Question

Given the following data set:

20    20    20    20    20    20    21   21    21    21    22    22    22    23    23    23   23    24    24    65
1) Calculate the mean
2) Calculate the median
3) Do you think the mean or the median better represents the data? EXPLAIN your reasoning
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Answer 1

Mean = 23.75

Median = 21.5

Explanation:

Mean = Sum of the all the observations divided by number of observations

Mean = 20 + 20 + 20 + 20 + 20 + 20 + 21+ 21 + 21 + 21 + 22 + 22 + 22 + 23 + 23 + 23 + 23 + 24 + 24 + 65 =
`475/20`

Mean =
`475/20`

Mean = 23.75

Median = sum of the middle two numbers divided by 2 (in case of even number of observations)

To know middle two numbers =
`n+1/2`

=
`21/2`

= 10.5

Median = 10th observation + 11th observation divided by 2

Median =
`21+22/2`

Median = 21.5

I think mean better represents the data than median because when answering the mean you take the average of all the numbers so it be approximately around the answers and each number can affect the mean in many ways while a median is when you put the numbers in order and you get the middle number, because it is a middle the number can be far away from the beginning number or ending number.