Describing Data

Question

Consider the following data set. Round your answers to the nearest hundredth as needed.

72	72	47	57	72
34	56	52	44	61

1. Mean = 
2. Median = 
3. Mode = 
4. Range = 
5. Sample Standard Deviation = 

Answer 1

Make sure you use the correct formula:

The population standard deviation uses this formula:

	=	population standard deviation
	=	the size of the population
	=	each value from the population
	=	the population mean

Use the above for the entire data set, not just a sample from it. Note that the denominator is N.

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On the other hand, if you are looking for the standard deviation of a sample taken from the entire population (as in this case), then use this formula:

	=	sample standard deviation
	=	the number of observations
	=	the observed values of a sample item
	=	the mean value of the observations

NOTE that the denominator is N-1. If you use a calculator, Desmos, or some other software, make sure it is providing what you are asked for.

Answer 2

Mean: Add all the numbers up and divide by the number of numbers (in this case 10)

Median: order the numbers from smallest to largest and find the one in the middle:

If there is an even number so that no number is in the middle, then average the two middle numbers (56 + 57)/2

Mode: With the numbers in order (from your calculation of the median), look for the number that appears the most often.

Range: With the numbers in order (from your calculation of the median), subtract the largest number from the smallest (72 - 34)

Sample Standard Deviation: I'm unsure if you are supposed to manually calculate this or if you can use a calculator with a standard deviation function. I will assume you can use a calculator. If you use desmos, type into a blank formula box on the left side of the graph the following command:

stdev(

then type in all the data (separated by commas) like this:

stdev(72,72,47,57,72,34,56,52,44,61) and it will give you the answer.