Question

Find the difference between the median and the mode of the following data set:

1 6 45 4 33 12 19 6 56 25 13 9

• A. 12.5
• B. 12
• C. 6.5
• D. 6

Answer 1

The correct option is C

6.5

Arranged data set is:

1 4 6 6 9 12 13 19 25 33 45 56

Median: The middle most value after arranging the given data.

Here, the number of observations is 12, which is an even number. So, we take the average of the two observations in the middle to find the value of median.

Median=$\frac{12+13}{2}$=12.5. (Mean of the $6^{th}$ and $7^{th}$ observation)

Mode: The observation that occurs most often in the data set.

We can find 6 two times in the data set. This is the most repeated value in the data set. The value of the mode is 6.

i.e., Mode=6.
Difference between median and mode of the given data set=12.5-6=6.5.