Question 1171255: Find the mean, median and mode of the following data:
69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Answer by math_tutor2020(3817)   (Show Source):
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Answers:
Mean = 43.7
Median = 47.85
Mode = None
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To get the mean, you add up the numbers and then you divide by 12. We divide by 12 since there are 12 values in the list. Adding up the numbers leads to 524.4, then divide that by 12 getting 524.4/12 = 43.7
To get the median, we first need to sort the data values
They sort to {13.8, 22.1, 23.2, 34.4, 43.8, 47.6, 48.1, 52.7, 53.2, 56, 60.2, 69.3}
Now cross off each pair of outer pair of values to get this smaller list
{22.1, 23.2, 34.4, 43.8, 47.6, 48.1, 52.7, 53.2, 56, 60.2}
Cross off the outer pair of values to get this new smaller list
{23.2, 34.4, 43.8, 47.6, 48.1, 52.7, 53.2, 56}
We keep going until we have 1 or 2 items left
{23.2, 34.4, 43.8, 47.6, 48.1, 52.7, 53.2, 56}
{34.4, 43.8, 47.6, 48.1, 52.7, 53.2}
{43.8, 47.6, 48.1, 52.7}
{47.6, 48.1}
We stop the process here and then add up these values to get 47.6+48.1 = 95.7
Then we cut that in half getting the median to be 95.7/2 = 47.85
The value 47.85 is directly in the middle of the data set.
The mode is the most frequent value. In this case, each item only shows up exactly one time, so there is no most frequent item. Sorting the data values helps see this more clearly. Therefore, the mode is the empty set or we just say "there is no mode".
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