Answers:
Both values are exact. The first value hasn't been rounded.
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Work Shown
Original data set = {97, 99, 81, 78, 73, 95, 33, 97, 64, 100, 85, 83, 85, 88, 79, 81, 93, 86, 83, 71}
Sorted data set = {33, 64, 71, 73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97, 97, 99, 100}
Add up the data values and you should get the sum 1651.
Divide this sum over the sample size n = 20 and we'll get the mean.
1651/20 = 82.55 this value is exact and hasn't been rounded.
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To get the median, we look at slots 10 and 11 because n/2 = 20/2 = 10
The middle-most value is between these two slots because n is an even number.
The values in slots 10 and 11 are 83 and 85 respectively.
The midpoint of which is (83+85)/2 = 84 which is the median.
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Here's another way to get the median.
What we'll do is cross off the first and last values of the sorted set.
{33, 64, 71, 73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97, 97, 99, 100}
turns into
{64, 71, 73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97, 97, 99}
Repeat that step again to get
{71, 73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97, 97}
Then do so again and again until we get a much smaller set. The goal is to reduce to either 1 element or 2 elements.
{73, 78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95, 97}
{78, 79, 81, 81, 83, 83, 85, 85, 86, 88, 93, 95}
{79, 81, 81, 83, 83, 85, 85, 86, 88, 93}
{81, 81, 83, 83, 85, 85, 86, 88}
{81, 83, 83, 85, 85, 86}
{83, 83, 85, 85}
{83,85}
We find that 83 and 85 are tied for the middle-most positions. Therefore, the midpoint (83+85)/2 = 84 is the median.
Each answer can be verified with a stats calculator.