Median

(conceptual explanation)

What is the Median?

Median

What is the Median?

Median

Here is a technical definition of the “median”:

What is the Median?

Median

Here is a technical definition of the “median”:

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

What is the Median?

Median

Here is a technical definition of the “median”:

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

What does this phrase mean?

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

28

54 8

3 54

13

3

25

10

Here’s an example:

6

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

283 54

13

25

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

8 10

283 54

13

25

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

43

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

43

283 54

13

25

8 10

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

283 54

13

25

In the second data set, there are also two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

285

13

25

In the second data set, there are also two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

3 4

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

3 54

13

In the second data set, there are also two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

2825

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

In the second data set, there are two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

Here’s an example:

5

6

4 83 10

283 54

13

25

Therefore, “5” is the

median for both data sets because the same

number of observations that are above BOTH

MEDIANS are also below BOTH MEDIANS.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

In the second data set, there are two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

Here’s an example:

5

6

4 83 10

283 54

13

25

Therefore, “5” is the

median for both data sets because the same

number of observations that are above BOTH

MEDIANS are also below BOTH MEDIANS.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

In the second data set, there are two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

Therefore, “5” is the

median for both data sets because the same

number of observations that are above BOTH

MEDIANS are also below BOTH MEDIANS.

Here’s an example:

5

6

4 83 10

283 54

13

25

Both data sets have the same median, even

though the mean is “6”in the first and “13” in the second data set.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

In the first data set, there are two

observations to the left of the MEDIAN “5”

and two observations to the right of the MEDIAN.

In the second data set, there are two

observations to the left of “5” of the MEDIAN

and two observations to the right of the MEDIAN.

Therefore, “5” is the

median for both data sets because the same

number of observations that are above BOTH

MEDIANS are also below BOTH MEDIANS.

Here’s an example:

54 83 10

283 54

25

Both data sets have the same median, even

though the mean is “6”in the first and “13” in the second data set.

6

13

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

Here’s an example:

5

6

4 83 10

283 54

13

25

Hence, the median is a most stable estimate of

the central tendency because it is based on the

unweighted scores.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

5

6

4 83 10

Here’s an example:

283 54

13

25

Extremely low or high scores are treated the

same as moderate scores.

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

5

6

4 8

54

13

3

25

10

Here’s an example:Extremely low or high scores are treated the

same as moderate scores.

328

What is the Median?

“The median represents the observation that divides the sample into halves regardless of the weight of the observations”.

28

5

6

4 8

3 54

13

25

Here’s an example:Extremely low or high scores are treated the

same as moderate scores.

3 10

What is the Median?

Note

Addition or removal of extreme scores changes the median very little.

What is the Median?

Note

In contrast, the mean is a less stable estimate of the central tendency because it is based on weighted scores.

What is the Median?

Note

In contrast, the mean is a less stable estimate of the central tendency because it is based on weighted scores.

The Mean

Weighted Scores

What is the Median?

Note

Where as the Median does not weight the scores and therefore is not influenced by extreme scores.

What is the Median?

Note

Where as the Median does not weight the scores and therefore is not influenced by extreme scores.

The Median

Unweighted Scores

Not as influenced by extreme scores

What is the Median?

Note

Where as the Median does not weight the scores and therefore is not influenced by extreme scores.

The Median

Unweighted Scores

Because they all have the same weight

What is the Median?