How did you arrive at the values of following mean median and mode?

Answer 1

• Mean

add up all the values and divide by the number of values.

• Median

Sort the values into order.

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.

• Mode

Look at the frequency of each value, or item (that is how many times each of the values appears). The mode is the one, or ones, with the highest frequency.

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