Question

For the following set of scores: 5,6,2,3,6,5,6,4,1,5,6,3,4 (13 scores in total) What score best identifies the center (average) for the distribution? 

Answer 1

Here the best measure is median because the data is neagtively skewed.

Which is the best measure of central tendency depends on the nature of data.

If the data is symmetric, mean is best

If the data is skewed, median is best, and

If the data is for nominal variable, mode is best

Here to understand the shape of data , first we create a frequency distribution of the data

The frequency distribution table is given below:

X	f
1	1
2	1
3	2
4	2
5	3
6	4

The understand the shape of distribution , we use the bar diagram

In place of bar diagram, one can also prepare the box plot or stem and leaf plot also.

In bar diagram, we can see the data is negatively skewed. Hence median is best measure of central tendency for this data.

Median : First we arrange the data is ascending order:

1,2,3,3,4,4,5,5,5,6,6,6,6

The middle most observation is the median value , here the middle observation is 7th data value i.e. Median = 5

Answer: Median is 5