Question

Using the following data determine the median, mode, and 47% percentile.

6,22,14,12,13,14,16,8,9,20,17,12,14

Answer 1

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

6   8   9   12   12   13   14   14   14   16   17   20   22   

So, the median is 14 .

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

6   8   9   12   12   13   14   14   14   16   17   20   22   

We see that the mode is 14 .

The first step is to sort values.

The sorted values are 6,8,9,12,12,13,14,14,14,16,17,20,22

Since there are 13 values, then n=13

Now, index $i=\frac{p}{100}*n=\frac{47}{100}*13=6.11$

So i=7

The percentile is at the position i=7, it is 14

So 47th percentile is 14