Question

Who do you calculate the %RSD ? calculate the %RSD to the correct number of sig. digits. to the correct number of sig. digits. 10.025, 10.025, 10.115, 10.251, 10.215, 10.151, 10.115

what does %RSD mean

Answer 1

Warning! Long Answer. Here's what I get.

Explanation:

The relative standard deviation (RSD) tells you whether the “regular” standard deviation of a collection of measurements is small or large in comparison with the mean of those measurements.

The formula for calculating the RSD is

`color(blue)(bar(ul(|color(white)(a/a)"RSD" = s/barx × 100%color(white)(a/a)|)))" "`

where

`s =`the standard deviation of the measurements
`barx =` the mean of the observations.

Your set of measurements is

`X = {10.025, 10.025, 10.115, 10.251, 10.215, 10.151, 10.115}`

Step 1. Calculate the mean of the values.

`barx = "10.025 + 10.025 + 10.115 + 10.25 + 10.215 + 10.151 + 10.115"/7 = 70.897/7 = 10.128`

Step 2. Calculate the standard deviation

The standard deviation represents the square-root of the average squared difference between each datum and the mean.

In symbols,

`s = sqrt(1/(n-1) sum_(i=1)^ncolor(white)(m)(x_i -barx)^2)`

Your calculator can probably do this calculation automatically.

However, we can set up a table to display the numbers it uses.

`ulbb(color(white)(mmmmmm)xcolor(white)(m)color(white)(mll)x-barxcolor(white)(m)(x_i -barx)^2)`
`color(white)(mmmmml)10.025color(white)(m)"-0.103"color(white)(mll)"0.010 638"`
`color(white)(mmmmml)10.025color(white)(m)"-0.103"color(white)(mll)"0.010 638"`
`color(white)(mmmmml)10.115color(white)(m)"-0.013"color(white)(mll)"0.000 173"`
`color(white)(mmmmml)10.251color(white)(ml)0.123color(white)(mll)"0.015 094"`

`color(white)(mmmmml)10.215color(white)(ml)0.087color(white)(mll)"0.007 544"`
`color(white)(mmmmml)10.151color(white)(ml)0.023color(white)(mll)"0.000 522"`
`color(white)(mmmmml)ul(10.115color(white)(m)"-0.013"color(white)(mll)"0.000 173")`
`color(white)(m)"Total" =70.897color(white)(mmmmmll)"0.044 783"`
`color(white)(m)"Mean"=10.128`

`s = sqrt(1/6 × "0.044 783") = 0.0863`

`"RSD" = 0.0863/10.128 × 100% = 0.85 %`

This RSD tells you that the regular standard deviation is less than 1 % of the average of your measurements.

An RSD of 1 % would probably be quite acceptable in an introductory chemistry course. It might not be acceptable at the third- or fourth-year level.