Students collected mass data for a group of coins. the mass of a single coin is 5.00 g. determine the accuracy and precision of the measurements.

Accuracy is how close a measurement nears the one recorded in the CRC Handbook.Values recorded in CRC Handbook were determined by many scientists.

Precision is how close  a measurement nears another measurement .We use standard deviation method to find precision.High standard deviation means low precision and low standard deviation indicates high precision

You determine if a value is accurate by comparing it to the accepted value.First find the difference between the experimental value and the accepted value (error) .Divide this value by the accepted value and multiply by 100% to get the percent error in the values.

%Error= (Experimental value-Accepted value)/accepted value × 100%

Precision is calculated by finding the average of the experimental values then subtracting the average from each measurement.These deviations are averaged to give the uncertainty value.plus or minus the uncertainty value says how precise a measurement is.

Given the mass of a single coin is 5.0g

For 5 coins, accuracy in mass will be

Actual mass will be = 5×5=25g

Experimental value is= 23.2

Error= 23.2-25.0=-1.8

%error= -1.8/25 *100 = -7.2%

For 10 coins,accuracy in mass will be

Actual mass= 5*10=50g

Experimental mass=54.5g

Error=54.5-50.0=4.5

%error= 4.5/50 *100= 9%

For 20 coins, accuracy in mass will be

Actual mass = 5*20 =100g

Experimental mass= 105.9

Error=105.9-100=5.9g

%Error= 5.9/100 *100 =5.9%

For 30 coins, accuracy in mass will be;

Actual mass=5*30=150g

Experimental mass=154.5g

Error=154.5-150=4.5

%Error=4.5/150 *100=3%

For 50 coins, accuracy in mass will be;

Actual mass=5*50=250g

Experimental mass=246.2g

Error=246.2-250= -3.8

%Error= -3.8/250 *100 = 1.52%

2. Precision

Finding the average of the Experimental values;

sum =23.2+54.5+105.9+154.5+246.2=584.3g

Number of values=5

Average=sum/number of values =584.3/5=116.86g

Subtracting the average from each measurement

23.2-116.86= -93.66

54.5-116.86= -62.36

105.9-116.86= -10.96

154.5-116.86=-37.64

246.2-116.86=-129.34

Find average of deviations to get uncertainty

-93.66-62.36-10.96+37.64+129.34=0

The precision of these set of measurements is 0