Histogram Test Drive

Try These Problems:

1. A batch of resistors is tested to see how close they come to the manufacturer's specification of 47 ohms. Data is tabulated in bins of 0.2 ohm as follows:
   

   Resistance (ohms)	Frequency
   46.0-46.2	3
   46.2-46.4	5
   46.4-46.6	6
   46.6-46.8	9
   46.8-47.0	5
   47.0-47.2	6
   47.2-47.4	5
   47.4-47.6	2
   47.6-47.8	3
   47.8-48.0	1

   
   Make a histogram of this data. From your plot, estimate the median resistance. What can you say about the accuracy and the precision of the manufacturer's specified resistance of 47 ohms?
   
   
2. Using their cosmic ray detector, teachers in the University of Rochester QuarkNet Center take counts of incident muons per minute at a given location to see if they can get a good "average" value for that place. Over the next 20 minutes, the following counts are taken:

   {98, 103, 104, 103, 101, 98, 99, 104, 100, 104, 98, 103, 105, 103, 102, 104, 104, 103, 99, 100}

   Make a histogram; calculate the median and the mean. How close are they to the peak of the histogram? How well-defined is the peak?
   
   
3. For the following dataset, decide on a bin size and make a histogram. Change the bin size and make another histogram. How do the two compare?

   {0.11, 0.20, 0.35, 0.21, 0.28, 0.03, 0.22, 0.21, 0.19, 0.06, 0.40, 0.20, 0.31, 0.25, 0.27, 0.18, 0.17, 0.22, 0.45, 0.01, 0.14, 0.23, 0.26, 0.13, 0.19}

4. Refer to the histogram below:
   
   Can you identify the main peak? Can you find 1-2 "bumps" in the data? What would you say the "noise level" of the data is (that is, at what frequency level does the data lose statistical significance)?
   

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