Question

Find the difference between the mode and median of the distribution of data

Answer 1

Step 1: Rewrite the dot plot in tabular form

Step : Compute the mode

From the table, we can see that the numer appears most ( that is the number with the highest frequence, f) is 4.

Therefore,

mode = 4

Step 3: Find the median

First arrange the data in ascending order. In this case, the data is already in ascending order.

If ∑f is odd, the median is the middle value which is at position

`(\sum f+1)/(2)`

If ∑f is even, the median is the average of the two values at positions

`(\sum f)/(2)\text{ and }(\sum f)/(2)+1`

In this case, ∑f = 12 is even.

Therefore, the median is the average of the numbers at position 6 and 7

number at position 6 is 3

number at position 7 is 4

Hence, the median is given by

`(3+4)/(2)=(7)/(2)=3.5`

median = 3.5

Step 4: Find the difference between the median and mode

The difference is given by

`4-3.5=0.5`

Hence the difference is 0.5