5.2)/(5) = 5.12`

Standard deviation:

Square root of the sum of the difference squared between each value and the mean, divided by the sample size, so:

`s = \sqrt{((5.1-5.12)^2 + (5-5.12)^2 + (4.9-5.12)^2 + (5.4-5.12)^2 + (5.2-5.12)^2)/(5)} = 0.172`

Thus the correct answer is given by option E.