Is the peak of the data also the median?

Answer 1

No, it is not.

They're quite different.

It's not quite clear what you mean by "peak". You could be referring to the maximum; i.e. the number that's greater than or equal to every other number in the set. Alternately you could be thinking of the mode, which is the number that occurs most frequently.

Either way, they're not the same as the median. The median is the "middle number" in a set of data. That is, it divides the set into two equal groups; those in one group are less than or equal to the median and those in the other are greater than or equal to the median.

Here are some examples:

S = {1, 9, 2, 8, 4, 12, 3, 5, 8}

First, put them in order: {1, 2, 3, 4, 5, 8, 8, 9, 12}

The maximum is the largest number, 12.

The median is 5, because there are four numbers (1, 2, 3, 4) less than or equal to 5 and four numbers greater than or equal.

The mode is 8 because it occurs more often than the other numbers.

T = {1, 5, 2, 9, 4, 3, 8, 7}

Put them in order: {1, 2, 3, 4, 5, 7, 8, 9}

The maximum is 9.

The median is 4.5 - because the set has an even number of elements, the median is the average of the two middle numbers.

The set doesn't have a mode because all numbers occur only one time.

U = {1, 3, 1, 1, 1, 1, 1}

The maximum is 3

The median is 1. Even though the set has an even number of elements, 1 divides the set into a lower half {1, 1, 1, 1} and an upper half {1, 1, 1, 3}

The mode is also 1 because it's the most frequently-occurring value.