If there is an odd number of values, the median is the one in the middle;
otherwise there are an even number of values and the median is the mean of the middle two.
If all the values have the same frequency, there is no mode.
As no numerical calculation is done to the items themselves, the mode average can be used with non-numeric datasets, for example a survey of favourite colours - the most popular colour(s) (that is the ones with the highest count) will be the modal colour(s).
For example:
Consider the values: 2, 5, 4, 9, 8, 9, 2, 4, 2
Mean:
(2 + 5 + 4 + 9 + 8 + 9 + 2 + 4 + 2) / 9 = 45 / 9= 5
Median:
sorted: 2, 2, 2, 4, 4, 5, 8, 9, 9
9 values, so middle one is the 5th value = 4
Mode:
Frequencies: 2 (3), 4 (2), 5 (1), 8 (1), 9 (2)
Highest frequency: 3 for value = 2
Now consider: 2, 5, 4, 9, 8, 9, 2, 4, 2, 5
Mean:
(2 + 5 + 4 + 9 + 8 + 9 + 2 + 4 + 2 + 5) / 10 = 50 / 10 = 5
Median:
sorted: 2, 2, 2, 4, 4, 5, 5, 8, 9, 9
10 values, so want the mean of the middle two. The middle two are the 5th and 6th values = 4 & 5; so median = (4 + 5) / 2 = 9 / 2 = 4.5
Note that in this case, the median is not one of the values.
Mode:
Frequencies: 2 (3), 4 (2), 5 (2), 8 (1), 9 (2)
Highest frequency: 3 for value = 2
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The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.
If a data set consists of 1000 different values can the mean and the median be the same
Yes, the median can be greater than the mean. It just depends on the values of the data. A simple series of 1,5,6 has 5 as the median, with a mean of 4.
Of a set of data the mode is the most, the median is the middle value in ascending order and the mean is the sum of the values divided by the number of values.
Mean = average formed by adding values together and dividing by the total number of values Mode = the most popular value Median = line up all values in order and take the middle value