Estimation of Errors

The best estimate (mean) of repeated readings: 

\[\mathrm{mean~}a=\frac{a_1+a_2+\cdots+a_n}{n}\]

Aim: Measure the external diameter (the outside width) of the cylinder. 

Required Equipment: 

Object: A hollow cylinder (like a pipe or a tube). 

Tool: A Vernier calliper. Think of this as a very precise ruler that can measure tiny fractions of a centimetre. This specific tool can measure down to a detail of 0.01 cm (this is called the least count). 

Procedure: 

Step 1: Taking the Measurements 

• You must measure the width of the cylinder in three different places.
• Why? Because the cylinder might not be perfectly round or the measurement might change slightly depending on where you measure it. Taking three readings helps make sure your final result is reliable. 

Step 2: Finding the Average Width (Mean Diameter) 

• Once you have your three measurements, you need to calculate the mean diameter.
• In simple terms: This means you add up your three measurements and then divide that total by three. This gives you the best estimated single value for the cylinder's width. 

Step 3: Figuring Out the Reliability (Error Calculations) 

After finding the average width, you need to calculate how accurate that average measurement is. This is done using two key error calculations: 

Conclusion:

• Absolute Mean Error: This calculation tells you, on average, how much your individual measurements were different from the final average width (the mean diameter). A smaller number here means your measurements were very consistent.
• Percentage Error: This calculation shows the error as a percentage of the total diameter. This is the easiest way to see how precise your overall measurement was. For example, an error of 1% means your measurement is very precise, whereas an error of 10% would mean it is not very precise.